普林斯頓大學出版社--The Princeton Companion to Applied Mathematics (早鳥價)

The Princeton Companion to Applied Mathematics

書籍基本資料

ISBN: 978-0691-150390 / US$99.50 / 1056頁 / 精裝 / 160 line illus. 8x10 inc.

出版社參考頁面：http://press.princeton.edu/titles/10592.html

定價：台幣3500元 / 特價：2800元 (不含編目加工費)

優惠截止日：2015年9月30日

預計出貨日：2015年10月20日

訂購方式：

1.      Google表單連結直接訂購：http://goo.gl/forms/6ZMnhzADPj
2.      下載訂購單，填寫後請Email至bknortonbknorton@gmail.com，或bknorton@bookman.com.tw

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書籍簡介

本書是普林斯頓大學出版社繼2008年Gowers主編的Princeton Companion to Mathematics 之後又一重要的數學參考書，以應用數學為工具，幫助解決在科學、工程與產業上的問題，也應用在各研究領域，如：生物或經濟。

本書按主題分類，提供近200詞條，以簡明易懂的方式書寫，涵蓋應數的關鍵概念與專門詞彙、公式、定律及功能、應數的主要分支，並精選數學模型來解釋其來龍去脈，提供樣本問題以及應數和其他學科的關聯，書籍的最後部份，提供各種觀點幫助學生精進數學書寫與研究方法。

本書由世界各地知名學者所組成的團隊編寫而成，納入延伸閱讀的書目、交互參照以及完整的索引，詳細目次如下：

Contents

Preface ix

Contributors xi

Part I Introduction to Applied Mathematics

I.1 What Is Applied Mathematics? 1

I.2 The Language of Applied Mathematics 8

I.3 Methods of Solution 27

I.4 Algorithms 40

I.5 Goals of Applied Mathematical Research 49

I.6 The History of Applied Mathematics 55

Part II Concepts

II.1 Asymptotics 79

II.2 Boundary Layer 80

II.3 Chaos and Ergodicity 80

II.4 Complex Systems 81

II.5 Conformal Mapping 82

II.6 Conservation Laws 84

II.7 Control 86

II.8 Convexity 87

II.9 Dimensional Analysis and Scaling 88

II.10 The Fast Fourier Transform 92

II.11 Finite Differences 93

II.12 The Finite-Element Method 94

II.13 Floating-Point Arithmetic 94

II.14 Functions of Matrices 95

II.15 Function Spaces 97

II.16 Graph Theory 99

II.17 Homogenization 102

II.18 Hybrid Systems 103

II.19 Integral Transforms and Convolution 104

II.20 Interval Analysis 104

II.21 Invariants and Conservation Laws 106

II.22 The Jordan Canonical Form 111

II.23 Krylov Subspaces 113

II.24 The Level Set Method 114

II.25 Markov Chains 116

II.26 Model Reduction 117

II.27 Multiscale Modeling 119

II.28 Nonlinear Equations and Newton’s Method 120

II.29 Orthogonal Polynomials 122

II.30 Shocks 122

II.31 Singularities 124

II.32 The Singular Value Decomposition 125

II.33 Tensors and Manifolds 127

II.34 Uncertainty Quantification 130

II.35 Variational Principle 133

II.36 Wave Phenomena 133

Part III Equations, Laws, and Functions of Applied Mathematics

III.1 Benford’s Law 135

III.2 Bessel Functions 137

III.3 The Black–Scholes Equation 137

III.4 The Burgers Equation 138

III.5 The Cahn–Hilliard Equation 138

III.6 The Cauchy–Riemann Equations 139

III.7 The Delta Function and Generalized Functions 139

III.8 The Diffusion Equation 142

III.9 The Dirac Equation 142

III.10 Einstein’s Field Equations 144

III.11 The Euler Equations 146

III.12 The Euler–Lagrange Equations 147

III.13 The Gamma Function 148

III.14 The Ginzburg–Landau Equation 148

III.15 Hooke’s Law 149

III.16 The Korteweg–de Vries Equation 150

III.17 The Lambert W Function 152

III.18 Laplace’s Equation 155

III.19 The Logistic Equation 157

III.20 The Lorenz Equations 158

III.21 Mathieu Functions 160

III.22 Maxwell’s Equations 161

III.23 The Navier–Stokes Equations 162

III.24 The Painlevé Equations 163

III.25 The Riccati Equation 165

III.26 Schrödinger’s Equation 167

III.27 The Shallow-Water Equations 167

III.28 The Sylvester and Lyapunov Equations 168

III.29 The Thin-Film Equation 169

III.30 The Tricomi Equation 170

III.31 The Wave Equation 171

Part IV Areas of Applied Mathematics

IV.1 Complex Analysis 173

IV.2 Ordinary Differential Equations 181

IV.3 Partial Differential Equations 190

IV.4 Integral Equations 200

IV.5 Perturbation Theory and Asymptotics 208

IV.6 Calculus of Variations 218

IV.7 Special Functions 227

IV.8 Spectral Theory 236

IV.9 Approximation Theory 248

IV.10 Numerical Linear Algebra and Matrix Analysis 262

IV.11 Continuous Optimization (Nonlinear and

Linear Programming) 281

IV.12 Numerical Solution of Ordinary Differential Equations 293

IV.13 Numerical Solution of Partial Differential Equations 305

IV.14 Applications of Stochastic Analysis 319

IV.15 Inverse Problems 326

IV.16 Computational Science 335

IV.17 Data Mining and Analysis 350

IV.18 Network Analysis 360

IV.19 Classical Mechanics 374

IV.20 Dynamical Systems 383

IV.21 Bifurcation Theory 393

IV.22 Symmetry in Applied Mathematics 402

IV.23 Kinetic Theory 411

IV.24 Continuum Mechanics 428

IV.25 Pattern Formation 441

IV.26 Fluid Dynamics 449

IV.27 Magnetohydrodynamics 458

IV.28 Earth System Dynamics 467

IV.29 Effective Medium Theories 483

IV.30 Mechanics of Solids 487

IV.31 Soft Matter 498

IV.32 Control Theory 505

IV.33 Signal Processing 515

IV.34 Applied Combinatorics and Graph Theory 527

IV.35 Combinatorial Optimization 539

IV.36 Algebraic Geometry 545

IV.37 Information Theory 554

IV.38 General Relativity and Cosmology 561

IV.39 Quantum Mechanics 573

IV.40 Random-Matrix Theory 581

Part V Modeling

V.1 The Mathematics of Adaptation (Or the Ten Avatars of Vishnu) 591

V.2 Sport 597

V.3 Inerters 604

V.4 Mathematical Biomechanics 609

V.5 Mathematical Physiology 616

V.6 Cardiac Modeling 623

V.7 Chemical Reactions 627

V.8 Divergent Series: Taming the Tails 634

V.9 Financial Mathematics 640

V.10 Portfolio Theory 648

V.11 Bayesian Inference in Applied Mathematics 658

V.12 A Symmetric Framework with Many Applications 661

V.13 Granular Flows 665

V.14 Modern Optics 673

V.15 Numerical Relativity 680

V.16 The Spread of Infectious Diseases 687

V.17 The Mathematics of Sea Ice 695

V.18 Numerical Weather Prediction 707

V.19 Tsunami Modeling 714

V.20 Shock Waves 722

V.21 Turbulence 726

Part VI Example Problems

VI.1 Cloaking 735

VI.2 Bubbles 737

VI.3 Foams 739

VI.4 Inverted Pendulums 743

VI.5 Insect Flight 745

VI.6 The Flight of a Golf Ball 748

VI.7 Automatic Differentiation 752

VI.8 Knotting and Linking of Macromolecules 754

VI.9 Ranking Web Pages 757

VI.10 Searching a Graph 759

VI.11 Evaluating Elementary Functions 761

VI.12 Random Number Generation 763

VI.13 Optimal Sensor Location in the Control of

Energy-Efficient Buildings 765

VI.14 Robotics 769

VI.15 Slipping, Sliding, Rattling, and Impact:

Nonsmooth Dynamics and Its Applications 772

VI.16 From the N-Body Problem to Astronomy and Dark Matter 774

VI.17 The N-Body Problem and the Fast Multipole Method 777

VI.18 The Traveling Salesman Problem 781

Part VII Application Areas

VII.1 Aircraft Noise 785

VII.2 A Hybrid Symbolic–Numeric Approach to

Geometry Processing and Modeling 789

VII.3 Computer-Aided Proofs via Interval Analysis 792

VII.4 Applications of Max-Plus Algebra 797

VII.5 Evolving Social Networks, Attitudes, and Beliefs—and Counterterrorism 802

VII.6 Chip Design 806

VII.7 Color Spaces and Digital Imaging 810

VII.8 Mathematical Image Processing 816

VII.9 Medical Imaging 819

VII.10 Compressed Sensing 826

VII.11 Programming Languages: An Applied Mathematics View 831

VII.12 High-Performance Computing 842

VII.13 Visualization 846

VII.14 Electronic Structure Calculations (Solid State Physics) 852

VII.15 Flame Propagation 856

VII.16 Imaging the Earth Using Green’s Theorem 861

VII.17 Radar Imaging 865

VII.18 Modeling a Pregnancy Testing Kit 869

VII.19 Airport Baggage Screening with X-Ray Tomography 871

VII.20 Mathematical Economics 873

VII.21 Mathematical Neuroscience 878

VII.22 Systems Biology 884

VII.23 Communication Networks 888

VII.24 Text Mining 892

VII.25 Voting Systems 896

Part VIII Final Perspectives

VIII.1 Mathematical Writing 901

VIII.2 How to Read and Understand a Paper 907

VIII.3 How to Write a General Interest Mathematics Book 910

VIII.4 Workflow 916

VIII.5 Reproducible Research in the Mathematical Sciences 920

VIII.6 Experimental Applied Mathematics 929

VIII.7 Teaching Applied Mathematics 937

VIII.8 Mathematics Media:

Representations of Mathematics in Popular Culture and Why These Matter 947

VIII.9 Mathematics and Policy 956

Index 967