Table of Contents
| MathematicaHandbook Table of Contents |
|
| Mathematica Usage Tutorials | |
| Intro to Mathematica 1 | Basic syntax, intro to replacement rules and functions |
| Intro to Mathematica 2 | Plotting,DEs,multi-line functions |
| Vectors & Integrals | Operations on vectors, multiple integrals, 3D graphics |
| Basic Numerical Functions | FindRoot,NSolve, LinearSolve, NIntegrate, etc. |
| Pattern Matching | x_, Map, pure functions Thread, Head, Apply, etc. |
| Input & Output | Importing and Exporting spreadsheets, graphics, etc. Using Wolfram curated data e.g. FinancialData |
| Images, Text & Sound | Image processing; string functions; working with .wav files, etc |
| Plotting& Graphics Examples | Many examples of 2D and 3D graphics, animations, etc. |
| Complex Variables | |
| Complex Arithmetic | Re<>Im, Arg, ComplexExpand, complex roots and functions |
| Complex Analysis | Residue, Cauchy-Riemann conditions, residue theorem |
| Topics in Complex Variables | Riemann surfaces, Argument principle, conformal mapping |
| Linear Algebra | |
| Solving Linear Equations | Under- and over determined systems, NullSpace, PseudoInverse |
| Determinants | Properties of determinants, minors, Wronskian, Cramer's rule |
| Transformations and Eigenvalues | Quadratic forms, ellipsoids, diagonalization, variational theorems non orthogonal bases, covariant and contravariant components |
| Cartesian Tensors | Tensor algebra; tensors as multilinear functions; transformation laws; Levi-Civita |
| Singular Values | SingularValueDecomposition theory and examples |
| Vector Analysis | |
| Cartesin Vector Analysis | |
| Non-Cartesian Vector Analysis | ∇ in polar, spherical, cylindrical coordinates |
| DiracDelta & Generalized functions | DiracDelta, UnitStep, multidimensional δ, series for δ |
| Ordinary Differential equations | |
| Analytic Solutions | First order DEs, constant coefficient systems, MatExp |
| Series and Special Functions | Regular and irregular singular points, Frobenius solutions Hermite, Legendre, Bessel, Hypergeometric functions |
| Greens Functions | Initial value problems; boundary value problems |
| Numerical Solutions & Nonlinear DEs | NDSolve phase space, spontaneous singularities |
| Boundary value problems | NDSolve, shooting method, eigenvalue problems, finite difference method |
| Partial Differential equations | |
| Derivation of equations | physically motivated derivation of Laplace, Diffusion, wave eq. |
| Separation of Variables | orthogonal functions for solutions of the standard equations of mathematical physics |
| Laplace Equation | |
| Diffusion Equation | |
| Wave Equation | |
| Series Solutions | |
| Cartesian BVP | Typical problems involving Fourier series |
| Cylindrical BVP | Typical problems involving Bessel function expansions |
| Spherical BVP | Typical problems involving expansions in Spherical harmonics |
| Numerical Solutions | Use of NDSolve for PDEs and finite difference numerical solutions |
| Finite Elements | mesh generation, weak solutions, numerical method for solutions for nonseparable problems |
| Point Source Solutions | Greens function for Laplace, Heat, Wave, equations |
| Fourier Series and Transforms | Fourier Series , transforms, and expansions in orthogonal functions |
| Lagrange Multipliers | Analytic and numerical constrained optimization, NMinimize |
| Calculus of Variations | Examples from mechanics, EulerEquations, FirstIntegrals |
| Asymtotic Analysis | Evaluating integrals using stationary phase, steepest decent, WKB |
| Perturbation Theory | ε expansion solutions for algebraic & differential equations |
| Dimensional Analysis | Units and PhysicalConstants packages, ReduceUnits, dimanal |
| Probability& Statistics | |
| Elementary Probability | Random variables, distribution functions, expectation values |
| Maximum Likelihood | Linear and nonlinear regression, confidence intervals |
| Utilities | Packages for working with DEs, dimensional analysis, etc. |
| Special Function Facts | Important properties of Bessel, Legendre, Laguerre , etc. |
| Applications & Case Studies | |
| Circuits | Review of elementary circuits, impedance, LRC circuits, switches |
| Normal Modes | Animations of blocks on springs, density of states, linearization |
| Fresnel Equations | Reflection and refraction of a vector wave at an interface |
| Wave Guides | Electromagnetic waves confined by conductors and dielectrics |
| Thermodynamic Derivatives | Symbolic calculations of thermodynamic derivatives |
| Fluid Mechanics | Navier-Stokes equation, vector Laplacian, vorticity |
| Multipole Expansions | Far field solutions to Laplace equation using cartesian tensors and spherical harmonics |
| Numerical Integration | Accuracy, Precision, MonteCarlo integration |
| Digital Sampling | Digital scope simulator, aliasing, Nyquist critical frequency |
| N Body Simulation | Simulating a gas of hard spheres; animations |
| Quantum Square well | Bound states of a 1D potential well |
| Quantum Harmonic Oscilator | Solution of quantum oscillator problem using series and DSolve |
| Hydrogen Atom | Schrödinger equation for hydrogenic atom; 3D graphics |
| Puzzles | |
| Who owns the zebra? | A logic puzzle |
| Sudoku | A number puzzle |
| Packages&Guides | a listing of standard packages and guides available in Version 10.0 documentation |
| References | |
| Index | |