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,multiline 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, CauchyRiemann 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; LeviCivita 
Singular Values  SingularValueDecomposition theory and examples 
Vector Analysis  
Cartesin Vector Analysis  
NonCartesian 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  NavierStokes 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 