MathematicaHandbook
Table of Contents

Preface
TOC
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.
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
Linear Algebra
Solving Linear equations Under- and over determined systems, NullSpace, PseudoInverse
Geometry of Eigenvalues Quadratic forms, ellipsoids,  variational theorems
Singular Values SingularValueDecomposition  theory and examples
Vector Analysis                  Vector calculus in 2 & 3D; Grad, Curl,
DiracDelta & Generalized Functions DiracDelta, UnitStep
Ordinary Differential equations
Analytic Solutions First order DEs,  constant coefficient systems, MatExp
Series Solutions and Special Regular and irregular singular points, Frobenius solutions
Functions Hermite, Legendre, Bessel, Hypergeometric functions        
Greens Functions
Initial Value Problems and Impulse Response
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
Separation of Variables orthogonal functions for solutions of φ=0 in
cartesian, spherical and cylindrical coordinates
Cartesian BVP Fourier series and finite difference numerical solutions
Cylindrical BVP Typical problems involving Bessel function expansions
Spherical BVP Typical problems involving expansions in Spherical harmonics
Point Source Solutions Greens function for Laplace, Heat, Wave,  equations
Fourier Series & 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
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
Thermodynamic derivatives Symbolic calculations of thermodynamic derivatives
Fluid Mechanics  Navier-Stokes equation, vector Laplacian, vorticity
Numerical Integration Accuracy, Precision, MonteCarlo integration
Digital Sampling  Digital scope simulator, aliasing, Nyquist critical frequency
    Quantum Square Well
    Quatum Harmonic Oscillator
Who Owns the Zebra? A logic puzzle
References
Index

---

Created by Mathematica  (May 28, 2006)