Math-254 Numerical Methods.

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Presentation transcript:

Math-254 Numerical Methods

Recommended Textbook: Introduction To Numerical Analysis Using MATLAB Author: Dr. Rizwan Butt Department of Mathematics College of Science King Saud University P. O. Box 2455 Riyadh, 11451, Saudi Arabia. E-mail: rizwanbu@ksu.edu.sa Publisher: Infinity Science Press (USA) ISBN: 978-1-934015-23-0 Year of Published: October, 2007 Reference Textbook: Numerical Analysis (Seventh Edition) Authors: Richard L. Burden and J. Douglas Faires

Examinations Schedule: Two midterm examinations and the final examination First Midterm Examination 20 marks After six weeks Second Midterm Examination 20 marks After thirteen weeks Final Examination 50 marks After fifteen weeks About 10 marks: 1- Computer Assignments 4 marks 2- Two Quizzes 4 marks 3- Exercises 2 marks

Topics for the Course Chapter 1 Number Systems and Error (1 lecture) Chapter 2 Solutions of Nonlinear Equations (13 lectures) Chapter 3 Systems of Linear Equations (13 lectures) Chapter 4 Approximating Functions (7 lectures) Chapter 5 Differentiation and Integration (7 lectures) Chapter 6 Ordinary Differential Equations (4 lectures)

Means of Solving Problems Analytical Methods Graphical Methods Numerical Methods Exact Solution Approximate Solution

What is Numerical Analysis ? 1- Numerical analysis can be defined as the development and implementation of techniques to find numerical solutions to mathematical problems. 2- It is an increasingly important link between pure mathematics and its application in science and technology. 3- With the accessibility of computers, it is possible now to get rapid and accurate solutions to many complex problems that give difficulties to the mathematician, engineer and scientist. 4. Frequently, numerical analysis is called the mathematics of scientific computing.

Types of Numerical Methods Direct Methods Iterative Methods Need finite number of steps. No need for initial approximation. Good for small problems. Chance of getting exact information about problems. Need infinite number of steps. Need for initial approximation. Good for large problems. No chance of getting exact information about problems.

Practical Justification Through MATLAB 1- In our lectures, practical justification of the methods is presented through computer examples through the use of MATLAB. 2- In recent years, the number of MATLAB users has dramatically increased. 3- The surge of popularity in MATLAB is related to the increasing popularity of UNIX and computer graphics. 4- To what extend numerical computations in the future will be programmed in MATLAB is uncertain.