Lectures (Video)

- 1. Forward Divided Difference 1
- 2. Forward Divided Difference 2
- 3. Backward Divided Difference 1
- 4. Backward Divided Difference 2
- 5. Central Divided Difference
- 6. Higher Order Derivatives : Theory
- 7. Higher Order Derivatives : Example
- 8. Accuracy of Divided Difference Formulas 1
- 9. Accuracy of Divided Difference Formulas 2
- 10. Divided Difference Approach
- 11. Polynomial Interpolation Method
- 12. Newton's Divided Difference Polynomial Method: Theory
- 13. Newton's Divided Difference Polynomial Method: Example

## Numerical Methods I

### Course Summary

This course is based on

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 I covers the numerical differentiation of continuous and discrete functions.
*Numerical Methods - Differentiation*made available by*Holistic Numerical Methods Institute, University of South Florida*under the*Creative Commons BY-NC-SA*license.### Reading Material

1.**Numerical Methods with Applications - Chapter 2**

Author: Autar Kaw et al.

Publisher: http://www.autarkaw.com

Published: May 4, 2010

ISBN: 978-0-578-05765-1

### Course Material

1.**A primer on differential calculus**

2.

**Physical problem**

How does the thermal expansion coefficient vary at different temperatures?

3.

**Test on numerical differentiation of continuous functions**

Test your knowledge of numerical differentiation of continuous functions

4.

**Test on numerical differentiation of discrete functions**

Test your knowledge of numerical differentiation of discrete functions

5.

**Comparing different methods**

Comparing the Forward Divided Difference, Backward Divided Difference & Central Divided Difference

6.

**Effect of Significant Digits**

Effect of Significant Digits on the Value of the Numerical Derivative