The Princeton Companion to Applied Mathematics

Editors: Dennis, Mark R., Glendinning, Paul and Martin, Paul A.
Publication Year: 2015
Publisher: Princeton University Press

Single-User Purchase Price: $99.50
Unlimited-User Purchase Price: $149.25
ISBN: 978-0-69-115039-0
Category: Mathematics & Statistics - Mathematics
Image Count: 410
Book Status: Available
Table of Contents

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more.

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Table of 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 Method
  • II.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 Manifolds
  • II.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 Equation
  • III.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 Analysis
  • IV.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
  • IV.17 Data Mining and Analysis
  • IV.18 Network Analysis
  • IV.19 Classical Mechanics
  • IV.20 Dynamical Systems
  • IV.21 Bifurcation Theory
  • IV.22 Symmetry in Applied Mathematics
  • IV.23 Quantum Mechanics
  • IV.24 Random-Matrix Theory
  • IV.25 Kinetic Theory
  • IV.26 Continuum Mechanics
  • IV.27 Pattern Formation
  • IV.28 Fluid Dynamics
  • IV.29 Magnetohydrodynamics
  • IV.30 Earth System Dynamics
  • IV.31 Effective Medium Theories
  • IV.32 Mechanics of Solids
  • IV.33 Soft Matter
  • IV.34 Control Theory
  • IV.35 Signal Processing
  • IV.36 Information Theory
  • IV.37 Applied Combinatorics and Graph Theory
  • IV.38 Combinatorial Optimization
  • IV.39 Algebraic Geometry
  • IV.40 General Relativity and Cosmology
  • Part V Modeling
  • V.1 The Mathematics of Adaptation (Or the Ten Avatars of Vishnu)
  • V.2 Sport
  • V.3 Inerters
  • V.4 Mathematical Biomechanics
  • V.5 Mathematical Physiology
  • V.6 Cardiac Modeling
  • V.7 Chemical Reactions
  • V.8 Divergent Series: Taming the Tails
  • V.9 Financial Mathematics
  • V.10 Portfolio Theory
  • V.11 Bayesian Inference in Applied Mathematics
  • V.12 A Symmetric Framework with Many Applications
  • V.13 Granular Flows
  • V.14 Modern Optics
  • V.15 Numerical Relativity
  • V.16 The Spread of Infectious Diseases
  • V.17 The Mathematics of Sea Ice
  • V.18 Numerical Weather Prediction
  • V.19 Tsunami Modeling
  • V.20 Shock waves
  • V.21 Turbulence
  • Part VI Example Problems
  • VI.1 Cloaking
  • VI.2 Bubbles
  • VI.3 Foams
  • VI.4 Inverted Pendulums
  • VI.5 Insect Flight
  • VI.6 The Flight of a Golf Ball
  • VI.7 Automatic Differentiation
  • VI.8 Knotting and Linking of Macromolecules
  • VI.9 Ranking Web Pages
  • VI.10 Searching a Graph
  • VI.11 Evaluating Elementary Functions
  • VI.12 Random Number Generation
  • VI.13 Optimal Sensor Location in the Control of Energy-Efficient Buildings
  • VI.14 Robotics
  • VI.15 Slipping, Sliding, Rattling, and Impact: Nonsmooth Dynamics and Its Applications
  • VI.16 From the N-Body Problem to Astronomy and Dark Matter
  • VI.17 The N-Body Problem and the Fast Multipole Method
  • VI.18 The Traveling Salesman Problem
  • Part VII Application Areas
  • VII.1 Aircraft Noise
  • VII.2 A Hybrid Symbolic-Numeric Approach to Geometry Processing and Modeling
  • VII.3 Computer-Aided Proofs via Interval Analysis
  • VII.4 Applications of Max-Plus Algebra
  • VII.5 Evolving Social Networks, Attitudes, and Beliefs—and Counterterrorism
  • VII.6 Chip Design
  • VII.7 Color Spaces and Digital Imaging
  • VII.8 Mathematical Image Processing
  • VII.9 Medical Imaging
  • VII.10 Compressed Sensing
  • VII.11 Programming Languages: An Applied Mathematics View
  • VII.12 High-Performance Computing
  • VII.13 Visualization
  • VII.14 Electronic Structure Calculations (Solid State Physics)
  • VII.15 Flame Propagation
  • VII.16 Imaging the Earth Using Green’s Theorem
  • VII.17 Radar Imaging
  • VII.18 Modeling a Pregnancy Testing Kit
  • VII.19 Airport Baggage Screening with X-Ray Tomography
  • VII.20 Mathematical Economics
  • VII.21 Mathematical Neuroscience
  • VII.22 Systems Biology
  • VII.23 Communication Networks
  • VII.24 Text Mining
  • VII.25 Voting Systems
  • Part VIII Final Perspectives
  • VIII.1 Mathematical Writing
  • VIII.2 How to Read and Understand a Paper
  • VIII.3 How to Write a General Interest Mathematics Book
  • VIII.4 Workflow
  • VIII.5 Reproducible Research in the Mathematical Sciences
  • VIII.6 Experimental Applied Mathematics
  • VIII.7 Teaching Applied Mathematics
  • VIII.8 Mediated Mathematics: Representations of Mathematics in Popular Culture and Why These Matter
  • VIII.9 Mathematics and Policy