This book is a translation and extension of the German version “Mathematica in der Theoretischen Physik” (1993; Zbl 0787.65089). The author demonstrates applications of the computer-algebra-system Mathematica, which is suitable for symbolic and numerical calculations as well as for graphical processing, to many problems from Theoretical Physics. After an extended introduction into Mathematica, examples from classical mechanics, electro-dynamics, quantum mechanics, nonlinear dynamics, general relativity, and the theory of fractals are treated. Compared with the German version, this book contains several new sections and examples including an extension of the dynamical formulation of classical mechanics by the Lagrange formalism (applied to rigid body motion and various types of pendula), and a discussion of Einstein’s field equations and the Schwarzschild solution.
It is shown how Mathematica can be used to support (resp. to replace) many of the “by-hand”-calculations which otherwise are usual in these fields, and to study the results instantaneously by means of graphical representations. In particular, advantage is taken of many functions (e.g., elliptic functions, Bessel functions, hypergeometric functions, spherical harmonics, Legendre-, Laguerre-, Hermite-polynomials) and operations (e.g., differentiation, symbolic and numerical integration, series expansion, root finding, Fourier transformation, geometric operations) which are available in Mathematica.
The book contains many sample programs, in written form in the text as well as on an attached disk.