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Lectures (Video)

Numerical Methods III

Course Summary

This course is based on Numerical Methods - Simultaneous Linear Equations made available by Holistic Numerical Methods Institute, University of South Florida under the Creative Commons BY-NC-SA license.
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part III covers the numerical methods for solving simultaneous linear equations. These include the Gaussian Elimination method, LU Decomposition and Gauss-Seidel method.

Reading Material

1. Numerical Methods with Applications - Chapter 4
Author: Autar Kaw et al.
Publisher: http://www.autarkaw.com
Published: May 4, 2010
ISBN: 978-0-578-05765-1

Course Material

1. Introduction to Matrix Algebra

2. Vectors

3. Binary Matrix Operations

4. Unary Matrix Operations

5. System of Equations

6. Test Your Knowledge of Background of Simultaneous Linear Equations

7. Physical Problem
Find constants of a regression model for coefficient of thermal expansion vs temperature.

8. Effect of Significant Digits on Solution of Equations

9. Saving of Computational Time for Finding Inverse of a Matrix using LU Decomposition

10. Adequacy of Solutions

11. Eigenvalues and Eigenvectors

12. Historical Notes - Gauss

13. Examples on Gaussian Elimination
Chemical Engineering
Civil Engineering
Computer Engineering
Electrical Engineering
Industrial Engineering
Mechanical Engineering

14. Examples on LU Decomposition
Chemical Engineering
Civil Engineering
Computer Engineering
Electrical Engineering
Industrial Engineering
Mechanical Engineering

15. Examples on Gauss-Seidel Method
Chemical Engineering
Civil Engineering
Computer Engineering
Electrical Engineering
Industrial Engineering
Mechanical Engineering

16. Sample Tests
Gaussian Elimination
LU Decomposition Method
Gauss-Seidel Method

Other Resources

Not available.

Software

Not available.


 

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