The Princeton companion to applied mathematics

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Cover; Title; Copyright; Contents; Preface; Contributors; Part I Introduction to Applied Mathematics; I.1 What Is Applied Mathematics?; I.2 The Language of Applied Mathematics; I.3 Methods of Solution; I.4 Algorithms; I.5 Goals of Applied Mathematical Research; I.6 The History of Applied Mathematics; Part II Concepts; II. 1 Asymptotics; II. 2 Boundary Layer; II. 3 Chaos and Ergodicity; II. 4 Complex Systems; II. 5 Conformal Mapping; II. 6 Conservation Laws; II. 7 Control; II. 8 Convexity; II. 9 Dimensional Analysis and Scaling; II. 10 The Fast Fourier Transform; II. 11 Finite Differences. II. 12 The Finite-Element MethodII. 13 Floating-Point Arithmetic; II. 14 Functions of Matrices; II. 15 Function Spaces; II. 16 Graph Theory; II. 17 Homogenization; II. 18 Hybrid Systems; II. 19 Integral Transforms and Convolution; II. 20 Interval Analysis; II. 21 Invariants and Conservation Laws; II. 22 The Jordan Canonical Form; II. 23 Krylov Subspaces; II. 24 The Level Set Method; II. 25 Markov Chains; II. 26 Model Reduction; II. 27 Multiscale Modeling; II. 28 Nonlinear Equations and Newton's Method; II. 29 Orthogonal Polynomials; II. 30 Shocks; II. 31 Singularities; II. 32 The Singular Value Decomposition. II. 33 Tensors and ManifoldsII. 34 Uncertainty Quantification; II. 35 Variational Principle; II. 36 Wave Phenomena; Part III Equations, Laws, and Functions of Applied Mathematics; III. 1 Benford's Law; III. 2 Bessel Functions; III. 3 The Black-Scholes Equation; III. 4 The Burgers Equation; III. 5 The Cahn-Hilliard Equation; III. 6 The Cauchy-Riemann Equations; III. 7 The Delta Function and Generalized Functions; III. 8 The Diffusion Equation; III. 9 The Dirac Equation; III. 10 Einstein's Field Equations; III. 11 The Euler Equations; III. 12 The Euler-Lagrange Equations; III. 13 The Gamma Function. III. 14 The Ginzburg-Landau EquationIII. 15 Hooke's Law; III. 16 The Korteweg-de Vries Equation; III. 17 The Lambert W Function; III. 18 Laplace's Equation; III. 19 The Logistic Equation; III. 20 The Lorenz Equations; III. 21 Mathieu Functions; III. 22 Maxwell's Equations; III. 23 The Navier-Stokes Equations; III. 24 The Painlevé Equations; III. 25 The Riccati Equation; III. 26 Schrödinger's Equation; III. 27 The Shallow-Water Equations; III. 28 The Sylvester and Lyapunov Equations; III. 29 The Thin-Film Equation; III. 30 The Tricomi Equation; III. 31 The Wave Equation; Part IV Areas of Applied Mathematics. IV. 1 Complex AnalysisIV. 2 Ordinary Differential Equations; IV. 3 Partial Differential Equations; IV. 4 Integral Equations; IV. 5 Perturbation Theory and Asymptotics; IV. 6 Calculus of Variations; IV. 7 Special Functions; IV. 8 Spectral Theory; IV. 9 Approximation Theory; IV. 10 Numerical Linear Algebra and Matrix Analysis; IV. 11 Continuous Optimization (Nonlinear and Linear Programming); IV. 12 Numerical Solution of Ordinary Differential Equations; IV. 13 Numerical Solution of Partial Differential Equations; IV. 14 Applications of Stochastic Analysis; IV. 15 Inverse Problems; IV. 16 Computational Science