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Math-254 Numerical Methods

Math-254 Numerical Methods. Recommended Textbook: Introduction To Numerical Analysis Using MATLAB Author: Dr. Rizwan Butt Reference Textbook: Numerical Analysis (Seventh Edition)

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Math-254 Numerical Methods

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  1. Math-254 Numerical Methods

  2. Recommended Textbook: Introduction To Numerical Analysis Using MATLAB Author: Dr. Rizwan Butt Reference Textbook: Numerical Analysis (Seventh Edition) Authors: Richard L. Burden and J. Douglas Faires

  3. Examinations Schedule: Two midterm examinations and the final examination First Midterm Examination 25 marks After 9weeks (2/3/1441) Second Midterm Examination 25 marks After 13 weeks (30/3/1441) Final Examination 40 marks About 10 marks: - Two Quizzes 10 marks

  4. Topics for the Course Chapter 1 Introduction (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)

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

  6. 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.

  7. Types of Numerical 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. Direct Methods Iterative Methods

  8. 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.

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