ce 206: engineering computation sessionaltanvirahmed.buet.ac.bd/ce 206/ce206_matlab...

CE 206 Engineering Computation Sessional

150 Credits 3hrsweek

Dr Tanvir Ahmed

Associate Professor

CE 206 Engg Computation Sessional Dr Tanvir Ahmed

Course Outline

Introduction to hi-level computational programming tools- MATLAB Mathematica etc

Application to numerical analysis- Basic matrix computations- Solving system of linear equations- Solving non-linear equations- Solving differential Equations- Interpolation and curve-fitting- Numerical differentiation- Numerical integration

Application to engineering problems- Solving mechanics problems- Numerical solution of equation of motion etc


Introduction to MATLAB

MATLAB (MATrix LABoratory) is a fully-functional programming language

Original code written by Cleve Moler of UNM in the 1970s later released as a commercial package by Mathworks Inc

Originally intended for interactive numerical computations

Interfaces with programs written in other languages(C++ Fortran)

Widely used in academia research institutionsand industry worldwide


MATLAB basics

MATLAB can be thought of as a super-powerful graphing calculator with many more buttons (ie built-in functions)

You can build up your own set of functions suited for a particular operation

It is an interpreted programming language-commands are executed line by line

It is capable of graphically representingcomputational results simultaneously

- Not possible in C++ Fortran


References and Resources

The MATLAB help file documentation- Provided with the MATLAB software- wwwmathworkscom

Materials in my web space(httpteacherbuetacbdtanvirahmed)- Lecture slides for CE206- ldquoAn introduction to MATLABrdquo David Griffith- ldquoGetting Started with MATLABrdquo Mathworks Inc

You will also need- Your CE205 Course referencesLecture slides


Course Layout

Class grading- Approximately one per week- Solving a problem in a given amount of time- Print out the codes and figures and keep it in file

Mid-term Assessment- Solving a problem in a given amount of time

Final ProjectAssignment- Individual or group submission

Final Quiz

Requirements- Basic familiarity with programming (eg CE204)- Knowledge on linear algebra differential equations

and numerical methods (CE 205)


MATLAB as a calculator

raquo -5(48+532)^2

ans =

-00488

raquo (3+4i)(3-4i)

ans =

25

raquo cos(pi2)

ans =

61230e-017

raquo exp(acos(03))

ans =

35470

2)32584(

5

)43)(43( ii

)2cos(

)30(cos 1

e

Basic arithmetic operators (+ ndash ) used in conjunction with brackets ( )

Built-in functions

sin() asin()

cos() acos()

tan() atan()

log() log10()

exp() sqrt()

abs() round()


Numbers and Formats

All computations in MATLAB are done in double precision (15 significant figures)


Variables

bull Variable names and their types do not have to be declared inMATLAB

bull If a statement is terminated with a semicolon ( ) the resultsare suppressed

bull Variable names must start with a letter followed by lettersdigits and underscores

bull The name of variable is not accepted if it is reserved word

Examplegtgt x=-13 y = 5x z = x^2+y

y =

-65

z =

104


Variables

Avoid using

ndash ans default variable name for the result

ndash pi π = 31415926 helliphellip

ndash eps ε= 22204e-016 smallest value by which two numbers can differ

ndash inf infin infinity

ndash NAN or nan not-a-number

Commands involving variables

ndash who lists the names of the defined variables

ndash whos lists the names and sizes of defined variables

ndash clear clears all variables

ndash clear name clears the variable name

ndash clc clears the command window


Vectors

- Entries within a row are separated by spaces or commas-Rows are separated by semicolons- Vector properties using size( ) and length( )

gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5


Other methods of vector creation

The colon operator generally a b c produces a vector of entries starting with the value a incrementing by the value buntil it gets to c

gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)

generates n equispaced points between a and b inclusive


Graphics plotting functions

gtgt x = linspace (0111)

gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor

Increasing the number of elements in x


Multiplots titles labels linestyles and colors

gtgt plot(xylsquob-xcos(3pix)g--)

gtgt legend(Sin curveCos curve)

gtgt title(Multi-plot )

gtgt xlabel(x axis) ylabel(y axis)

gtgt grid


Subplot example

gtgt subplot(221) plot(xy)

gtgt xlabel(x)ylabel(sin 3 pi x)

gtgt subplot(222) plot(xcos(3pix))

gtgt xlabel(x)ylabel(cos 3 pi x)

gtgt subplot(223) plot(xsin(6pix))




subplot(m n p)

subplot splits the figure window into an mxn array of small axes and makes the pth one active Note - the first subplot is at the top left then the numbering continues across the row


Subplot example


Formatted text on plots

gtgt set(0Defaultaxesfontsize16)

gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)

gtgt plot(nx[0 max(n)]exp(1)[1 1]

--markersize8)

gtgt title(x_n = (1+1n)^nfontsize12)

gtgt xlabel(n) ylabel(x_n)

gtgt legend(x_ny = e^1 = 2718284)

gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2

gtgt plot(xylinewidth2)

gtgt legend(y = x^3sin^2 3pi x4)

gtgt xlabel(xlsquo)

plot the first 100 terms in the sequence xn given by xn =[1 + 1n]n and then graph the function Ф(x) = x3 sin2(3πx) on the interval -1 le x le 1

Default font changed

Markersizechanged

Subscriptsuperscript

LineWidthchanged

Latin characters





Adding additional plots

hold on and hold off

hold on tells MATLAB to keep the current data plotted and add the results of any further plot commands to the graph Hold off releases the hold on the figure

raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on

raquo plot(xexp(-x)r)

0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010


Other plotting commands semilogx semilogy

x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)


Other plotting commands loglog

10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices

A 2-D array or matrix of data is entered row by row with spaces (or commas) separating entries within the row and semicolons separating the rows

gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9

Extracting bits of matrices

A(jk) gives jrsquoth row krsquoth columnA(2312) rows 2 through 3 and columns 1 through 2A([13] ) all of rows 1 and 3A( 1) first column


Numerical Array Concatenation

raquo a=[1 23 4]

a =

1 2

3 4

raquo cat_a=[a 2a 3a 4a 5a 6a]

cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a

Use [ ] to combine existing arrays as matrix ldquoelementsrdquo


More on Matrices

zeros(n) Returns a n ⅹ n matrix of zeros

zeros(mn) Returns a m ⅹ n matrix of zeros

rand(mn) Returns a m ⅹ n matrix of random numbers

eye(mn) Returns a m ⅹ n Identity matrix

ones(n) Returns a n ⅹ n matrix of ones

ones(mn) Returns a m ⅹ n matrix of ones

size(A)

For a m ⅹ n matrix A returns the row vector [mn] containing the number of rows and columns in matrix

length(A)Returns the larger of the number of rows or columns in A


Diagonal Matrix

First define a vector containing the values of the diagonal entries (in order) then use the diag function to form the matrix

gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2

This command is useful when we need to construct very large matrices

If A is a matrix diag(A) extracts the diagonal elements of the matrix


Sparse Matrix

These are generally large matrices that have a very small proportion of non-zero entries

gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]

gtgt S = sparse (ijv)

S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12

Creating a 5-by-4 sparse matrix S having only 3 non-zero valuesS(12) = 10 S(33) = 11 and S(54) = 12

The ldquofullrdquo command displays the sparse matrix


Matrix operations

Transpose B = Arsquo

Addition and Subtraction

C = A+B C = A-B

Scalar Multiplication

B = αA where α is a scalar

Matrix Multiplication

C = A B

Matrix Inverse B = inv(A) A must be a square matrix

Matrix powers B = A A A must be a square matrix

Determinant det(A) A must be a square matrix

Operators ^ and have two modes of operation-standard-element-wise


Standard matrix product operation


Elementwise matrix operations

To do element-wise operations use the dot ( ^) BOTH dimensions must match (unless one is scalar)


for loop

Used when we want to repeat a segment of the code several times

gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )

gtgt hold on xlabel(n)

gtgt plot(119 F(119)F(220)- )

gtgt legend(Ratio of terms f_n-1f_n)

gtgt plot([0 20] (sqrt(5)-1)2[11]--)

Example Test the assertion that the ratio of the two successive values in the Fibonacci series approach the golden ratio of (radic5-1)2 ie fnfn-1 = (radic5-1)2 where n = 345 hellip


while loop

when we want to repeat a segment of the code several times until some logical condition is satisfied

The while loop is used when we do not know for certain how many iterations may be needed

gtgt S = 1 n = 1

gtgt while S+ (n+1)^2 lt 100

n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91

Example What is the greatest value of n that can be used in the sum

and get a value less than 100


Logical and relational operators

== Equal

~= Not equal

gt Greater than

lt Less than

gt= Greater or equal

lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000

gtgt x gt 3 amp x lt 4

ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0

Matlab represents true and false by means of the integers 0 and 1


Flow control using ifelseelseif

Example Given x= sin(linspace(010pi100)) how many of the entries are positive

count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1


The find command for vectors

Example Produce a plot for y = e-x2 sin(3πx) and mark all the points that have a value of y greater than 02

gtgt x = -1051

gtgt y = sin(3pix)exp(-x^2)

gtgt k = find(y gt 02)

k =

Columns 1 through 12

9 10 11 12 13 22 23

24 25 26 27 36


37 38 39

gtgt plot(xy) hold on

gtgt plot(x(k)y(k)olsquo)

returns a list of the positions (indices) of the elements of a vector satisfying a given condition

Example 1 Given x= sin(linspace(010pi100)) how many of the entries are positive


Avoiding loops efficient coding

count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

Count=length(find(xgt0))

Example 2 find the sum 12 + 22 + 32 + helliphelliphelliphelliphellip +1002

sum_sq=0

for n=1100

sum_sq = sum_sq + n^2

end

Sum_sq=sum((1100)^2)

Using the ldquofindrdquo command

Vectorization



Built-in functions (eg find sum) will make it faster to write and execute

count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

Vectorized code is more efficient for MATLAB

Use indexing and matrix operations to avoid loops


Advanced graphics plotting surfaces

- The command meshgrid is used to construct the (x y) gridpointsat certain intervals

- Evaluate the function z = f(xy) at all the gridpoints

-Use a surface plot feature (eg meshsurf) to plot the surface

Example Plot the surface defined by z = (x - 3)2 + (y ndash 2)2 for 2le x le 4 amd 1 le y le 3

[XY] = meshgrid(224 123)

Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y


Advanced graphics surf and shading[XY] = meshgrid(224 123)

Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y


Advanced graphics contour plot

x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)

contour(XYZLineWidth2)

Takes the same arguments as surf or mesh

Example Plot the contour of the surface defined by z = (sinx) (cosy) for ndashπ le x le πand - π le y le π

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)


Specialized plotting functions

polar-to make polar plots

polar(00012picos((00012pi)2))

bar-to make bar graphs

bar(110rand(110))

quiver-to add velocity vectors to a plot

[XY]=meshgrid(110110)

quiver(XYrand(10)rand(10))

stairs-plot piecewise constant functions

stairs(110rand(110))

fill-draws and fills a polygon with specified vertices

fill([0 1 05][0 0 1]r)

Script files are ASCII (text) files containing MATLAB commands

Commonly known as m-files because they have a m extension


Scripting

List of output(s)


Function m-files

function [A] = area(abc)

Compute the area of a triangle whose

sides have length a b and c

Inputs

abc Lengths of sides

Output

A area of triangle

s = (a+b+c)2

A = sqrt(s(s-a)(s-b)(s-c))

end of area

Example Write a function m-file which calculates the area of a triangle having sides a b and c using the formula Area = Where s = (a+b+c)2))()(( csbsass

List of inputs

The function name Also the name of the m-file where the function definition will be stored

Purpose of the function and how it can be used Mainly to aid the futureusers

The code

MATLAB functions are generally overloaded1048766 Can take a variable number of inputs1048766 Can return a variable number of outputs

You can overload your own functions by having variable input and output arguments

The following function plots a sine wave with frequency f1 on the range [0 2π] uses f1 as the input but displays a message when two inputs are given


Function overloading

function plotSin(f1f2)

x=linspace(02pif116+1)

figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2

disp(Two inputs were given)

end

built in function nargin

contains the number of inputs


Course Outline

Introduction to hi-level computational programming tools- MATLAB Mathematica etc

Application to numerical analysis- Basic matrix computations- Solving system of linear equations- Solving non-linear equations- Solving differential Equations- Interpolation and curve-fitting- Numerical differentiation- Numerical integration

Application to engineering problems- Solving mechanics problems- Numerical solution of equation of motion etc









MATLAB basics












Course Layout




Final Quiz





raquo -5(48+532)^2

ans =

-00488

raquo (3+4i)(3-4i)

ans =

25

raquo cos(pi2)

ans =

61230e-017

raquo exp(acos(03))

ans =

35470

2)32584(

5

)43)(43( ii

)2cos(

)30(cos 1

e


Built-in functions

sin() asin()

cos() acos()

tan() atan()

log() log10()

exp() sqrt()

abs() round()


Numbers and Formats



Variables






y =

-65

z =

104


Variables

Avoid using













Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end











MATLAB basics












Course Layout




Final Quiz





raquo -5(48+532)^2

ans =

-00488

raquo (3+4i)(3-4i)

ans =

25

raquo cos(pi2)

ans =

61230e-017

raquo exp(acos(03))

ans =

35470

2)32584(

5

)43)(43( ii

)2cos(

)30(cos 1

e


Built-in functions

sin() asin()

cos() acos()

tan() atan()

log() log10()

exp() sqrt()

abs() round()


Numbers and Formats



Variables






y =

-65

z =

104


Variables

Avoid using













Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end









Course Layout




Final Quiz





raquo -5(48+532)^2

ans =

-00488

raquo (3+4i)(3-4i)

ans =

25

raquo cos(pi2)

ans =

61230e-017

raquo exp(acos(03))

ans =

35470

2)32584(

5

)43)(43( ii

)2cos(

)30(cos 1

e


Built-in functions

sin() asin()

cos() acos()

tan() atan()

log() log10()

exp() sqrt()

abs() round()


Numbers and Formats



Variables






y =

-65

z =

104


Variables

Avoid using













Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end





raquo -5(48+532)^2

ans =

-00488

raquo (3+4i)(3-4i)

ans =

25

raquo cos(pi2)

ans =

61230e-017

raquo exp(acos(03))

ans =

35470

2)32584(

5

)43)(43( ii

)2cos(

)30(cos 1

e


Built-in functions

sin() asin()

cos() acos()

tan() atan()

log() log10()

exp() sqrt()

abs() round()


Numbers and Formats



Variables






y =

-65

z =

104


Variables

Avoid using













Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Numbers and Formats



Variables






y =

-65

z =

104


Variables

Avoid using













Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Variables






y =

-65

z =

104


Variables

Avoid using













Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Variables

Avoid using













Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Vectors


gtgt a = [1 2 3 4 5 ]

a =

1 2 3 4 5

gtgt b = [246810]

b =

2

4

6

8

10

gtgt size(a)

ans =

1 5

gtgt length(a)

ans =

5




gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end






gtgt 37

ans =

3 4 5 6 7

gtgt 0320106

ans =

03200 04200 05200

gtgt -14-03-2

ans =

-14000 -17000 -20000

linspace (abn)





gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end






gtgt y = sin(3pix)

gtgt plot(xy)

xy 3sin

10 xfor








gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end









gtgt grid


Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Subplot example









subplot(m n p)



Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Subplot example




gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end






gtgt n = 1100 x = (1+1n)^n

gtgt subplot (211)


--markersize8)




gtgt

gtgt subplot (212)

gtgt x = -2022 y = x^3sin(3pix)^2



gtgt xlabel(xlsquo)



Markersizechanged


LineWidthchanged

Latin characters








raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end










raquo x = 012pi

raquo y = sin(x)

raquo plot(xyb)

raquo grid on

raquo hold on


0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end



0 1 2 3 4 5 6 7 8 9 1010

0

102

104

106

108

1010



x = 00110

semilogx(10^xx)

100

102

104

106

108

1010

0

1

2

3

4

5

6

7

8

9

10

x = 00110

semilogy(x 10^x)



10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end





10-1

100

101

102

100

1010

1020

1030

1040

1050

x = logspace(-12)

loglog(xexp(x)-s)

grid on


Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Matrices


gtgt A = [1 2 3 4 5 6 7 8 9]

A =

1 2 3

4 5 6

7 8 9





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end





raquo a=[1 23 4]

a =

1 2

3 4


cat_a =

1 2 2 4

3 4 6 8

3 6 4 8

9 12 12 16

5 10 6 12

15 20 18 24

Use square

brackets [ ]

4a



More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




More on Matrices







size(A)




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Diagonal Matrix


gtgt d = [-3 4 2] D = diag(d)

d =

-3 4 2

D =

-3 0 0

0 4 0

0 0 2




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Sparse Matrix


gtgt i = [1 3 5] j = [234]

gtgt v = [10 11 12]


S =

(12) 10

(33) 11

(54) 12

gtgt T = full(S)

T =

0 10 0 0

0 0 0 0

0 0 11 0

0 0 0 0

0 0 0 12




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




Matrix operations



C = A+B C = A-B




C = A B











for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end









for loop


gtgt F(1) = 0 F(2) = 1

gtgt for i = 320

F(i) = F(i-1) + F(i-2)

end

gtgt plot(119 F(119)F(220)o )


gtgt plot(119 F(119)F(220)- )


gtgt plot([0 20] (sqrt(5)-1)2[11]--)



while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end




while loop



gtgt S = 1 n = 1


n = n+1 S = S + n^2

end

gtgt [n S]

ans =

6 91





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end





== Equal

~= Not equal

gt Greater than

lt Less than


lt= Less or equal

amp ampamp And

| || Or

x =

-20000 31416 50000

-50000 -30000 -10000


ans =

0 1 0

0 0 0

gtgt x gt 3 | x == -3

ans =

0 1 1

0 1 0





count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end






count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end

-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end



-1 -08 -06 -04 -02 0 02 04 06 08 1-1

-08

-06

-04

-02

0

02

04

06

08

1




gtgt x = -1051



k =


9 10 11 12 13 22 23

24 25 26 27 36


37 38 39







count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end






count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end



sum_sq=0

for n=1100


end



Vectorization




count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end






count=0

for n=1length(x)

if x(n)gt0

count=count+1

end

end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end










Z = (X-3)^2-(Y-2)^2

mesh(XYZ)

title(Saddle)

xlabel(x)ylabel(y)

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end





Z = (X-3)^2-(Y-2)^2

surf(XYZ)

title(Saddlelsquo)

shading faceted

shading flat

colormap(gray)2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y

2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y2

25

3

35

4

1

15

2

25

3-1

-05

0

05

1

x

Saddle

y



x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end





x=-pi01pi

y=-pi01pi

[XY]=meshgrid(xy)

Z =sin(X)cos(Y)




-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

-4

-2

0

2

4

-4

-2

0

2

4-1

-05

0

05

1

mesh(XYZ) hold on

contour(XYZ)






bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end








bar(110rand(110))







fill([0 1 05][0 0 1]r)




Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end






Scripting

List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end



List of output(s)


Function m-files




Inputs


Output

A area of triangle

s = (a+b+c)2


end of area


List of inputs



The code








figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end










figure

if nargin == 1

plot(xsin(f1x))

elseif nargin == 2


end



ce 206: engineering computation sessionaltanvirahmed.buet.ac.bd/ce 206/ce206_matlab...

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