書籍基本資料
ISBN: 978-0691-150390 / US$99.50 / 1056頁 / 精裝 / 160 line
illus. 8x10 inc.
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：
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2. 下載訂購單，填寫後請Email至bknortonbknorton@gmail.com，或bknorton@bookman.com.tw
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
