DEPARTMENT OF
SYSTEMS ENGINEERING
Syllabus: SE – 301- Numerical Methods
First Semester 2004-2005 (041)
Instructor : Dr. Moustafa Elshafei
Office : Room # 22-135
Office Hours :
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.
Course Objectives: The course aims to
introduce numerical methods used for the solution of engineering problems. The
course emphasizes algorithm development and programming and application to
realistic engineering problems.
Pre-requisite : ICS 101, & MATH 201
Textbook : “Numerical Methods for Engineers”, Steven C. Chapra and Raymond P. Canale.
Other references: W. Cheney and Kincaid, Numerical
Mathematics and Computing. 4th Edition..
Course Outcomes: at the end of this course
Student should be able to:
1. Use Taylor Series to approximate functions and evaluate the approximations
error.
2. Understand and program algorithms to locate the roots of equations.
3. Understand and program algorithms to solve linear system of equations.
4. Learn how to smooth engineering collected data using least square method.
5. Use polynomials to interpolate engineering collected data or approximate
function
6. Understand and program algorithms to evaluate the derivative or the integral
of a given function and evaluate the approximation error.
7. Understand and program to solve engineering Ordinary Differential Equations
(ODE) or Partial Differential Equations (PDE).
8. Understand 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.
Computer usage:
Students are encouraged to learn and use MATLAB to write programs to solve
computer homework assignments. However students who master other computer
programming language may use it as well.
ABET category: content
as estimated by faculty member who prepared this course description. •
Mathematical Sciences: 1 credit • Engineering Science: 2 credits
Important Notes:
• University Rules regarding attendance will be strictly followed.
• Absence from class does not excuse a missed quiz or homework assignment.
• Late homework will be penalized.
Grading :
• Attendance +HW + Computer Homework 15% (-1% per absence)
• Computer Exam 10% • Quizzes 15%
• Midterm (topics 25%
• Final exam 35% ( Topics 5-8)
TOPICS:
1. Introductory material: Review of Taylors
series (sec 4.1),
2 Lectures
absolute and relative errors, Rounding and chopping,
Computer errors in representing numbers (sec 3.1-3.4).
--------------------------------------------------------------------------------------------------------
2. Locating roots of algebraic equations Bisection method (sec 5.2) 4 Lectures
Newton method (sec 6.2), Secant method (sec 6.3)
-------------------------------------------------------------------------------------------------------
3. Systems of linear equations: naïve Gaussian elimination 4 Lectures
(sec 9.2) Gaussian elimination with scaled partial pivoting
and Tridiagonal systems (handouts)
-----------------------------------------------------------------------------------------------------
4. The method of Least squares; Smoothing of data and the 2 Lectures
method of least squares (sec 17.1-17.2), and Examples of the
least squares principles (sec. 17.1.5).
-----------------------------------------------------------------------------------------------------
5. Interpolation and numerical differentiation; Polynomial 4 Lectures
interpolation (sec. 18.1-18.2), Errors in polynomial interpolation Estimating
derivative and Richardson Extrapolation (sec. 23.1-23.2, appl. Chap24).
------------------------------------------------------------------------------------------------------
6. Numerical Integration: Definite integral (sec. 21.1), 4 Lecturers
Trapezoid rule (sec. 21.1.1), Romberg algorithm (sec 22.2). ….
Gaussian quadrature (sec 22.3 )
------------------------------------------------------------------------------------------------------
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 25.4), higher-order Systems Predictor-corrector
Boundary value problems: A discretization method (sec. 27.1, 27.2.4).
----------------------------------------------------------------------- ---------------------------------
8. Partial differential equations: Parabolic problems (sec 29.1) 2 Lectures
and Hyperbolic problems (sec 30.1).
----------------------------------------------------------------------------------------------------------
Revision
1 Lecture