Lectures (Video)
- 1. Naive Gaussian Elimination : Theory Part 1
- 2. Naive Gaussian Elimination : Theory Part 2
- 3. Naive Gauss Elimination Method : Example Part 1
- 4. Naive Gauss Elimination Method: Example Part 2
- 5. Pitfalls of Naive Gauss Elimination Method
- 6. Round of Error : Example Part 1
- 7. Round of Error : Example Part 2
- 8. Round of Error : Example Part 3
- 9. Gaussian Elimination with Partial Pivoting: Theory
- 10. Gauss Elimination with Partial Pivoting: Part 1
- 11. Gauss Elimination with Partial Pivotin : Part 2
- 12. Gauss Elimination with Partial Pivoting: Part 3
- 13. Partial Pivoting: Round of Error Part 1
- 14. Partial Pivoting: Round of Error Part 2
- 15. Partial Pivoting: Round of Error Part 3
- 16. Determinant of a Matrix using Forward Elimination
- 17. Determinant of a Matrix using Forward Elimination: Example
- 18. LU Decomposition: Basis
- 19. LU Decomposition Method: Example
- 20. Why LU Decomposition: Part 1
- 21. Why LU Decomposition: Part 2
- 22. Decomposing A Square Matrix: Part 1
- 23. Decomposing A Square Matrix: Part 2
- 24. Finding the Inverse of a Matrix
- 25. Finding the Inverse of a Matrix: Example
- 26. Gauss-Seidel Method Theory: Part 1
- 27. Gauss-Seidel Method Theory: Part 2
- 28. Gauss-Seidel Method Example: Part 1
- 29. Gauss-Seidel Method Example: Part 2
- 30. Gauss-Seidel Method Pitfalls and Advantages: Part 1
- 31. Gauss-Seidel Method Pitfalls and Advantages: Part 2
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 4Author: 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 Algebra2. 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
