King Fahd University of Petroleum & Minerals

College of Computer Sciences and Engineering

Information and Computer Science Department

 

CISE 301: Numerical Methods (3-0-3) [Core Course]

 

Syllabus – Summer Semester 2011-2012 (113)

 

Website:  Blackboard (WebCT) http://webcourses.kfupm.edu.sa

 

Class Time, Venue and Instructor Information:

 

 

Sec.

Time

Venue

Instructor

Office Hours

02

SUMT

10:30-11:45am

24/112

Dr. EL-SAYED EL-ALFY

Office: 22-108

Phone: 03-860-1930

E-mail: alfy@kfupm.edu.sa,

http:faculty.kfupm.edu.sa/ics/alfy

 

 

SUM

11:50am-12:40PM

(or by appointment)

04

SUMT

12:45-14:00pm

 

Course Catalog Description

 

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

 

Pre-requisites:  (ICS 101 or ICS103) and MATH 201

 

 

Course Objectives

 

This course aims to introduce numerical methods used for the solution of engineering problems. It emphasizes algorithm development and programming and application to realistic engineering problems.

 

Course Learning Outcomes

 

Upon completion of the course, you should be able to:

  1. Use Taylor Series to approximate functions and evaluate the approximations error.
  2. Program algorithms to locate the roots of nonlinear equations.
  3. Program algorithms to solve linear system of equations.
  4. Smooth engineering collected data using least square method.
  5. Use polynomials to interpolate engineering collected data or approximate function
  6. Program algorithms to evaluate the derivative or the integral of a given function and evaluate the approximation error.
  7. Program to solve engineering Ordinary Differential Equations (ODE) or Partial Differential Equations (PDE).
  8. Grasp 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.

 

Required Material

 

      Numerical Methods for Engineers, 6/e, by Steven C. Chapra and Raymond P. Canale. -- McGraw-Hill Higher Education 2010.

      Lecture Notes

 

Other Recommended References

 

      Numerical Mathematics and Computing, 4/e. by W. Cheney and Kincaid.

      Applied Numerical Analysis, 3/e, by Gerald and Wheatley -- Addison-Wesley 1984.

 

Grading Policy

 

 

 

Assessment Tool

Weight

Homework Assignments & Quizzes

10%

Class Activities and Attendance

5%

Computer Homework + project

5%

Major Exam I     (Unites 1,2,3)  [ Tuesday of the 3rd Week at 4:30-6:30]

25%

Major Exam II   ( Unites 4,5,6) [ Tuesday of the 6th Week at  4:30-6:30]

25%

Final Exam ( Unites 7,8,9) [Date: as announced by the registrar]

30%

 

 

 

 

 

Attendance:

Students are expected to attend all classes. Official excuse for an authorized absence must be presented to the instructor no later than one week following the absence. DN grade will be given if the number of unexcused absences is 6 or more. University Rules regarding attendance will be strictly followed. 1% penalty will be given for each unexcused absence. Absence from class does not excuse a missed quiz or homework assignment. If you are planning to be absent tell me in advance.

 

Computer usage:

 

Students may use FORTRAN, MATLAB or C Language (PC or UNIX versions) or any other language to write programs to solve computer homework assignments.

 

Other Important Notes:  

·         Absence from class does not excuse a missed quiz or homework assignment.

·         Late homework will be penalized. Assignments are not accepted if the solution is posted.

·         Cheating, or attempting to cheat, or violating instructions and examination regulations shall render the offender subject to punishment in accordance with the Students Disciplinary Rules as issued by the University Council (A38).” taken from the KFUPM “Academic Regulations” document.
Tentative Schedule

 

Unit

Unit  Details

75 Minute Lecturers

HW Problems

1

Introductory material:                    

Approximation and round-off error, Significant figures (Sec 3.1),

Accuracy and precision(Sec 3.2), Error definitions(Sec 3.3), Round-off errors(Sec 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-Raphson method (sec 6.2),  Secant method (Sec 6.3),

Multiple roots (Sec 6.4),  Systems of nonlinear equations (Sec 6.5.2)

4

 

3

Systems of linear equations:                            

Naïve Gaussian elimination(sec 9.2),

Gaussian elimination with scaled partial pivoting (Sec 9.4)

Gauss-Jordan method (Sec 9.7) ,  Tri-diagonal systems(Sec 11.1)

3

 

4

The Method of Least Squares;                                                                       

Linear Regression (Sect 17.1), Polynomial Regression (17.2),

Multiple Linear Regression (Sec 17.3),   Nonlinear least squares

3

 

5

Interpolation :

Introduction                                                                        

Newton’s Divided Difference method (Sec. 18.1),

Lagrange  interpolation (Sec 18.2),  Inverse Interpolation (Sec 18.4)

2.5

 

6

Numerical Differentiation:

Estimating derivatives and Richardson’s Extrapolation (sec. 23.1-23.2).

2.5

 

7

Numerical Integration:                                                                                   

Trapezoid rule (sec. 21.1), Romberg algorithm (sec 22.2).

 Gauss Quadrature (sec 22.3 )*

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).

7

 

9

Partial differential equations:                                                                       

Elliptic Equations (sec 29.1-29.2)and

Parabolic Equations (sec 30.1-30.4).

3

 

 

 

30 Lectures

 

 

 

 

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