· 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.