Course Contents :
Survey of capabilities. Interacting with front end, Help and documentation. Core Language: Expressions, Rules, Procedural programming, Lists, Variables and Functions, String Manipulations, External operations. Mathematical Functions, Mathematical Data, Visualization and Graphics: Function Visualization, Data Visualization, 2D, 3D, Parametric visualization as well as animation. Core Mathematics: Calculus, Polynomial algebra, Numbers and Precision, Equation solving, Optimization; Linear Algebra, Fourier, Complex Analysis; Probability and Statistics; Generating probability distributions, Curve fitting. Open source wares such as Scilab, Sage, Python. Throughout the Sessions the following topics will be emphasized as examples: (1) Ordinary Differential Equations (Motion of a particle in a prescribed potential, phase space) (2) Solving Systems of Equations (linear systems, matrix methods, nonlinear systems), (3) Analysis of Data (curve fitting, spectral analysis), (4) Partial Differential Equations (wave and diffusion equations, Schrodinger equation). (5) Special Functions: Gamma, Erf, Bessel and Elliptic functions and integrals, Dirac delta. Various orthogonal polynomials. (6) Stochastic Methods (random number generators, kinetic theory, random walks).
1. S. Wolfram, The Mathematica book (5th ed.). Champaign, IL: Wolfram Research (2003). 2. T. Davis, K. Sigmon, MATLAB primer (7th ed.). Chapman and Hall/CRC.Boca Raton, FL, (2004). 3. R. L. Zimmerman, F. I. Olness, Mathematica for Physics (2nd Ed.) Addison Wesley (2002). 4. A. Gilat, MATLAB: An introduction with applications (3rd Ed.) Wiley, Hoboken, NJ (2007). 5. M. Lutz, Learning Python, (5th Ed.) O'Reilly, CA (2013).