The Princeton Companion to Applied Mathematics
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:
$186.50

Unlimited-User Purchase Price:
$279.75
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.
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