COURSE CONTRACT - WeeblyRIAU UNIVERSITY FAKULTY OF TEACHER TRAINING AND EDUCATION Department : Mathematics and Science Education Program : Mathematics Education 1 COURSE CONTRACT Course

RIAU UNIVERSITY FAKULTY OF TEACHER TRAINING AND EDUCATION

Department : Mathematics and Science Education Program : Mathematics Education

1

COURSE CONTRACT

Course Name

Course Code

Semester Days/ hours

Place Course Status

Course Prerequisites

Numerical Methods

KPL 11131

Odd

2013/2014

Tuesday/

07.30-10.00

F8

compulsory

1. Calculus I 2. Calculus II 3. Linear Algebra 4. Computer and

Programming

1. Benefits Courses for Students Students understand the types of numerical methods that can be used to solve mathematical problems.

2. 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 examples

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.

3. 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 experience 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 1. Atkinson, Kendall E., 1985., Elementary Numerical Analysis.Iowa: John Wiley & Sons.

2. Anton, Howard., 1991., Aljabar Linear Elementery (5th

Edition ). Jakarta: Erlangga. 3. Froberg, Carl-Erik., 1974. Introduction to Numerical

Analysis., Addison-Wesly. Publishing Company. 4. Mathews, Jhon. H., 1992., Numerical Methods for

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

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

6. Susila, I. Nyoman. 1993. Elementary Numerical Method. Bandung: Depdikbud.

Media: LCD 6. Student task

Task 1 Week 1 Giving the task : Tuesday/3 September 2013 Submission of assignments : Tuesday/10 September 2013 Make the pseudo code to calculate the number of runs following. 1. nbbbbH 321

2. nnbababaHKDB 2211

3. P = 1 +21

+ 31

+ ... + m1

4. !

1!3

1!2

11n

FAK

5. nn xxxxPT )1(1 32

6. )!2(

)1(!6!4!2

12642

nxxxxCOSX

nn

7. )!12(

)1(!5!3

12153

nxxxxSINX

nn

Task 2 Week 2 Giving the task : Tuesday/10 September 2013 Submission of assignments : Tuesday/17 September 2013 A. 1. Find the absolute error, relative error, and digits of accuracy on the

following approximation of the true value. a. a = 3,8213454 dan a = 3,8213

b. b = 76380 dan b = 76000 c. c = 0,000087 dan c = 0,00008

2. Write 20.000; 537,235; 0,00056432; -90,654 in floating point. 3. Convert the following binary system to decimal format.

a. 110011 b. 101,1101 c. 0,10000001 4. Convert the following decimal numbers to binary.



3

a. 366 b. 4,25 c. 61

d. 3,14

5. Convert the following hexadecimal numbers to binary form. a. 1F,C b.FFF c.11,1

6. Convert from decimal to hexadecimal a. 161 b. 0,3359375 c. 0,1

B. 1. Write analyze of an algorithm to calculate the amount of the

following series.

a. EXP = 1 + x (x-1) + !2

)2(2 xx +

!3)3(3 xx

+ … + !

)(n

nxx n

b. P = 1! a1 + 2! a2 + 3!a3 + 4! a4 + ….

c. E = 1 + a1x + !2

a 2 x +

!3a 3 x

+ … + !

a n

nx

2. Find the absolute error, relative error, and digits of accuracy on the

following approximation of the true value. a. a = 0,000087 dan a = 0,000095

b. b = 0,000057 dan b = 0,000051 c. c = 243,05 dan c = 242,16

d. d = 1325 dan d = 1328 3. Write 10.000, 2367,2435: 0,000056432; -900,6254 in floating point.

4. Convert : a. (- 534,425)10 = (……….…)2 b. (11001100,101)2 = (…………..)10 c. (CAF,B5)16 = (....................)2 d. (ABCE,75)16 = (……….…)2 e. (153,9375)10 = (…………..)16 f. (2465,725)10 = (……….…)2 g. (11011011,0101)2 = (…………..)10

Task 3 Week 3 Giving the task : Tuesday/17 September 2013 Submission of assignments : Tuesday/24 September 2013 1. Determine the location of the roots of the following equation using

the dual graph. a. x + cos x = 0 b. x2 + sin x – 2 = 0 c. e-x + sin x = 0 d. 1 – x – e-2x = 0 e. 2x + tan x = 0 f. 2x2 – e-x = 0

2. Determine the location of the roots of the following polynomial equation.

a. x3 – 5 x + 3 = 0 b. x4 – x3 – 2x – 34 = 0 c. 2x3 – x – 3 = 0 d. 4x3 – 2x – 6 = 0 e.

3. Apply the algorithm for the bisection methods to calculate approximations of the following of the roots of nonlinear equations with EPS = 0.1. 1. f(x) = x2 - ex = 0 with a = - 1 dan b = 0



4

2. f(x) = ex – 4x = 0, with a = 0 dan b = 1 3. f(x) = e-x – ln x = 0, with a = 1 dan b = 2 4. f(x) = x2 – ln x -3 = 0, with a = 0,5 dan b = 2 5. f(x) = cos x + 1 – x = 0, with a = 0,6 dan b = 1,5 (x in radian)

Task 4 Week 4 Giving the task : Tuesday Selasa/24 September 2013 Submission of assignments : Tuesday Selasa/1 Oktober 2013 1. Apply the algorithm for the method of false position to calculate

approximations of the following of the roots of nonlinear equations with EPS = 0.01. a. f(x) = x2 - ex = 0, with a = - 1 dan b = 0 b. f(x) = ex – 4x = 0, with a = 0 dan b = 1 c. f(x) = e-x – ln x = 0, with a = 1 dan b = 2 d. f(x) = x2 – ln x -3 = 0, with a = 0,5 dan b = 2 e. f(x) = cos x + 1 – x = 0, with a = 0,6 dan b = 1,5 ( x in radian)

2. Apply the algorithm for Newton Raphson method to calculate approximations of the following of the roots of nonlinear equations with EPS = 0.01 and maximum iteration (M)= 3. a. f(x) = ex – 4x = 0, with initial guesses x0 = 0,5 b. f(x) = e-x – ln x = 0, with initial guesses x0 = 1,5 c. f(x) = x2 – ln x -3 = 0, with initial guesses x0 = 1,5 d. f(x) = cos x + 1 – x = 0, with initial guesses x0 = 1 (x in radian)

Task 5 Week 5 Giving the task : Tuesday/1 October 2013 Submission of assignments : Tuesday/8 October 2013 1. Apply the algorithm to determine the secant approximation method

roots of the following nonlinear equation with EPS = 0.01 and maximum iterations (M) = 3. a. f(x) = x2 - ex = 0 dengan tebakan awal x0 = - 0,5 dan x1 = - 0,7 b. f(x) = ex – 4x = 0, dengan tebakan awal x0 = 0,5 dan x1 = 1 c. f(x) = e-x – ln x = 0, dengan tebakan awal x0 = 1,5 dan x1 = 2 d. f(x) = x2 – ln x -3 = 0, dengan tebakan awal x0 = 1,5 dan x1 = 2 e. f(x) = cos x + 1 – x = 0, dengan tebakan awal x0=1 dan x1=1,5 (x dalam radian)

2. Apply algorithm modified Newton-Raphson method for polynomial

approximation to determine the roots of the following polynomial equation with EPS = 0.01 and maximum iterations (M) = 4. a. x3 – 5x + 3 = 0, dengan tebakan awal x0 = 2 b. x4 – x3 – 2x – 34 = 0, dengan tebakan awal x0 = 3 c. 2x3 – x – 3 = 0, dengan tebakan awal x0 = 1 d. 4x3 – 2x – 6 = 0, dengan tebakan awal x0 = 0,5

Task 6 Week 7 Giving the task : Tuesday/22 October 2013 Submission of assignments : Tuesday/29 October 2013

1. Apply subtitution backward algorithm to find of the following the solution of systems of linear equations (SLE)

a. –x + 3x2 – 6x3 - x4 = 8 b. 3x1 – 2x2 + x3 – x4 = 8 3x2 + 4x3 + 2x4 = 2 3x2 – 2x3 - x4 = 4 x3 + 3x4 = 4 - x3 + 4x4 = 5 2x4 = -10 2x4 = 6 2. Write analize to find subtitution foward algorithm.

Task 7



5

Week 8 Giving the task : Tuesday/29 October 2013 Submission of assignments : Tuesday/12 November 2013 Define the following SLE solution using Gaussian elimination with partial pivoting.

1. 4 x1 + 5x2 – 6x3 = 18 2. 2x1 + 4x2 – 6x3 = -4 2 x1 - 7x3 = 29 x1 + 5x2 + 3x3 = 10 -5x1 – 5x2 = -63 x1 + 3x2 + 2x3 = 5

Task 8 Week 9 Giving the task : Tuesday /12 November 2013 Submission of assignments : Tuesday / 19 November 2013 Define the following SLE solution with Doolittle and Crout decomposition.

x1 + 2x2 – 12x3 + 8x4 = 27 5x1 + 4x2 + 7x3 – 2x4 = 4 -3x1 + 7x2 + 9x3 + 5x4 = 11 6x1 – 12x2 – 8x3 + 3x4 = 49

Define the following SLE solution with Cholesky decomposition.

8x1 + 2x2 – x3 + x4 = 27 2x1 + 4x2 + x3 – 2x4 = 4 -x1 + x2 + 9x3 + 5x4 = 11 x1 – 2x2 + 5x3 + x4 = 49

Task 9 Week 10 Giving the task : Tuesday/ 19 November 2013 Submission of assignments : Tuesday/26 November 2013 1. Gunakan iterasi Jacobi sampai 3 iterasi dengan tebakan awal

(0,0,0) untuk mencari solusi SPL berikut.

Apakah iterasi Jacobi akan konvergen ke selesaian ?

2. Gunakan iterasi Gauss Seidel sampai 3 iterasi dengan tebakan awal (0,0,0) untuk mencari solusi SPL berikut.

Apakah iterasi Gauss Seidel akan konvergen ke selesaian ?

a. 4x – y = 15 b. 8x – 3y = 10

x + 5y = 9 -x + 3y = 1

c. 5x - y + z = 10 d. 2x + 8y - z = 11

2x + 8y - z = 11 5x - y + z = 10

-x + y + 4z = 3 -x + y + 4z = 3

Task 10



6

Week 12 Giving the task : Tuesday/ 26 November 2013 Submission of assignments : Tuesday/ 3 December 2013 1. Write the algorithms for analysis and Newton's divided difference formula 2. Calculate the interpolated value for x = 4 (to 3 decimal places) wearing Newton divided difference interpolation

x 1 2 3 5 6 f(x) 4,75 4 5,25 19,75 36

Task 11 Week 13 Giving the task : Tuesday/ 3 December 2013 Submission of assignments : Tuesday/ 10 December 2013

1. Show:

a. f[x-1,x-2,x-1,x0] = 30

3

!3 hf

b. f[x0,x1,x2,x3] = ))()(( 302010

0

xxxxxxf

))()(( 312101

1

xxxxxxf

))()(( 321202

2

xxxxxxf

))()(( 231303

3

xxxxxxf

3. It is known data points below.

x 0,0 0,3 0,6 0,9 1,2 1,5 f(x) 1 0,9554 0,8253 0,6216 0,3624 0,0707

Interpolation specify: x = 0.29, 0.67 and x = 1.45

4. Show:

p2(x) = f0 + f[xo,x1](x – xo) + f[xo,x1,x2](x-xo)(x-x1) Equivalent to:

p2(x) = fo + ofr

!1+ of

rr 2

!2)1(

Task 12 Week 14 Giving the task : Tuesday/ 10 December 2013 Submission of assignments : Tuesday/ 17 December 2013 Calculate the interpolation value for x = 4 (to 3 decimal places) wear Lagrange interpolation

x 1 2 3 5 6 f(x) 4,75 4 5,25 19,75 36



7

Task 13 Week 15 Giving the task : Tuesday/17 December 2013 Submission of assignments : Tuesday/24 December 2013

It is known : dxxx

1

0 1

a. Calculate the exact value b. Calculate the composition of the trapezoidal rule approximation wear with M = 1, M = 2 and M = 4 c. Calculate the error for each M.

Task 14 Week 16 Giving the task : Tuesday/ 24 December 2013 Submission of assignments : Tuesday/31 December 2013

It is known : dxxx

1

0 1

a. Calculate the exact value b. Calculate the composition of the Simpson rule approximation wear with M = 2, M = 4 and M = 8 c. Calculate the error for each M.

Task 15 Week 17 Giving the task : Tuesday/ 31 December 2013 Submission of assignments : Tuesday/7 January 2013 Show :

4(3

)( 2102

2

0

fffhxpx

x

with p2(x) is Lagrange polynom orde 2.

7. Criteria for Assessment of Student Learning Outcomes

Student’s learning outcomes assessment is done by giving quizzes, exams, and assignments are assested by. Assessment is given if a student lecture attendance of at least 80%. Students are considered successful if it has been rated at least (C) It is assessed Weight Task 15% Midterm exam (Quiz 1) 35% Finalterm exam (Quiz 2 and 3)

50%



8

ASSESSMENT The total value Letter Quality

> 85 A 80 < N ≤ 85 A- 75< N ≤ 80 B+ 70< N ≤ 75 B 65< N ≤ 70 B- 60< N ≤ 65 C+ 50< N ≤ 60 C 45≤ N ≤ 50 D < 45 E

8. Course schedule

Date Discussion Topics Reading / Chapter/Page 3 - 9 - 2013 (1st Week)

Preliminary a. Algorithm

Textbook/Chapter I/1-8

10 - 9 - 2013 (2nd Week)

b. Error and the type of matter

Textbook/Chapter I/8-18

17 - 9 - 2013 ( 3rd Week)

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

Textbook/ChapterII/19-37

24 - 9 - 2013 (4th Week)

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

Textbook/Chapter II/37-47

1 - 10 - 2013 (5th Week)

e.Secant Method f. Modification of the N-R method for polynomial

Textbook/Chapter II/47-64

8 - 10 - 2013 (6th Week)

1st Quiz -

22 - 10 - 2013 (7th Week)

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

Textbook/Chapter III/65-69

29 - 10 - 2013 (8st Week)

b.Gaussian Elimination and Pivoting

Textbook/Chapter III/69-80

12 -11 - 2013 (9th Week)

c. Method of Factorization (Doolittle, Crout and Cholesky)

Textbook/chapter III/80-96

19 -11 - 2013 (10th Week)

d. Jacobi Method and Gauss Seidel Method

Textbook/chapter III/96-104

26 -11 - 2013 (11th Week)

2nd Quiz

3 -12 - 2013 (12th Week)

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

Textbook/Chapter IV/112-124

10 -12 - 2013 c. Interpolation at a point within the Textbook/Chapter IV/124-136



9

(13th Week) same (Newton’s Forward and Backward Difference Interpolation)

17 -12 - 2013 (14th Week)

d. Lagrange’s Interpolation Textbook/Chapter IV/137-141

24 -12 - 2013 (15th Week)

Numerical Integral a. Trapezoidal Rule

Textbook/Chapter V/143-150

31 -12 - 2013 (16th Week)

b. Simpson’s Rules.

Textbook/Chapter V/150-159

7 -1 - 2014 (17th Week)

3rd Quiz -

9. Lecturer Teaching Evaluation

Assessment of the lecturer’s teachig ability, performed by students

10. Name of Lecturer Dr. Atma Murni, M.Pd

Pekanbaru, 1st September 2013 Lecturer, Dr. Atma Murni, M.Pd NIP. 196210041986032002

Documents

COURSE CONTRACT - WeeblyRIAU UNIVERSITY FAKULTY OF TEACHER TRAINING AND EDUCATION Department : Mathematics and Science Education Program : Mathematics Education 1 COURSE CONTRACT Course