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:
Attendance :
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.
Grading:
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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