Computational Physics is consisted on techniques to approximate mathematical procedures (e.g., integrals). Approximations are needed because we either cannot solve the procedure analytically (e.g., the standard normal cumulative distribution function) or because the analytical method is intractable (e.g., solving a set of a thousand simultaneous linear equations for a thousand unknowns).  By end of this course, participants will be able to apply the Computational Physics for the following mathematical procedures and topics: differentiation, nonlinear equations, and simultaneous linear equations, interpolation, regression, integration, and ordinary differential equations. Additionally, they will be able to calculate errors and implement their relationship to the accuracy of the numerical solutions. 

PRE-REQUISITES

To be prepared for this course, students should have a passing grade in introductory physics, integral calculus, differential calculus, and ordinary differential equations.

Contents

1. Basics of Numerical Computation

2. Principles of Computer Operations

3. Roots of Equations (Real roots by Iterative method, Newton Raphson method, Regula Falsi method,Bisection method)

4. Numerical Integration (Trapezoidal method, Simpson’s method and Gauss Quadrature method)

5. Numerical Solutions of ODEs (Euler’s method, Modified Euler’s method, RK4 method)

6. Interpolation and Extrapolation (Finite Difference, Newton Forward Difference method, Newton Backward Difference method, Difference Operators, Linear Interpolation, Interpolating

Polynomials, the Lagrange Interpolating Polynomial)

7.  starting with MALAB® (Complete Book Chapters mentioned in serial no. 8 to 14)

8. Creating Arrays and Mathematical Operations with Arrays

9. Using Script Files and Managing Data

10. Implementation of Numerical Analysis in MATLAB®

11. Two Dimensional and Three Dimensional Plots

12. User Defined Functions and function Files

13. Symbolic Math

14. Modeling and Simulations

15. Case Study

Recommended Books

1. Introduction to Numerical Methods by Peter A. Sark, The Macmillan Company, Collier-Macmillan Limited, London (1970)

2. MATLAB® An Introduction with Applications by Amos Gilat, John Wiley and Sons, Inc. (2011)

Suggested Books

3. Introduction to Computational Physics by M. L. Jong, Addison Wesley Publishing Company

    Inc., Massachusetts (1991)

4. Introduction to Numerical Methods by Peter A. Sark, The Macmillan Company, Collier-

Macmillan Limited, London (1970)

3.Computational Techniques in Physics by P. K. Macheown & D. J. Merman, Adm Hilger,

Bristol (1987)