SE301: NUMERICAL METHODS
TERM 041(Fall 2004)
Instructor: Dr. Samir Hasan Al-Amer
Office : 22-141 Phone 3749
E-mail : firstname.lastname@example.org
Office hours Sun and Tue 11:20-12:50 , Wed 10:00-11:00 or by appointment
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 EngineersĒ. 4th Ed.
Course Outcomes: at the end of this course Student should be able to:
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||10%|
|Midterm Exam||25 % Toipcs 1,2,3,4 Oct 24, 2004|
|Final Exam||25 % Topics 5,6,7,8, 9|
Absolute and relative errors, Rounding and chopping, Computer, errors in representing numbers (sec 3.1-3.4). Review of Taylor series (sec 4.1),
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)
Systems of linear equations:
NaÔve Gaussian elimination(sec 9.2), Gaussian elimination with scaled partial pivoting and Tri-diagonal systems, Gauss-Jordan method (Sec 9.7)
The Method of Least Squares;
Linear Regression (Sect 17.1), Polynomial Regression (17.2) Multiple Linear Regression (Sec 17.3)
Newtonís Divided Difference method (Sec. 18.1), Lagrange interpolation (Sec 18.2), Inverse Interpolation (Sec 18.4)
Trapezoid rule (sec. 21.1), Romberg algorithm (sec 22.2). Gauss Quadrature (sec 22.3 )
Estimating derivatives and Richardsonís Extrapolation (sec. 23.1-23.2).
Ordinary differential equations:
Eulerís method (sec 25.1), Improvements of Eulerís method (sec 25.2), Runge-Kutta 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).
Partial differential equations:
Elliptic Equations (sec 29.1-29.2)and Parabolic Equations (sec 30.1-30.4).