SE301: NUMERICAL METHODS

TERM 033(Summer)

Instructor:   Dr. Samir Hasan Al-Amer

Office     : 22-141         Phone 3749

E-mail : samir@ccse.kfupm.edu.sa

Office hours   Sat, Mon, Tue 10:30-11:30 ,    Sun 10:30-12:30    or by appointment

Visit the course WebCT site for more information and course material

Course Objectives: The course aims to introduce numerical methods that are critical for the solution of modern engineering problems. The course emphasizes algorithms development and applications to realistic engineering problems.

Catalog Description: Introduction to error analysis.  Roots of nonlinear equations. Solution of linear algebraic equations. Numerical differentiation and integration. Interpolation. Least squares and regression analysis. Numerical solution of ordinary and partial differential equations. Engineering case studies.

Prerequisite: ICS 101 (or ICS 102) ,  MATH 201

Textbook:  S.C. Chapra and R. P. Canale, "Numerical Methods for Engineers”. 4th Ed.

Course Outcomes: at the end of this course Student should be able to:

1. Use Taylor Series to approximate functions and evaluate the approximations error.
2. Understand and program algorithms to locate the roots of equations.
3. Understand and program algorithms to solve linear system of equations.
4. Learn how to smooth engineering collected data using least square method.
5. Use polynomials to interpolate engineering collected data or approximate function
6. Understand and program algorithms to evaluate the derivative or the integral of a given function and evaluate the approximation error.
7. Understand and program algorithms to solve engineering Ordinary Differential Equations  (ODE) or Partial Differential Equations (PDE).
8. Understand relationships among methods, algorithms and computer errors.
9. Apply numerical and computer programming to solve common engineering problems.
10. Apply versatile software tools in attacking numerical problems.

Attendance :

• University regulation will be strictly enforced.
• a DN grade will be given if you missed 7 classes or more.
• 1% will deducted from the attendance grade for each unexcused absence.
• Official Excuses should be submitted with in one week.
• If you miss a class it is your responsibility to cover the topic yourself.
• Absence from class does not excuse a missed quiz or homework assignment

Homework:  Homework must be submitted on time. Late homework submissions if accepted are penalized. Absence is not an excuse for late submission. You can do the engineering case studies in MATLAB. If you want to used another programming language check with the instructor first.

 Attendance and Homework 15% Quizzes 25 % Major Exam 1 15 % Toipcs 1,2          July  11,2004 Major Exam 2 20 %  Topics 3, 4 , 5   July  27,2004 Final Exam 25 %   Topics 6,7,8

TOPICS:

1.             Introductory material: Review of Taylors series (sec 4.1),                            3 Lecturers

absolute and relative errors, Rounding and chopping, Computer

errors in representing numbers (sec 3.1-3.4).

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2.             Locating roots of algebraic equations Bisection method (sec 5.2)              5 Lectures

Newton method (sec 6.2), Secant method (sec 6.3)

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3.                    Systems of linear equations:  naïve Gaussian elimination                             5 Lectures

(sec 9.2)  Gaussian elimination with scaled partial pivoting

and Tridiagonal systems

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4.             The method of Least squares;  Smoothing of data and the                          3 Lectures

method of least squares (sec 17.1-17.2), and Examples of

the least squares principles (sec. 17.1.5).

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5.             Interpolation and numerical differentiation;  Polynomial                              5 Lectures

interpolation (sec. 18.1-18.2), Errors in polynomial interpolation

Estimating derivative and Richardson

Extrapolation (sec. 23.1-23.2, appl. Chap24).

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6.             Numerical Integration:  Definite integral (sec. 21.1),                                          5 Lecturers

Trapezoid rule (sec. 21.1.1), Romberg algorithm (sec 22.2).

Gaussian Quadrature (sec 22.3 )

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7.             Ordinary differential equations:  Taylor's series method                               6  Lectures

(sec 25.1), Runge-kutta methods (sec.25.3),  Methods

for first order system (sec 25.41), higher-order Systems

Predictor-corrector Boundary value problems:

A discretization method (sec. 27.1, 27.2.4).

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8.             Partial differential equations: Elliptic Equations (sec 29.1)                            3 Lectures

and Parabolic Equations (sec 30.1-30.4).

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