Lectures (Video)
- 1. Trapezoidal Rule Derivation
- 2. Trapezoidal Rule: Example
- 3. Trapezoidal Rule Multiple Segment Rule: Motivation
- 4. Trapezoidal Rule Multiple Segment Rule: Derivation
- 5. Trapezoidal Rule Multiple Segment Rule: Example Part 1
- 6. Trapezoidal Rule Multiple Segment Rule: Example Part 2
- 7. Trapezoidal Rule Multiple Segment Rule: Error Derivation
- 8. Trapezoidal Rule Multiple Segment Rule: Error Example
- 9. Method of Undetermined Coefficients:Trapezoidal Rule Derivation
- 10. Simpson's One Third Rule Derivation
- 11. Simpsons Rule of Integration: Example
- 12. Multiple Segment Simpson Rule Derivation Part 1
- 13. Multiple Segment Simpson Rule Derivation Part 2
- 14. Multiple Segment Simpson Rule Example Part 1
- 15. Multiple Segment Simpson Rule Example Part 2
- 16. Multiple Segment Trapezoidal Rule Error: Derivation
- 17. Multiple Segment Trapezoidal Rule Error: Example
- 18. Richardsons Extrapolation of Trapezoidal Rule: Theory
- 19. Richardsons Extrapolation of Trapezoidal Rule: Example
- 20. Romberg Integration Theory: Part 1
- 21. Romberg Integration Theory: Part 2
- 22. Method of Undetermined Coefficients: Trapezoidal Rule Derivation
- 23. 2-pt Gaussian Quadrature Rule: Derivation
- 24. n-pt Gaussian Quadrature Rule: Discussion
- 25. Converting Limits of Integration
- 26. Gaussian Quadrature Rule: Example
- 27. 1-pt Gaussian Quadrature Rule: Derivation
- 28. Complete Derivation of Two Point Gaussian Quadrature Rule: Part 1
- 29. Complete Derivation of Two Point Gaussian Quadrature Rule: Part 2
- 30. Complete Derivation of Two Point Gaussian Quadrature Rule: Part 3
Numerical Methods VI
Course Summary
This course is based on Numerical Methods - Integration 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 VI covers the numerical integration using the trapezoidal rule, Simpson rule, Romberg method and Gaussian Quadrature rule.
Reading Material
1. Numerical Methods with Applications - Chapter 7Author: Autar Kaw et al.
Publisher: http://www.autarkaw.com
Published: May 4, 2010
ISBN: 978-0-578-05765-1
Course Material
1. What is Integration?2. A Primer on Integral Calculus
3. Test Your Knowledge of Background of Integral Calculus
4. Physical Problem
A physical problem of finding if the shaft has contracted enough to be shrink fit into a hollow hub.
5. Integrating Discrete Function
6. Integrating Improper Integrals
7. Historical Notes - Newton
8. Historical Notes - Cotes
9. Historical Notes - Gauss
10. Historical Notes - Simpson
11. Historical Notes - Romberg
12. Examples of Trapezoidal Method
Chemical Engineering
Civil Engineering
Computer Engineering
Electrical Engineering
Industrial Engineering
Mechanical Engineering
13. Examples of Simpson's 1/3 Rule
Chemical Engineering
Civil Engineering
Computer Engineering
Electrical Engineering
Industrial Engineering
Mechanical Engineering
14. Examples of Romberg Method
Chemical Engineering
Civil Engineering
Computer Engineering
Electrical Engineering
Industrial Engineering
Mechanical Engineering
15. Examples of Gauss-Quadrature Method
Chemical Engineering
Civil Engineering
Computer Engineering
Electrical Engineering
Industrial Engineering
Mechanical Engineering
16. Sample Tests
Trapezoidal Method
Simpsons 1/3 Rule
Romberg Method
Gauss-Quadrature Method
