SE301: NUMERICAL METHODS
TERM 041(Fall 2004)
Instructor: Dr. Samir Hasan AlAmer
Office : 22141 Phone 3749
Email : samir@ccse.kfupm.edu.sa
Office hours Sun and Tue 11:2012:50 , Wed 10:0011:00 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”. 4^{th} 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  10% 
Computer Exam  10% 
Quizzes  20 % 
Midterm Exam  25 % Toipcs 1,2,3,4 Oct 24, 2004 
Final Exam  25 % Topics 5,6,7,8, 9 
TOPICS:
TOPIC 
Lecturers  
1 
Introductory material: Absolute and relative errors, Rounding and chopping, Computer, errors in representing numbers (sec 3.13.4). Review of Taylor series (sec 4.1), 
3 
2 
Locating roots of algebraic equations: Graphical Methods ( Sec 5.1), Bisection method (Sec 5.2),Newton method (sec 6.2), Secant method (sec 6.3), Systems of nonlinear equations (6.5.2) 
4 
3 
Systems of linear equations: Naïve Gaussian elimination(sec 9.2), Gaussian elimination with scaled partial pivoting and Tridiagonal systems, GaussJordan method (Sec 9.7)

4 
4 
The Method of Least Squares; Linear Regression (Sect 17.1), Polynomial Regression (17.2) Multiple Linear Regression (Sec 17.3) 
2 
5 
Interpolation: Newton’s Divided Difference method (Sec. 18.1), Lagrange interpolation (Sec 18.2), Inverse Interpolation (Sec 18.4) 
3 
6 
Numerical Integration: Trapezoid rule (sec. 21.1), Romberg algorithm (sec 22.2). Gauss Quadrature (sec 22.3 ) 
4 
7 
Numerical Differentiation: Estimating derivatives and Richardson’s Extrapolation (sec. 23.123.2). 
2 
8 
Ordinary differential equations: Euler’s method (sec 25.1), Improvements of Euler’s method (sec 25.2), RungeKutta methods (sec.25.3), Methods for systems of equations (sec 25.4), Multistep Methods (Sec 26.2), Boundary value problems (Sec. 27.1, 27.2.4).

5 
9 
Partial differential equations: Elliptic Equations (sec 29.129.2)and Parabolic Equations (sec 30.130.4). 
2 
Revision  1 