Lectures (Video)

- 1. Background of Bisection Method
- 2. Algorithm of Bisection Method
- 3. Example of Bisection Method
- 4. Advantages & Drawbacks of Bisection Method
- 5. Derivation of Newton-Raphson Method
- 6. Example for Newton-Raphson Method
- 7. Advantages & Drawbacks for Newton-Raphson Method: Part 1
- 8. Advantages & Drawbacks for Newton-Raphson Method: Part 2
- 9. Derivation from Taylor Series of Newton-Raphson Method
- 10. No Divide Unit: Newton Raphson Approach
- 11. No Divide Unit: Example
- 12. Square Root of Number: Newton-Raphson Approach
- 13. Square Root of Number: Example
- 14. Derivation of Secant Method: Approach 1
- 15. Derivation of Secant Method: Approach 2
- 16. Algorithm of Secant Method
- 17. Example of Secant Method

## Numerical Methods II

### 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 II covers the numerical methods for solving nonlinear equations including the bisection method, newton-raphson method and the secant method.
*Numerical Methods - Nonlinear Equations*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 3**

Author: Autar Kaw et al.

Publisher: http://www.autarkaw.com

Published: May 4, 2010

ISBN: 978-0-578-05765-1

### Course Material

1.**Get Acquainted with Solving Quadratic Equations**

2.

**On Solving a Cubic Equation Exactly**

3.

**Test your Knowledge on Background of Nonlinear Equations**

4.

**Physical Problem**

To shrink fit a cylinder into a hollow hub, the cylinder needs to be cooled down. To find out how much cooling needs to be done, you need to solve a nonlinear equation.

5.

**Historical Background - Newton**

6.

**Historical Background - Raphson**

7.

**Historical Background - Galois**