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.

• 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).

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2. Locating roots of algebraic equations Bisection method (sec 5.2)                       4 Lectures

Newton method (sec 6.2), Secant method (sec 6.3)

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3. Systems of linear equations: naïve Gaussian elimination                                      4 Lectures

(sec 9.2) Gaussian elimination with scaled partial pivoting

and Tridiagonal systems (handouts)

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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).

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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).

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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 )

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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).

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8. Partial differential equations: Parabolic problems (sec 29.1)                                          2 Lectures

and Hyperbolic problems (sec 30.1).

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Revision                                                                                                                           1 Lecture