COURSE CONTRACT Course Name

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1 COURSE CONTRACT Course Name Numerical Methods Course Code KPL Semester Odd /4 Days/ hours Tuesday/ 7.-. Place F8 Course Status compulsory Course Prerequisites. Calculus I. Calculus II. Linear Algebra 4. Computer and ming. Benefits Courses for Students Students understand the types of numerical methods that can be used to solve mathematical problems.. Course Description The topics covered are: error, iteration, the roots of nonlinear equations, interpolation, linear systems of equations, and integrals. Emphasis is placed on understanding of how the numerical methods. For each topic begins with underlying theory. Detailed eamples lead students in calculations required for understanding the algorithm. For the application of computer programming, algorithm presentation wearing pseudo code that easily translated into programming languages such as Pascal or Fortran. The topics are presented in five chapters and each chapter comes with a variety of questions with some questions and emphasizing how the calculations can be done wearing a calculator or simple program.. Learning Objectives of Course a. Students gain an intuitive understanding of some numerical methods for basic problems in mathematics. b. Students are master on the concept of an error, the need to analyze and assess. c. Students develop eperience in implementing numerical methods using computers. 4. Learning Strategies Lectures held using lectures, discussion, assignments and discussions. The learning model is performed directly learning model. 5. Learning Resources/ Learning Resources :

2 Media of learning 6. Student task. Atkinson, Kendall E., 985., Elementary Numerical Analysis.Iowa: John Wiley & Sons.. Anton, Howard., 99., Aljabar Linear Elementery (5 th Edition ). Jakarta: Erlangga.. Froberg, Carl-Erik., 974. Introduction to Numerical Analysis., Addison-Wesly. Publishing Company. 4. Mathews, Jhon. H., 99., Numerical Methods for Mathematics, Science and Engineering. New Delhi: Prentice-Hall international. 5. Sastry, S. S.,98., Introduction Methods of Numerical Analisis. New Delhi. 6. Susila, I. Nyoman. 99. Elementary Numerical Method. Bandung: Depdikbud. Media: LCD Task Week Giving the task : Tuesday/ September Submission of assignments : Tuesday/ September Make the pseudo code to calculate the number of runs following.. H b b b bn. HKDB a b ab a n bn. P = m FAK!! n! PT ( ) 4 6 COSX! 4! 6! 5 SINX! 5! n n n ( ) (n)! n n ( ) (n )! Task Week Giving the task : Tuesday/ September Submission of assignments : Tuesday/7 September A.. Find the absolute error, relative error, and digits of accuracy on the following approimation of the true value. a. a =,8454 dan â =,8 b. b = 768 dan bˆ = 76 c. c =,87 dan ĉ =,8. Write.; 57,5;,564; -9,654 in floating point.. Convert the following binary system to decimal format. a. b., c., n 4. Convert the following decimal numbers to binary.

3 a. 66 b. 4,5 c. 6 d.,4 5. Convert the following headecimal numbers to binary form. a. F,C b.fff c., 6. Convert from decimal to headecimal a. 6 b.,5975 c., B.. Write analyze of an algorithm to calculate the amount of the following series. a. EXP = + (-) + ( )! b. P =! a +! a +!a + 4! a ( )! + + n ( n) n! c. E = + a + a a a n + + +!! n!. Find the absolute error, relative error, and digits of accuracy on the following approimation of the true value. a. a =,87 dan â =,95 b. b =,57 dan bˆ =,5 c. c = 4,5 dan ĉ = 4,6 d. d = 5 dan dˆ = 8. Write., 67,45:,564; -9,654 in floating point. 4. Convert : a. (- 54,45) = (. ) b. (,) = (..) c. (CAF,B5) 6 = (...) d. (ABCE,75) 6 = (. ) e. (5,975) = (..) 6 f. (465,75) = (. ) g. (,) = (..) Task Week Giving the task : Tuesday/7 September Submission of assignments : Tuesday/4 September. Determine the location of the roots of the following equation using the dual graph. a. + cos = b. + sin = c. e - + sin = d. e - = e. + tan = f. e - =. Determine the location of the roots of the following polynomial equation. a. 5 + = b. 4 4 = c. = d. 4 6 = e.. Apply the algorithm for the bisection methods to calculate approimations of the following of the roots of nonlinear equations with EPS =... f() = - e = with a = - dan b =

4 . f() = e 4 =, with a = dan b =. f() = e - ln =, with a = dan b = 4. f() = ln - =, with a =,5 dan b = 5. f() = cos + =, with a =,6 dan b =,5 ( in radian) Task 4 Week 4 Giving the task : Tuesday Selasa/4 September Submission of assignments : Tuesday Selasa/ Oktober. Apply the algorithm for the method of false position to calculate approimations of the following of the roots of nonlinear equations with EPS =.. a. f() = - e =, with a = - dan b = b. f() = e 4 =, with a = dan b = c. f() = e - ln =, with a = dan b = d. f() = ln - =, with a =,5 dan b = e. f() = cos + =, with a =,6 dan b =,5 ( in radian). Apply the algorithm for Newton Raphson method to calculate approimations of the following of the roots of nonlinear equations with EPS =. and maimum iteration (M)=. a. f() = e 4 =, with initial guesses =,5 b. f() = e - ln =, with initial guesses =,5 c. f() = ln - =, with initial guesses =,5 d. f() = cos + =, with initial guesses = ( in radian) Task 5 Week 5 Giving the task : Tuesday/ October Submission of assignments : Tuesday/8 October. Apply the algorithm to determine the secant approimation method roots of the following nonlinear equation with EPS =. and maimum iterations (M) =. a. f() = - e = dengan tebakan awal = -,5 dan = -,7 b. f() = e 4 =, dengan tebakan awal =,5 dan = c. f() = e - ln =, dengan tebakan awal =,5 dan = d. f() = ln - =, dengan tebakan awal =,5 dan = e. f() = cos + =, dengan tebakan awal = dan =,5 ( dalam radian). Apply algorithm modified Newton-Raphson method for polynomial approimation to determine the roots of the following polynomial equation with EPS =. and maimum iterations (M) = 4. a. 5 + =, dengan tebakan awal = b. 4 4 =, dengan tebakan awal = c. =, dengan tebakan awal = d. 4 6 =, dengan tebakan awal =,5 Task 6 Week 7 Giving the task : Tuesday/ October Submission of assignments : Tuesday/9 October. Apply subtitution backward algorithm to find of the following the solution of systems of linear equations (SLE) a = 8 b. + 4 = = - 4 = = = 5 4 = - 4 = 6. Write analize to find subtitution foward algorithm. Task 7 4

5 Week 8 Giving the task : Tuesday/9 October Submission of assignments : Tuesday/ November Define the following SLE solution using Gaussian elimination with partial pivoting = = -4-7 = = -5 5 = = 5 Task 8 Week 9 Giving the task : Tuesday / November Submission of assignments : Tuesday / 9 November Define the following SLE solution with Doolittle and Crout decomposition = = = = 49 Define the following SLE solution with Cholesky decomposition = = = = 49 Task 9 Week Giving the task : Tuesday/ 9 November Submission of assignments : Tuesday/6 November. Gunakan iterasi Jacobi sampai iterasi dengan tebakan awal (,,) untuk mencari solusi SPL berikut. Apakah iterasi Jacobi akan konvergen ke selesaian?. Gunakan iterasi Gauss Seidel sampai iterasi dengan tebakan awal (,,) untuk mencari solusi SPL berikut. Apakah iterasi Gauss Seidel akan konvergen ke selesaian? a. 4 y = 5 b. 8 y = + 5y = y = c. 5 - y + z = d. + 8y - z = + 8y - z = 5 - y + z = - + y + 4z = - + y + 4z = Task 5

6 Week Giving the task : Tuesday/ 6 November Submission of assignments : Tuesday/ December. Write the algorithms for analysis and Newton's divided difference formula. Calculate the interpolated value for = 4 (to decimal places) wearing Newton divided difference interpolation 5 6 f() 4,75 4 5,5 9,75 6 Task Week Giving the task : Tuesday/ December Submission of assignments : Tuesday/ December. Show: f! h f ( )( )( ) f )( )( ) f )( )( ) f )( )( ) a. f[ -, -, -, ] = b. f[,,, ] = ( ( (. It is known data points below.,,,6,9,,5 f(),9554,85,66,64,77 Interpolation specify: =.9,.67 and = Show: p () = f + f[ o, ]( o) + f[ o,, ](- o)(- ) Equivalent to: r f! r( r ) f p () = fo + o + o! Task Week 4 Giving the task : Tuesday/ December Submission of assignments : Tuesday/ 7 December Calculate the interpolation value for = 4 (to decimal places) wear Lagrange interpolation 5 6 f() 4,75 4 5,5 9,75 6 6

7 Task Week 5 Giving the task : Tuesday/7 December Submission of assignments : Tuesday/4 December It is known : d a. Calculate the eact value b. Calculate the composition of the trapezoidal rule approimation wear with M =, M = and M = 4 c. Calculate the error for each M. Task 4 Week 6 Giving the task : Tuesday/ 4 December Submission of assignments : Tuesday/ December It is known : d a. Calculate the eact value b. Calculate the composition of the Simpson rule approimation wear with M =, M = 4 and M = 8 c. Calculate the error for each M. Task 5 Week 7 Giving the task : Tuesday/ December Submission of assignments : Tuesday/7 January Show : p h ( ) ( f 4 f f with p () is Lagrange polynom orde. 7. Criteria for Assessment of Student Learning Outcomes Student s learning outcomes assessment is done by giving quizzes, eams, and assignments are assested by. Assessment is given if a student lecture attendance of at least 8%. Students are considered successful if it has been rated at least (C) It is assessed Weight Task 5% Midterm eam (Quiz ) 5% Finalterm eam 5% (Quiz and ) 7

8 ASSESSMENT The total value Letter Quality > 85 A 8 < N 85 A- 75< N 8 B+ 7< N 75 B 65< N 7 B- 6< N 65 C+ 5< N 6 C 45 N 5 D < 45 E 8. Course schedule Date Discussion Topics Reading / Chapter/Page Preliminary Tetbook/Chapter I/-8 ( st Week) a. Algorithm b. Error and the type of matter Tetbook/Chapter I/8-8 ( nd Week) The roots of nonlinear equations Tetbook/ChapterII/9-7 ( rd Week) a. Localization Root b. The Bisection Methods (4 th Week) c.the Method of False Position d.newton Raphson Method (N-R) Tetbook/Chapter II/ (5 th Week) (6 th Week) - - (7 th Week) (8 st Week) - - (9 th Week) ( th Week) ( th Week) - - ( th Week) e.secant Method Tetbook/Chapter II/47-64 f. Modification of the N-R method for polynomial st Quiz - Linear Systems of Equations a. Upper and Lower of Triangular Linear Systems b.gaussian Elimination and Pivoting c. Method of Factorization (Doolittle, Crout and Cholesky) d. Jacobi Method and Gauss Seidel Method nd Quiz Interpolation a. Linear and Quadratic Interpolation b. Newton Divided Difference Interpolation) Tetbook/Chapter III/65-69 Tetbook/Chapter III/69-8 Tetbook/chapter III/8-96 Tetbook/chapter III/96-4 Tetbook/Chapter IV/ c. Interpolation at a point within the Tetbook/Chapter IV/4-6 8

9 ( th Week) same (Newton s Forward and Backward Difference Interpolation) (4 th Week) d. Lagrange s Interpolation Tetbook/Chapter IV/ (5 th Week) - - (6 th Week) Numerical Integral Tetbook/Chapter V/4-5 a. Trapezoidal Rule b. Simpson s Rules. Tetbook/Chapter V/ (7 th Week) rd Quiz - 9. Lecturer Teaching Assessment of the lecturer s teachig ability, performed by students Evaluation. Name of Lecturer Dr. Atma Murni, M.Pd Pekanbaru, st September Lecturer, Dr. Atma Murni, M.Pd NIP