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## Numerical Methods IV

### Course Summary

This course is based on Numerical Methods - Interpolation 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 IV covers interpolation using the Direct method, Newton divided difference method, Lagrange method and Spline interpolation.

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

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