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 TOCNarrow_1.png
  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
  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
Created with the Wolfram Language