lesson plan meeting 1 - numericmethod.weebly.com · finding algorithm for the bisection method. 6....

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LESSON PLAN Meeting 1

Material Code Sks Semester

Numerical Methods KPL 11131 3 Odd 2013/2014

Basic Competence 1.1 Explaining definition of numerical method, characteristic of numerical method, and write

down the algorithm of some mathematical problems. Indicator Write down the algorithm of some mathematical problems. Material Definition of numerical method, characteristic of numerical method, and write down the

algorithm of some mathematical problems. Learning Method Approaches / Models problem based learning

Method Assignments, discussions, question and answer

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Learning Activities Stage Learning Activities Media/ Learning Resources

Preliminary Provide motivation, deliver course descriptions, general competence of numerical methods, learning strategies and assessment systems.

Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary Numerical Analysis.Iowa:

John Wiley & Sons. 2. Froberg, Carl-Erik., 1974. Introduction to Numerical Analysis.,

Addison-Wesly. Publishing Company. 3. Mathews, Jhon. H., 1992., Numerical Methods for Mathematics,

Science and Engineering. New Delhi: Prentice-Hall international. 4. Sastry, S. S. ,1983., Introduction Methods of Numerical Analisis.

New Delhi. 5. Susila, I. Nyoman. 1993. Elementary Numerical Methods. Bandung:

Depdikbud.

Presentation Discuss the characteristics of numerical methods. Discuss the making of the algorithm on math problems. Giving exercise of making algorithm.

Closing Draw conclude the definition and characteristics of numerical methods. Giving individual assignment about making algorithm

Evaluation : 1. Type of task : Task individual 2. Form of Instruments: Description objective

Pekanbaru, 1st September 2013 Lecturer

Dr. Atma Murni, M.Pd NIP. 196210041986032002

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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence 1.2 Determining some errors in a calculation and distinguishing direct and indirect

calculation. Indicator 1. Determining some errors in a calculation.

2. Distinguishing direct and indirect calculation Material Error and the type of matter Learning Method Approaches / Models direct learning.


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Preliminary Provide motivation, remind students about the characteristics of numerical methods, delivering learning objectives

Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary Numerical Analysis.Iowa:

John Wiley & Sons. 2. Froberg, Carl-Erik., 1974. Introduction to Numerical Analysis.,


Science and Engineering. New Delhi: Prentice-Hall international. 4. Sastry, S. S. ,1983., Introduction Methods of Numerical Analisis.

New Delhi. 5. Susila, I. Nyoman. 1993. Elementary Numerical Methods.

Bandung: Depdikbud.

Presentation Discuss on error Discuss the type of error and error propagation. Giving exercises on error.

Closing Draw conclusion the definition and characteristics of error Giving individual assignment of error




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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence 1.3 Determining location of the root of nonlinear equation using tabulation and graph (single

and double) and polynomial equation Indicator 1. Determining location of the root of nonlinear equation using tabulation.

2. Determining location of the root of nonlinear equation using a single graph. 3. Determining location of the root of nonlinear equation using double graph. 4. Determining location of the root of polynomial equation. 5. Finding algorithm for the bisection method. 6. Calculating the root approximation of non linear using bisection equation methods.

Material The roots of nonlinear equations a. Localization Root b. The Bisection Methods

Learning Method Approaches / Models cooperative learning type STAD and discovery learning Method Assignments, discussions, question and answer

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Preliminary Remind students of the types of nonlinear equations and transcendent function graph. Motivate and communicate learning objektives.

Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary Numerical

Analysis.Iowa: John Wiley & Sons. 2. Froberg, Carl-Erik., 1974. Introduction to Numerical

Analysis., Addison-Wesly. Publishing Company. 3. Mathews, Jhon. H., 1992., Numerical Methods for

Mathematics, Science and Engineering. New Delhi: Prentice-Hall international.

4. Sastry, S. S. ,1983., Introduction Methods of Numerical Analisis. New Delhi.

5. Susila, I. Nyoman. 1993. Elementary Numerical Methods. Bandung: Depdikbud.

Presentation Discuss the location of the roots of nonlinear equations. Discuss two methods for finding solutions to nonlinear equations. Finding algorithm for the bisection method. Giving exercises to applicate the algorithm of the bisection method .

Closing Draw conclude of the working of the bisection method. Giving individual assignment of the location of the roots of nonlinear equations and the bisection method.




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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence 2.1 Finding the algorithm of the bisection method, the method of false position, Newton Raphson

method, and Secant method, and the modification N-R method for polynomial. Indicator 1. Finding the formula of false position method

2. Finding the algorithm of false position method. 3. Making false position method program (translating the algorithm of false position method into the

Pascal programming language. 4. Calculating the roots approximations of nonlinear equations with false position methods. 5. Finding the formula of Newton Raphson method. 6. Finding the algorithm of Newton Raphson methods. 7. Making Newton Raphson method program 8. Calculate the roots approximations of nonlinear equations with Newton Raphson methods

Material c.The Method of False Position d. Newton Raphson Method (N-R)

Learning Method Approaches / Models Cooperative learning type STAD Method Assignments, discussions, question and answer

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Preliminary Discuss the material, to motivate and communicate learning objektives. Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary

Numerical Analysis.Iowa: John Wiley & Sons. 2. Froberg, Carl-Erik., 1974. Introduction to

Numerical Analysis., Addison-Wesly. Publishing Company.

3. Mathews, Jhon. H., 1992., Numerical Methods for Mathematics, Science and Engineering. New Delhi: Prentice-Hall international.



Presentation Discuss the method of false position and Newton Raphson method to find the roots of the equation is not linear approximation. Finding the algorithm of the method of false position and Newton Raphson method. Giving exercises to applicate the algorithm of the false position method and the Newton Raphson method.

Penutup Closing

Menyimpulkan cara kerja metode Posisi Palsu dan metode Newton Raphson. Draw conclusion the working of the method of false position and Newton Raphson method. Giving individual task about the application of the algorithm of the false position method and Newton Raphson method.




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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence 2.1 Calculating the approximation root of non linear using the bisection methods, the false position method,

Newton Raphson method, Secant method, and the modification N-R for polynomial method. Indicator 1. Finding the formula of false position method

2. Finding the algorithm of false position method. 3. Making false position method program (translating the algorithm of false position method into the Pascal

programming language. 4. Calculating the roots approximations of nonlinear equations with false position methods. 5. Finding the formula of Newton Raphson method. 6. Finding the algorithm of Newton Raphson methods. 7. Making Newton Raphson method program 8. calculate the roots approximations of nonlinear equations with Newton Raphson methods

Materi Material

1. Finding the formula of secant methods.. 2. Finding the algorithm of secant method. 3. Creating programs of secant method. 4. Calculating the roots of approximations of nonlinear equations trough secant methods. 5. Finding the formula of modification N-R method for polynomial. 6. Finding algorithm of modification N-R method for polynomial. 7. Creating program N-R modifications method for polynomial. 8. Calculate the roots approximations of nonlinear equations trough modified N-R method for polynomial.

Learning Method Approaches / Models cooperative learning type STAD Method Assignments, discussions, question and answer

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Preliminary Remind students concluded the bisection method and the false position, to motivate and communicate learning objektives.


Analysis.Iowa: John Wiley & Sons. 2. Froberg, Carl-Erik., 1974. Introduction to Numerical Analysis.,

Addison-Wesly. Publishing Company. 3. Mathews, Jhon. H., 1992., Numerical Methods for




Presentation Discuss the secant method and the modification N-R method for polynomial to find solution. Finding algorithms of the secant method and the modified N-R method. Giving exersises the application of the algorithm gives the secant method and the modified N-R for polynom.

Closing Draw conclusion the working of the secant method and the modified N-R method for polynomial. Giving individual assignment the secant method and the modified N-R method for polynomial.




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Basic Competence 3.1 Finding for algorithm subtitution backward, forward subtitution, Gaussian elimination with partial and simple pivoting. 3.2 Finding the solution of linear systems of equations by applying the Gaussian elimination algorithm with partial and simple pivoting.

Indicator 1. Finding substitution backward algorithm. 2. Finding solutions upper triangular system of linear equations by applying substitution backwards algorithm. 3. Finding subtitution advanced algorithms. 4. Finding solutions of lower triangular linear equations system by applying advanced algorithms

Material Linear Systems of Equations a. Upper and Lower of Triangular Linear Systems

Learning Method Approaches / Models discovery learning.


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Preliminary Remind students about the matrix, to motivate and communicate learning objectives.

Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary






Presentation Finding a general formula of the upper triangular linear system. Giving exercises the application of the algorithm the upper triangular linear system Finding a general formula of the lower triangular linear system in group. Giving exercises the application of the algorithm of the lower triangular linear system

Closing Draw conclusions about the upper triangular system of linear equations and the lower triangular systems of linear equations. Giving individual assignment of the upper triangular linear system and lower triangular of linear systems.




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Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence 3.1 Finding for algorithm subtitution backward, forward subtitution, Gaussian

elimination with partial and simple pivoting. 3.2 Finding the solution of linear systems of equations by applying the Gaussian

elimination algorithm with partial and simple pivoting. Indicator 1. Discovering simple pivoting strategy algorithm.

2. Determine the solution of SLE with simple pivoting strategy Material b. Gaussian Elimination and Pivoting Learning Method Approaches / Models discovery learning


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Preliminary Remind students of the upper triangular linear system of material and lower triangular linear system, motivate and communicate learning objektives.







Presentation Discuss the simple pivoting strategy to find a solution SLE. Finding algorithm of the Gaussian elimination. Gives exercise to implementation algorithm of the Gaussian elimination.

Closing Draw conclusions about the solution of system of linear equations with a simple pivoting strategy. Giving individual assignment on the application of the simple pivoting strategy.




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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence Finding algorithm and completed the system of linear equations (SLE) with

Decomposition Doolittle, Crout and Cholesky Indicator 1. Finding algorithms Doolittle decomposition method.

2. determine the solution of SLE with Decomposition Doolittle, 3. Finding algorithms Crout decomposition method. 4. Determine the solution of SLE with Decomposition Crout. 5. Finding algorithms Cholesky decomposition method. 6. Determine the solution of SLE with Decomposition Cholesky

Material c. Method of Factorization (Doolittle, Crout and Cholesky) Learning Method Approaches / Models cooperative learning type Jigsaw


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Preliminary Motivating, communicate learning objektives and remind students to substitution forward and backward.

Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary






Presentation Discuss Doolitlle Decomposition, Crout decomposition and Cholesky decomposition to find solution of systems of linear equations. Finding Doolitlle decomposition algorithm. Assign students find Crout decomposition algorithm in group. Finding the Cholesky decomposition algorithm. Giving exercises to application on Decomposition Doolitlle algorithm, Decomposition Crout algorithm and Cholesky decomposition algorithm.

Closing Draw conclusions about the working Doolitlle Decomposition, Crout Decomposition and Cholesky Decomposition Giving individual assignment on Doolitlle Decomposition, Crout Decomposition, and Cholesky Decomposition




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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence Finding algorithm and completing SLE with Jacobi Iteration and Gauss- Seidel iteration Indicator 1. Finding algorithms of Jacobi iteration

2. Determine the solution of SLE with Jacobi iteration 3. Finding algorithms of Gauss Seidel iteration. 4. Determine the solution of SLE with Gauss Seidel iteration

Material d. Jacobi Iteration and Gauss Seidel Iteration Learning Method Approaches / Models cooperative learning type Jigsaw


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Preliminary Remind students about the kinds of methods that have been discussed to find solution systems of linear equations. Motivate and communicate learning objektives.

Media: LCD Sumber Belajar: Learning Resources 1. Atkinson, Kendall E., 1985., Elementary Numerical






Presentation Discuss Jacobi iteration and Gauss Seidel iteration for finding solutions systems of linear equations Finding algorithm Jacobi iteration and Gauss Seidel iteration Giving exercises to applicate algorithm Jacobi iteration and Gauss Seidel iteration

Closing Conclude how the Jacobi iteration and Gauss Seidel iteration Giving individual assignment of the Jacobi iteration and Gauss Seidel iteration




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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence Estimating value between the data points with linear interpolation, quadratic, Newton divided difference,

Newton's forward and backward difference, and Lagrange Indicator 1. Estimating value between the data points with linear interpolation

2. Estimating value between the data points with quadratic interpolation. 3. Estimating value between the data points with Newton divided difference

Material Interpolation a. Linear and Quadratic Interpolation b. Newton Divided Difference Interpolation)

Learning Method Approaches / Models cooperative learning type STAD Method Assignments, discussions, question and answer

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Preliminary Motivate and communicate learning objektives Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary Numerical






Presentation Discuss linear interpolation, quadratic interpolation, and Newton's divided difference interpolation to estimate values between data points. Discuss how to find a general formula of linear interpolation, quadratic interpolation and Newton's divided difference interpolation . Finding linear interpolation algorithm, quadratic interpolation and Newton's divided difference interpolation . Giving examination to applicated of linear interpolation, quadratic interpolation and Newton's divided difference interpolation.

Closing Conclude about linear interpolation, quadratic interpolation and Newton divided difference Giving individual assignment on linear interpolation, quadratic interpolation and Newton divided difference




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Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014 Basic Competence Estimating value between the data points with linear interpolation, quadratic, Newton divided

difference, Newton's forward and backward difference, and Lagrange Indicator Estimating value between the data points with Newton's forward difference and Newton's

backward difference. Material c. Interpolation at a point within the same (Newton’s Forward Difference and Newton’s

Backward Difference ) Learning Method Approaches / Models cooperative learning type STAD


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Preliminary Remind students of the different Newton interpolation, motivate and communicate learning objectives.


Analysis.Iowa: John Wiley & Sons. 2. Froberg, Carl-Erik., 1974. Introduction to Numerical Analysis.,


Science and Engineering. New Delhi: Prentice-Hall international.



Presentation Discuss of the forward difference interpolation Newton Discuss general formula of the forward and backward difference interpolation Newton Finding algorithm of the Newton’s forward difference interpolation and Newton’s backward difference interpolation. Giving examination to applicate of forward difference interpolation Newton

Closing Conclude about the forward and backward difference interpolation Newton Giving individual assignment about the forward and backward difference interpolation Newton




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LESSON PLAN

Meeting 14 Material Code Sks Semester


Basic Competence Estimating value between the data points with linear interpolation, quadratic, Newton divided difference, Newton's forward difference and Newton's backward difference, and Lagrange’s interpolation.

Indicator Estimating value between the data points Lagrange’s interpolation.

Material d. Lagrange’s Interpolation

Learning Method Approaches / Models cooperative learning type STAD


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Learning Activities

Stage Learning Activities Media/ Learning Resources Preliminary Remind students interpolation on the material that has been studied,

motivate, deliver learning objectives. Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary Numerical






Presentation Discuss Lagrange’s interpolation to estimate values between data points right. Discuss general formula Lagrange’s interpolation Finding algorithm of the Lagrange’s interpolation Giving examination of Lagrange’s interpolation

Closing Concluded on Lagrange’s interpolation Giving individual assignment on Lagrange’s interpolation




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LESSON PLAN

Meeting 15 Material Code Sks Semester


Basic Competence Estimating area under the curve with numerical integral using Trapezoid composition’s rule, Simpson composition’s rule, Gauss Legendre quadrature.

Indicator Estimating area under the curve with numerical integral using trapezoid composition’s rule.

Material Numerical Integral a. Trapezoidal Rule

Learning Method Approaches / Models

cooperative learning type STAD


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Learning Activities

Stage Learning Activities Media/ Learning Resources Preliminary Remind students of the definite integral and calculate the area

under the curve, giving motivation, delivering learning objectives.







Presentation Discuss the trapezoidal composition’s rule to estimate the area under the curve Finding algorithm trapezoidal composition’s rule Provide training trapezoidal composition’s rule

Closing Conclude about the trapezoidal composition’s rule Giving individual tasks of the trapezoidal composition’s rule

Evaluation : 1. Type of task : Task individual 2. Form of Instruments: Description objectives



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LESSON PLAN

Meeting 16

Material Code Sks Semester Numerical Methods KPL 11131 3 Odd 2013/2014

Basic Competence Estimating area under the curve with numerical integral using Trapezoid composition’s rule,

Simpson composition’s rule, Legendre and Gauss quadrature. Indicator Estimating area under the curve with the numerical integral using Simpson composition's rule. Material b. Simpson’s Rules. Learning Method Approaches /

Models cooperative learning type STAD


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Learning Activities

Stage Learning Activities Media/ Learning Resources Preliminary Remind students of the trapezoidal composition’s

rule, motivate, deliver learning objectives. Media: LCD Learning Resources 1. Atkinson, Kendall E., 1985., Elementary Numerical Analysis.Iowa: John

Wiley & Sons. 2. Froberg, Carl-Erik., 1974. Introduction to Numerical Analysis., Addison-

Wesly. Publishing Company. 3. Mathews, Jhon. H., 1992., Numerical Methods for Mathematics, Science

and Engineering. New Delhi: Prentice-Hall international. 4. Sastry, S. S. ,1983., Introduction Methods of Numerical Analisis. New

Delhi. 5. Susila, I. Nyoman. 1993. Elementary Numerical Methods. Bandung:

Depdikbud.

Presentation Discussed the Simpson composition’s rule for estimating the area under the curve. Finding algorithm Simpson composition’s rule. Provide training Simpson composition’s rule.

Closing Conclude about the Simpson composition’s rule. Giving individual tasks of the composition of Simpson's rule




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