CISE 301 Numerical Methods
Catalog Description
A course on roots of nonlinear equations, solutions of systems of
linear equations,
numerical differentiation and numerical integration,
interpolation,
least squares
regression
analysis, numerical solution of a
ordinary
differential equation and
partial
differential equation, introduction to
error analysis,
and 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.
Prerequisites
ICS 101 & MATH 201.
Textbook
Steven C. Chapra and
Raymond P. Canale, Numerical Methods for Engineers, 5th Edition
References
W. Cheney and Kincaid, Numerical Mathematics and Computing, 4th Edition.
Course Outcomes
At the end of this course, students should be able to:
-
Use Taylor Series to approximate
functions and evaluate the approximation errors.
-
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 a 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 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 to
solve numerical problems.
Computer Usage
Basic knowledge of Excel and
MATLAB is required. Every student is
required to have a WebCT account as homework solutions, exam solutions,
grades, etc will be posted in the course WebCT.
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 not be accepted.
Method of assessment
|
Homework |
15 |
| Computer Homework |
10 |
| Quizzes |
10 |
| Major I |
20 |
| Major II |
20 |
| Final exam |
25 |
Topics
|
1.
Introduction to
numerical methods: Absolute and relative errors, Rounding and chopping, Computer errors
in representing numbers, Review of Taylor series |
4 Lectures |
| 2. Roots of Equations:
Graphical Methods, Bisection method, Newton
method, Secant method, Systems of nonlinear
equations |
6 Lectures |
| 3.
Systems of Linear Equations:
Naïve Gaussian elimination, Gaussian elimination with scaled partial
pivoting and Tri-diagonal systems, Gauss-Jordan method |
6 Lectures |
| 4. Method
of Least Squares:
Linear Regression, Polynomial Regression, Multiple Linear
Regression |
4 Lectures |
| 5. Interpolation:
Newton’s Divided Difference method, Lagrange
interpolation, Inverse Interpolation |
4 Lectures |
| 6. Numerical Integration:
Trapezoid rule, Simpson’s Rules, Romberg algorithm |
6 Lecturers |
| 7. Numerical Differentiation:
Numerical Differentiation, Estimating derivatives and
Richardson Extrapolation |
2.5 Lectures |
| 8. Ordinary Differential Equations:
Euler’s method, Improvements of Euler’s method, Runge-Kutta methods, Methods for systems of
equations, Adaptive RK Methods, Multistep
Methods, Boundary value problems |
9 Lectures |
| 9. Partial Differential Equations:
Elliptic Equations, Parabolic Equations |
3.5 Lectures |
Instructor
Dr Muhammad bin Fahad Al–Salamah
King Fahd University of Petroleum and Minerals
Department of Systems Engineering
Term: Fall, 2006
الوصف: جذور المعادلات الغير الخطية، وحلول نظم المعادلات الجبرية الخطية، التفاضل والتكامل العددي، الاستيفاء ، المربعات الصغرى، وتحليل الانحدار، مقدمة تحليل الأخطاء.
المادة: الطرق العددية
مدرس المادة: الدكتور محمد بن فهد السلامة
برنامج الهندسة الصناعية
و النظم
قسم هندسة النظم
جامعة الملك فهد للبترول و المعادن |