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