SE301 Numerical Methods

SE301: NUMERICAL METHODS

TERM 042(Spring 2005)

                         Instructor:   Dr. Samir Hasan Al-Amer

               Office     : 22-141         Phone 3749

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

                           Office hours   Sun and Tue 9:00-10:00 ,    Mon 11:00-12:50    or by appointment

COMPUTER ASSIGNMENTS

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:

Use Taylor Series to approximate functions and evaluate the approximations error.

Understand and program algorithms to locate the roots of equations.

Understand and program algorithms to solve linear system of equations.

Learn how to smooth engineering collected data using least square method.

Use polynomials to interpolate engineering collected data or approximate function

Understand and program algorithms to evaluate the derivative or the integral of a given function and evaluate the approximation error.

Understand and program algorithms to solve engineering Ordinary Differential Equations (ODE) or Partial Differential Equations (PDE).

Understand relationships among methods, algorithms and computer errors.

Apply numerical and computer programming to solve common engineering problems.

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 the language you learned in ICS101 or ICS102. If you want to used another programming language check with the instructor first.

Grading:

Attendance 5%

Homework+ Computer Project 15%

Quizzes + Computer Exam 15%

Major Exam 1 20 % Topics 1,2,3

Major Exam 2 20 % Topics 4, 5,6

Final 25 % Topics 7,8, 9

  TOPICS:

TOPIC
Lecturers

1 Introductory material:
Absolute and relative errors, Rounding and chopping, Computer, errors in representing numbers (sec 3.1-3.4).   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 Tri-diagonal systems, Gauss-Jordan 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. 23.1-23.2).
2

8
Ordinary differential equations:

Euler’s method (sec 25.1), Improvements of Euler’s 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).

5

9
Partial differential equations:

Elliptic Equations (sec 29.1-29.2)and Parabolic Equations (sec 30.1-30.4).
2

Revision 1

Attendance	5%
Homework+ Computer Project	15%
Quizzes + Computer Exam	15%
Major Exam 1	20 % Topics 1,2,3
Major Exam 2	20 % Topics 4, 5,6
Final	25 % Topics 7,8, 9

	TOPIC	Lecturers
1	Introductory material: Absolute and relative errors, Rounding and chopping, Computer, errors in representing numbers (sec 3.1-3.4). 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 Tri-diagonal systems, Gauss-Jordan 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. 23.1-23.2).	2
8	Ordinary differential equations: Euler’s method (sec 25.1), Improvements of Euler’s 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).	5
9	Partial differential equations: Elliptic Equations (sec 29.1-29.2)and Parabolic Equations (sec 30.1-30.4).	2
	Revision	1