The basics of computer algebra and the language of Mathematica are described. This title will lead toward an understanding of Mathematica that allows the reader to solve problems in physics, mathematics, and chemistry. Mathematica is the most widely used system for doing mathematical calculations by computer, including symbolic and numeric calculations and graphics. It is used in physics and other branches of science, in mathematics, education and many other areas. Many important results in physics would never be obtained without a wide use of computer algebra.
Author(s): Andrey Grozin (auth.)
Series: Graduate Texts in Physics
Edition: 1
Publisher: Springer International Publishing
Year: 2014
Language: English
Pages: 219
Tags: Numerical and Computational Physics;Computer Applications in Chemistry;Particle and Nuclear Physics;Mathematical Applications in the Physical Sciences
Front Matter....Pages i-x
Front Matter....Pages 1-1
Computer Algebra Systems....Pages 3-7
Overview of Mathematica ....Pages 9-19
Expressions....Pages 21-26
Patterns and Substitutions....Pages 27-33
Functions....Pages 35-42
Mathematica as a Programming Language....Pages 43-53
Gröbner Bases....Pages 55-62
Calculus....Pages 63-71
Numerical Calculations....Pages 73-78
Risch Algorithm....Pages 79-90
Linear Algebra....Pages 91-98
Input–Output and Strings....Pages 99-104
Packages....Pages 105-108
Front Matter....Pages 109-109
Plots....Pages 111-123
Trigonometric Functions....Pages 125-126
Quantum Oscillator....Pages 127-132
Spherical Harmonics....Pages 133-137
Adding Angular Momenta in Quantum Mechanics....Pages 139-143
Classical Nonlinear Oscillator....Pages 145-151
Quantum Nonlinear Oscillator....Pages 153-160
Front Matter....Pages 109-109
Riemann Curvature Tensor....Pages 161-163
Multi- ζ Functions....Pages 165-171
Rainbow....Pages 173-191
Cyclohexane....Pages 193-208
Problems for Students....Pages 209-211
Back Matter....Pages 213-219
