(Physics P9)

The course is intended as an introduction to computers and computational methods in physics. No previous experience with computers is required, although it will be useful. The course is primarily targeted towards second year undergraduate physics students. It is assumed that the standard P5 sequence of classes has either been taken, or is in the process of being completed. Topics to be covered in class will include:

· Why Mathematica? Starting Mathematica. Textual and notebook interfaces. Menus. Online help. The kernel. Overview and brief Mathematica Tour.

· Arithmetic. Exact and numerical representation of numbers. Arbitrary precision, indeterminate and infinite numbers. Pseudo-random numbers. Transcendental and complex numbers. Elementary mathematical functions. Variables. Trigonometric expressions. Complex expansion. Lists and their manipulation.

· Input. Notebooks. Loading packages. Error Messages. Aborting a calculation. Symbolic computation. Transforming and simplifying algebraic expressions.

· Solving algebraic equations. Elimination. Differentiation. Integration. Summation. Limits. Taylor series. Operations on series. Differential equations. Vector analysis.

· Numerical solution of equations. Root finding. Numerical integration. Multidimensional integrals. Numerical solution of ordinary differential equations. Accuracy of solutions. Minima and Maxima. Curve fitting.

· Defining functions. Repeated operations. Lists, tables and their manipulation. Vectors, Matrices and common operations.

· Graphics. 2-d function plots. Useful options. List plots. Contour and density plots. 3-d surface plots. Parametric plots. Displaying vector fields. Reading and writing data files. Generating fortran code.

· Physics Applications. Pendulum motion. Forced Oscillator. Solution and graphing of the Kepler problem. Illustration of Precession. Henon-Heiles system and chaotic motion. Study of the Lorentz system. Generation and display of electric force fields.

Recommended Books:

Mathematica, by S. Wolfram (Addison Wesley, 1974).

Herbert W. Hamber, PSII 3172 (x5596).