Lectures (Video)

- 1. Linear Interpolation
- 2. Quadratic Interpolation
- 3. Cubic Interpolation: Part 1
- 4. Cubic Interpolation: Part 2
- 5. Newton's Divided Difference Polynomial (Linear): Theory
- 6. Newton's Divided Difference Polynomial (Linear): Example
- 7. Newton's Divided Difference Polynomial (Quadratic): Theory
- 8. Newton's Divided Difference Polynomial (Quadratic): Example Part 1
- 9. Newton's Divided Difference Polynomial (Quadratic): Example Part 2
- 10. Newton's Divided Difference Polynomial (General Order): Theory Part 1
- 11. Newton's Divided Difference Polynomial (General Order): Theory Part 2
- 12. Newton's Divided Difference Polynomial (General Order): Example Part 1
- 13. Newton's Divided Difference Polynomial (General Order): Example Part 2
- 14. Lagrangian Interpolation: Theory
- 15. Lagrangian Interpolation (Linear): Example
- 16. Lagrangian Interpolation (Quadratic): Example Part 1
- 17. Lagrangian Interpolation (Quadratic): Example Part 2
- 18. Lagrangian Interpolation (Cubic): Example Part 1
- 19. Lagrangian Interpolation (Cubic): Example Part 2
- 20. Linear Spline Interpolation: Theory
- 21. Linear Spline Interpolation: Example
- 22. Quadratic Spline Theory: Part 1
- 23. Quadratic Spline Theory: Part 2
- 24. Quadratic Spline Interpolation: Example: Part 1
- 25. Quadratic Spline Interpolation: Example: Part 2

## Numerical Methods IV

### 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 IV covers interpolation using the Direct method, Newton divided difference method, Lagrange method and Spline interpolation.
*Numerical Methods - Interpolation*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 5**

Author: Autar Kaw et al.

Publisher: http://www.autarkaw.com

Published: May 4, 2010

ISBN: 978-0-578-05765-1

### Course Material

1.**What is Interpolation?**

2.

**History of Interpolation**

3.

**Test Your Knowledge on Background of Interpolation**

4.

**Physical Problem**

Find the thermal expansion coefficient of steel at a specific temperature to find out whether a steel shaft will cool down enough to shrink fit into a hollow hub. The thermal expansion coefficient is to be found by using interpolation from a given table of thermal expansion coefficient of steel as a function of temperature.

5.

**The Lurking Dangers of Extrapolation!**

6.

**Why is Higher Order Interpolation a Bad Idea?**

7.

**Comparison of Spline and Polynomial Interpolation**

8.

**How Choice of Points of Interpolation Affects Approximations!**

9.

**How Splines Can Help in Developing a Shorter Path for a Robot**

10.

**Historical Notes - Runge**

11.

**Historical Notes - Newton**

12.

**Historical Notes - Lagrange**

13.

**Examples on Direct Method of Interpolation**

Chemical Engineering

Civil Engineering

Computer Engineering

Electrical Engineering

Industrial Engineering

Mechanical Engineering

14.

**Examples on Newton's Divided Difference Polynomial Method**

Chemical Engineering

Civil Engineering

Computer Engineering

Electrical Engineering

Industrial Engineering

Mechanical Engineering

15.

**Examples on Lagrange Method of Interpolation**

Chemical Engineering

Civil Engineering

Computer Engineering

Electrical Engineering

Industrial Engineering

Mechanical Engineering

16.

**Examples on the Spline Method of Interpolation**

Chemical Engineering

Civil Engineering

Computer Engineering

Electrical Engineering

Industrial Engineering

Mechanical Engineering

17.

**Sample Tests**

Direct Method of Interpolation

Newton's Divided Difference Polynomial Method

Lagrange Method

Spline Method of Interpolation