sem 1 & 2-syllabus-cbcs--dt-01-02--2013

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B.Sc. SEMESTER -1

MATHEMATICS PAPER BSMT-101 (A) - Theory

GEOMETRY & CALCULUS

UNIT 1: [ 25 MARKS + 10 MARKS MCQ ]

(a) Polar, spherical & cylindrical co-ordinates:

Polar Co-ordinates in R 2, distance between two points in polar Co-ordinates. Polar

equations of a straight line, polar equations of circle. Relation between Cartesian and

polar coordinates, Relation between Cartesian and spherical coordinates, Relation

between Cartesian and cylindrical coordinates.

(b) Sphere: General equation of sphere with center (α, β, γ) and radius a. Plane section of a sphere,

intersection of two spheres, inertia of sphere and a line.

(c) Successive differentiation:

Successive differentiation, Calculation of nth derivative, Some standard results for nth

derivatives ofax

e , mxa , )sin( bax , )cos( bax ,

mbax )( ,1)(

bax ,

)log( bax , )sin( cbxeax , )cos( cbxe

ax . Leibnitz’s Theorem and its examples.

(d) Mean value theorems:

Roll’s theorem and problems related to it, Lagrange’s mean value theorem and problems

related to it, Cauchy’s mean value theorem and problems related to it.

(e) Taylor’s theorem, expansions and indeterminate forms:

Taylor’s theorem (Without proof), Maclaurin’s theorem (Without proof), Taylor’s and

Maclaurin’s infinite series expansions, expansions of

x

e , xsin , xcos ,n

x)1( ,)1log( x under proper conditions.

(f) Indeterminate Forms:

La’ hospital’s rules for various indeterminate forms (Without proof).Various

indeterminate forms like0

0 form,

form, 0. form, form,

00 form,

0

form.




Notes:

There shall be SIX periods of 55 minutes per week for Mathematics- BSMT-101(A)-

Theory.

There shall be one question paper of 70 marks & 21

2 hours for Mathematics- BSMT-

101(A)-Theory

Format of Question Paper

There shall be TWO sections in this paper i.e. Section- A and Section -B.

Section – A

Section- A is of 20 Marks with 20 MCQ type questions (multiple choice questions) coveringthe whole syllabus in equal weight-age.

Section – B

Section B is of 50 Marks with the following type of TWO questions covering the whole

syllabus in equal weight-age, each of twenty five marks

Question 1 and 2 will cover unit 1 and 2 respectively.

Question no. (A) Answer any three out of six 6 Marks(B) Answer any three out of six 9 Marks

(C) Answer any two out of five 10 Marks _________

TOTAL 25 MARKS

Reference Books :

The Elements of Co-ordinate Geometry by S.L. Loney

Mac Millan & Co.

Elementary Treatise on Co-ordinate geometry of three dimensions by R.J.T. Bell MacMillan & Co.

A Text book of Analytical Geometry of three dimensions by P.K. Jain & Khalid Ahmad

Differential Calculus by Shanti Narayan

Differential Calculus by Gorakh Prasad

Integral Calculus by Shanti Narayan

Integral Calculus by Gorakh Prasad

Differential Equations by D. A. Murray

Three Dimension Geometry, Krishna Prakashan Mandir, Meerut.

A Text book of Calculus, S. C. Arora and Ramesh Kumar,Pitamber Publishing Company Ltd. Delhi.




SAURASHTRA UNIVERSITY

RAJKOT.Syllabus of B.Sc. Semester-1

According to Choice Based Credit System

Effective from June – 2010

(Updated on date:- 01-02-2013

and updation implemented from June - 2013)

Programme: B.Sc.

Semester: 1

Subject: Mathematics

Course code: BSMT-101(B) (Practical)

Title of Course: Mathematics Practical

Total Marks of

External Practical

Examination:

35 Marks

Total Marks of

Internal Practical

Examination:

15 Marks

Continuous internal assessment

of practical work

Total Marks of

Practical Examination:

External 35 Marks

Internal 15 Marks

_______________________

Total 50 Marks

Credit Of The Course 3 Credits




SAURASHTRA UNIVERSITY, RAJKOT.

B.Sc. SEMESTER - 1 (CBCS)MATHEMATICS PAPER- BSMT-101(B) (Practical)

Mathematics Practical

[ 50 Marks / 3Hours]

Practical No . (1) Draw the graph of y = sinx or y = cosx or y = tanx

Practical No . (2) Draw the graph of y = secx or y = cosecx or y = cot x

Practical No . (3) Draw the graph of y = sin-1x or y = cos-1x or y = tan-1x.

Practical No . (4) Draw the graph of y = sec-1x or y = cosec-1x or y = cot -1x.

Practical No . (5) Draw the graph of parabola y2 = 4ax for a < 0 or a > 0

Practical No . (6) Draw the graph of ellipse2 2

2 2 1

x y

a b

or hyperbola2 2

2 2 1

x y

a b

Practical No. (7) To solve given example of successive differentiation.

(a) Find the nth derivative of y =

(b) Show that the nth derivative of y = tan-1x is

yn = (-1)(n-1).(n-1) [sin{n( )}sinn( )]

(c) If y = x log then prove that

yn = (-1)n.(n-2) { - }

(d) If y = sinmx + cosmx then show that

yn =

Practical No. (8) To solve given example of Mean value Theorem.

(a) Using Lagrange’s mean value theorem show that

log(1+x) x for x 0 and hence

0 - 1 for x 0

(b) Using Lagrange’s mean value theorem show that

x - sinx x for x 0




(c) Using Cauchy’s mean value theorem show that

(c) eb – ea = cec log(b/a) where 0 a c b ,ab 0

(d) Using Cauchy’s mean value theorem show that

bb – aa = cc{blog(b)- alog(a)} where a c b

Practical No. (9) To solve given example of reduction formula.

(a)

dx (b)

(b)

(d)

Ans: (a) (b) (c) (d)

Practical No.(10) To solve given example of Bernoulli’s Differential Equation.

(a)

Solve : + ytanx = y3secx ,

Ans. Y=

(b)

Solve : + ytanx = ,

Ans. Y2 sec2x = 2log( secx + tanx )+c

(c)

Solve : + ycosx = y3sin2x,

Ans.y-2 =(1+2sinx) + c e2sinx

(d)

Solve : (x3y3 + xy)dx = dy ,

Ans. y-2 = (1-x2)+ c




Notes :

There shall be SIX periods of 1 hour per week per batch of 15 students.

10 practical should be done during semester-1.

At the time of examination candidate must bring his/her own practical journal

duly certified and signed by H.O.D.

There shall be one question paper of 35 Marks and 3 Hours for practical

examination

There shall be 15 marks for Internal Practical Examination

(i.e. Continuous internal assessment of performance of each student during the

practical work.)

Format of Question Paper for Practical Examination

Question 1 Answer any THREE out of FIVE [ 9+9+9= 27 Marks

Question 2 Journal and Viva: [ 8 Marks

Question 3: Internal Practical Examination [ 15 Marks

TOTAL [ 50 Marks







Effective from June – 2010



Program: B.Sc.

Semester: 2


Course code: BSMT-201 (A) - Theory

Title of Course: Geometry, Trigonometry

And Matrix Algebra

Section-wise

Distribution of Marks

for External

Examination:

Section-A

(MCQ test) 20 Marks

Section-B

(Descriptive type) 50 Marks

__________________________

Total Marks 70 Marks

Segment-wise

Distribution of Marks

for Internal

Examination:

Assignments 10 Marks

QUIZ test 10 Marks

Internal exam. 10 Marks

_________________________

Total Marks 30 Marks





B.Sc. SEMESTER -2

MATHEMATICS PAPER BSMT – 201 (A) Theory

GEOMETRY, TRIGONOMETRY AND MATRIX ALGEBRA


[a] Cylinder :

Definition of a cylinder, equation of a cylinder with given

Generating parallel to the line x y z

l m n and guiding curve ax2+ 2hxy + by2 + 2gx +

2fy + c = 0, z = 0. The equation of right circular cylinder with axis

x y z

l m n

and radius r.

[b] Concept of a matrix:

Some special matrices, adjoint of a matrix, Non-singular and singular matrices, inverse

of a matrix, Symmetric and skew symmetric matrices, Hermitian and skew Hermitian

matrices

Rank of a matrix:Elementary row and column operations on a matrix, row and column vectors, linear

independence of row and column matrices, rank of a matrix, row and column rank of a

matrix, equivalence of row and column ranks.

Eigen values of a matrix :

Characteristic equation of a matrix, eigen values and eigen vectors of a matrix, Cayley-

Hamilton theorem and its use in finding inverse of a matrix. Application of a matrices to

solve a system of linear (homogeneous and non-homogeneous both) equations.Theorems on consistency of a system of linear equations.

[c] Sequences:

Definition of a sequence, bounded sequences. Convergence of a sequence,

subsequences, Monotonic sequences, Cauchy’s sequence, General principle of

convergence of sequence (without proof). Some important sequences.n

n ;

n

aaan

21





[a] De’Moivre’s theorem:

De’Moivre’s theorem and its ap plications, Value of az, zC or R.

Expansions of ncos , nn tan,sin :

Expansions of ncos , nn tan,sin in terms of tan,sin,cos respectively.

(n being positive integer) Expansions of nn

sin,cos in a series of cosines or sines

of multiples of (n being positive integer ). Expansion of trigonometric functions. i.e.

expansions of sin ,cos , tan in terms of .

[b] Exponential, circular and hyperbolic functions:

Exponential, circular and hyperbolic functions.

Logarithmic & inverse functions:

Logarithmic functions for complex and real numbers

Inverse circular and hyperbolic functions for complex and real numbers.

Notes:

There shall be SIX periods of 55 minutes per week for Mathematics- BSMT-201(A)-

Theory.

There shall be one question paper of 70 marks & 21

2 hours for Mathematics- BSMT-

201(A)-Theory

Format of Question Paper

There shall be TWO sections in this paper i.e. Section- A and Section -B.

Section – A

Section- A is of 20 Marks with 20 MCQ type questions (multiple choice questions) covering

the whole syllabus in equal weight-age.

Section – B

Section B is of 50 Marks with the following type of TWO questions covering the whole

syllabus in equal weight-age, each of twenty five marks .

Question 1 and 2 will cover unit 1 and 2 respectively.

Question no. (A) Answer any three out of six 6 Marks(B) Answer any three out of six 9 Marks

(C) Answer any two out of five 10 Marks _________

TOTAL 25 MARKS




Reference Books:

The Elements of Co-ordinate Geometry by S.L. Loney Mac Millan & Co.

Elementary Treatise on Co-ordinate geometry of three dimensions by R.J.T. Bell Mac

Millan & Co.

A Text book of Analytical Geometry of three dimensions by P.K. Jain & Khalid Ahmad

Theory of matrices by Shanti Narayan

Plane Trigonometry Part -2 by S.L.Loney Mac Millan & Co.

A Course of Mathematical Analysis by Shanti Narayan

Mathematical Analysis by S.C. Malik

Mathematical Analysis by T.M. Apostol

Real Analysis by R.R. Goldberg

Three Dimension Geometry by Krishna Prakashan Mandir,Meerut.







Effective from June - 2010



Programme: B.Sc.

Semester: 2


Course code: BSMT-201(B) (Practical)

Title of Course: Mathematics Practical.

Total Marks of

External Practical

Examination:

35 Marks

Total Marks of

Internal Practical

Examination:

15 Marks

Continuous internal assessment

of practical work

Total Marks of

Practical Examination:

External 35 Marks

Internal 15 Marks

_______________________

Total 50 Marks





SAURASHTRA UNIVERSITY, RAJKOT.

B.Sc. SEMESTER -2 (CBCS)MATHEMATICS PAPER- BSMT-201(B) (Practical)

Mathematics Practical

[ 50 Marks / 3Hours]

Practical No. (1) Draw the graph of y =ex or y = 2 x or y = 3 x.

Practical No. (2) Draw the graph of y =loge x or y = log10 x.

Practical No. (3) Draw the graph of y =sinh x or y = cosh x.

Practical No. (4) Draw the graph of y =sech x or y = cosech x

Practical No. (5) Draw the graph of y =tanh x or y = coth x.

Practical No. (6) Draw the graph of cardioid.

Practical (7)

To find inverse of a matrix using Cayley- Hamilton theorem

Practical No(7) (a)

a =

1 0 1

0 1 0

0 0 1

Answer:- b = inv(a)

b =

1 0 -1

0 1 0

0 0 1

Practical No(7) (b)

a =

2 -1 1

-1 2 -11 -1 2

Answer:- b = inv(a)

b =

0.7500 0.2500 -0.2500

0.2500 0.7500 0.2500

-0.2500 0.2500 0.7500

Practical No(7) (c)

a = 2 1 -1

0 2 1

5 2 -3




Answer:- b = inv(a)

b =

8 -1 -3

-5 1 2

10 -1 -4

Practical No(7) (d)

a =

1 0 2

2 -1 3

4 1 8

Answer:- b = inv(a)

b =

-11 2 2

-4 0 1

6 -1 -1

Practical No(8)

To find inverse of a matrix using Gauss-Elimination Method

Practical No(8) (a)

a =

7 -3 -3

-1 1 0

-1 0 1

Answer:- b = inv(a)b =

1 3 3

1 4 3

1 3 4

Practical No(8) (b)

a =

-4 -3 -3

1 0 1

4 4 3

Answer:- b = inv(a)

b =

-4 -3 -3

1 0 1

4 4 3




Practical No(8) (c)

a =

1 -8 10

0 2 -3

0 -1 2

Answer:- b = inv(a)

b =

1 6 4

0 2 3

0 1 2

Practical No(8) (d)

a =

5 8 4

2 3 2

1 2 1

Answer:- b = inv(a)

b = 1 0 -4

0 -1 2

-1 2 1

Practical No(9)

To solve the system of simultaneous linear algebraic equations using

Gauss Elimination Method.

Practical No(9) (a)

3x + y - z = 3

2x - 8y + z = -5

x - 2y + 9z = 8

Answer: - x = 1, y = 1, z =1

Practical No(9) (b)

28x + 4y - z = 32

x + 3y + 10z = 24

2x + 17y + 4z = 35 Answer: - x = 0.9936, y = 1.5070, z =1.8485

Practical No(9) (c)

3x + 4y - z = 8

-2x + y + z = 3

x + 2y - z = 2

Answer: - x = 1, y = 2, z = 3

Practical No(9) (d)

10x + y + z = 12

2x +10y + z = 132x + 2y + 10z = 14

Answer: - x = 1, y = 1, z = 1



Practical No(10)

To solve the given system of simultaneous linear algebraic equations

using Gauss-Jordan Method.

Practical No(10) (a)

10x + y + z = 12

2x + 10y + z = 13

x + y + 5z = 7

Answer: - x = 1, y = 1, z = 1

Practical No(10) (b)

10x + y + z = 12

x + 10y - z = 10

x - 2y + 10z = 9

Answer: - x = 1, y = 1, z = 1

Practical No(10) (c)

10x + y + z = 12

x + 10y + z = 12

x + y +10z = 12

Answer: - x = 1, y = 1, z = 1

Practical No(10) (d)

x + 2y + z = 8

2x + 3y + 4z = 20

x + 3y + 2z = 16 Answer: - x = 1, y = 2, z = 3

Notes :

There shall be SIX periods of 1 hour per week per batch of 15 students.

10 practical should be done during semester-2.

At the time of examination candidate must bring his/her own practical journal

duly certified and signed by H.O.D.

There shall be one question paper of 35 Marks and 3 Hours for practical

examination

There shall be 15 marks for Internal Practical Examination

(i.e. Continuous internal assessment of performance of each student during the

practical work.)

Format of Question Paper for Practical Examination

Question 1 Answer any THREE out of FIVE [ 9+9+9= 27 Marks

Question 2 Journal and Viva: [ 8 Marks

Question 3: Internal Practical Examination [ 15 Marks

TOTAL [ 50 Marks

sem 1 & 2-syllabus-cbcs--dt-01-02--2013

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