Overview:
This book includes broadly expanded coverage of the original German-language version published by Springer-Verlag, with more than 100 pages of additional content material than in the original work. It includes many more examples, and these new topic sections below have been added to the six chapters which comprise this volume:
Classical mechanics: discrete systems, harmonic and anharmonic oscillators, linear and chaotic pendula, the two-body problem, the brachistochrone Electrodynamics: potential and electric fields of discrete charge distributions Quantum mechanics: the Schrödinger equation Nonlinear dynamics: the Korteweg-de Vries equation General relativity: orbits, Einstein's field equations, Schwarzschild metric, Reissner Nordstrom solution for a charged mass point Fractals: the Koch curve, multi-fractals, the renormalization group
In addition, Mathematica in Theoretical Physics includes an introduction to Mathematica that is specifically designed for physicists and engineers. There is also an introduction to programming in Mathematica. This expanded coverage strengthens the original work and provides increased accessibility to a wider readership.
A main aim of this book is to solve physical problems and deal with their underlying theoretical concepts, while using Mathematica to derive numeric and analytic solutions. Mathematica allows users to perform in-depth analysis of scientific computations and results. Containing a wide selection of examples, exercises and references, this text/reference shows readers how to use Mathematica as a problem-solving tool to assist students in better grasping theoretical physics, and to help researchers in their everyday work. It is intended for those working in all areas of physics, applied mathematics, and the other physical sciences. Only a basic understanding of theoretical concepts in physics is assumed. The appendices contain information on how to use the diskette, and a brief glossary of terms and functions.
Contents:
Preface
Chapter 1: Introduction
Basics, Structure of Mathematica, Symbolic calculations, Numerical calculations, Graphics, Interactive use of Mathematica
Chapter 2: Classical Mechanics
The Mechanics of discrete systems, Two coupled harmonic oscillators, The pendulum, The damped driven pendulum, Linear chain, The two-body problem, Vibrations of a membrane, Dynamical formulation, Exercises
Chapter 3: Electrodynamics
Potential and electric fields of discrete charge distributions, Boundary problem of electrostatics, Two ions in the Penning trap, The center of mass motion, Relative motion of the ions, Exercises
Chapter 4: Quantum mechanics
The Schrödinger equation, One dimensional potential, The harmonic oscillator, Anharmonic oscillator, Motion in the central force field, Exercises
Chapter 5: Nonlinear dynamics
The Korteweg-de Vries equation, Solution of the Korteweg-de Vries equation, Soliton solutions of the Korteweg-de Vries equation, Conservation laws of the Korteweg-de Vries equation, Derivation of conservation laws, Numerical solution of the Korteweg-de Vries equation, Exercises
Chapter 6: General Relativity
The orbits in general relativity, Quasi elliptic orbits, Asymptotic circles, Light bending in the gravitational field, Einstein's field equations (vacuum case), Examples for metric tensors, The Christoffel symbols, The Riemann tensor, Einstein's field equations, The Cartesian space, Cartesian space in cylindrical coordinates, Euclidean space in polar coordinates, The Schwarzschild solution, The Schwarzschild metric in Eddington-Finkelstein form, Dingle's metric, Schwarzschild metric in Kruskal coordinates, The Reissner-Nordstrom solution for a charged mass point, Exercises
Chapter 7: Fractals
Measuring a borderline, The Koch curve, Multi-fractals, Multi-fractals with common scaling factor, The renormalization group, Exercises,
Appendix
Program installation, Glossary of files and functions, Mathematica functions
References
Index
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