Handbook of applied mathematics: Selected results and methods
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York
Van Nostrand Reinhold
1983
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 1265 S. |
| ISBN: | 0442238665 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
1 Formulas from Algebra, Trigonometry and Analytic Geometry 1
H. Lennart Pearson
1.1 The Real Number System 1
1.2 The Complex Number System 2
1.3 Inequalities 5
1.4 Powers and Logarithms 5
1.5 Polynomial Equations 9
1.6 Rational Functions and Partial Fractions 15
1.7 Determinants and Solution of Systems of Linear Equations 16
1.8 Progressions 21
1.9 Binomial Theorem, Permutations and Combinations 22
1.10 The Trigonometric Functions 23
1.11 Analytic Geometry of Two Space 40
1.12 Analytic Geometry of Three Space 58
1.13 References and Bibliography 81
2 Elements of Analysis 83
H. Lennart Pearson
2.1 Sequences 83
2.2 Infinite Series 85
2.3 Functions, Limits, Continuity 90
2.4 The Derivative 93
2.5 The Definite Integral 99
2.6 Methods of Integration 105
2.7 Improper Integrals 111
2.8 Partial Differentiation 115
2.9 Multiple Integrals 120
2.10 Infinite Products 126
2.11 Fourier Series 126
2.12 References and Bibliography 128
vii
viii Contents
3 Vector Analysis 129
Gordon C. Oates
3.0 Introduction 129
3.1 Coordinate Systems 129
3.2 Vector Algebra 135
3.3 Vector Calculus 141
3.4 Successive Operations 156
3.5 Vector Fields 162
3.6 Summary 165
3.7 Bibliography 178
4 Tensors 179
Bernard Budiansky
4.0 Introduction 179
4.1 Vectors in Euclidean 3 D 179
4.2 Tensors in Euclidean 3 D 184
4.3 General Curvilinear Coordinates in Euclidean 3 D 191
4.4 Tensor Calculus 194
4.5 Theory of Surfaces 201
4.6 Classical Interlude 213
4.7 An Application: Continuum Mechanics 218
4.8 Tensors in n Space 223
4.9 Bibliography 225
5 Functions of a Complex Variable 226
A. Richard Seebass
5.0 Introduction 226
5.1 Preliminaries 226
5.2 Analytic Functions 229
5.3 Singularities and Expansions 242
5.4 Residues and Contour Integrals 248
5.5 Harmonic Functions and Conformal Mapping 257
5.6 Acknowledgments 268
5.7 References and Bibliography 269
6 Ordinary Differential and Difference Equations 271
Edward R. Benton
6.0 Introduction 271
6.1 Basic Concepts 271
6.2 First Order Linear Differential Equations 279
Contents ix
6.3 Second Order Linear Differential Equations with Constant
Coefficients 283
6.4 Second Order Linear Differential Equations with Variable
Coefficients 290
6.5 Linear Equations of High Order and Systems of Equations 307
6.6 Eigenvalue Problems 315
6.7 Nonlinear Ordinary Differential Equations 323
6.8 Approximate Methods 327
6.9 Ordinary Difference Equations 336
6.10 References 342
7 Special Functions 344
Victor Barcilon
7.0 Introduction 344
7.1 Exponential Integral and Related Functions 346
7.2 Gamma Function and Related Functions 348
7.3 Error Function and Related Functions 351
7.4 Bessel Functions 353
7.5 Modified Bessel Functions 359
7.6 Orthogonal Polynomials 361
7.7 Hypergeometric Functions and Legendre Functions 369
7.8 Elliptic Integrals and Functions 372
7.9 Other Special Functions 375
7.10 References and Bibliography 377
8 First Order Partial Differential Equations 378
Jirair Kevorkian
8.0 Introduction 378
8.1 Examples of First Order Partial Differential Equations 379
8.2 Geometrical Concepts, Qualitative Results 386
8.3 Quasilinear Equations 400
8.4 Nonlinear Equations 422
8.5 References 447
9 Partial Differential Equations of Second and Higher Order 448
Carl E. Pearson
9.0 Survey of Contents 448
9.1 Derivation Examples ¦ 448
9.2 The Second Order Linear Equation in Two Independent Variables 453
9.3 More General Equations 459
9.4 Series Solutions 462
x Contents
9.5 Transform Methods 465
9.6 The Perturbation Idea 467
9.7 Change of Variable 469
9.8 Green s Function 473
9.9 Potential Theory 482
9.10 Eigenvalue Problems 484
9.11 Characteristics 486
9.12 Variational Methods 493
9.13 Numerical Techniques 496
9.14 References 509
10 Integral Equations 512
Donald F. Winter
10.1 Introduction 512
10.2 Definitions and Classifications 513
10.3 Origin of Integral Equations 519
10.4 Nonsingular Linear Integral Equations 527
10.5 Singular Linear Integral Equations 547
10.6 Approximate Solution of Integral Equations 558
10.7 Nonlinear Integral Equations 564
10.8 References 569
11 Transform Methods 571
Gordon E. Latta
11.0 Introduction 571
11.1 Fourier s Integral Formula 571
11.2 Laplace Transforms 578
11.3 Linearity, Superposition, Representation Formulas 585
11.4 The Wiener Hopf Technique 592
11.5 Abel s Integral Equation, Fractional Integrals, Weyl Transforms 601
11.6 Poisson s Formula, Summation of Series 606
11.7 Hilbert Transforms, Riemann Hilbert Problem 609
11.8 Finite Transforms 622
11.9 Asymptotic Results 624
11.10 Operational Formulas 625
11.11 References 630
12 Asymptotic Methods 631
Frank W. J. Olwer
12.1 Definitions 631
12.2 Integrals of a Real Variable 636
12.3 Contour Integrals 643
Contents xi
12.4 Further Methods for Integrals 648
12.5 Sums and Sequences 658
12.6 The Liouville Green (or JWKB) Approximation 667
12.7 Differential Equations with Irregular Singularities 675
12.8 Differential Equations with a Parameter 680
12.9 Estimation of Remainder Terms 691
12.10 References and Bibliography 695
13 Oscillations 697
Richard E. Kronauer
13.0 Introduction 697
13.1 Lagrange Equations 697
13.2 Conservative Linear Systems, Direct Coupled 700
13.3 Systems with Gyroscopic Coupling 709
13.4 Mathieu Hill Systems 712
13.5 Oscillations with Weak Nonlinearities 718
13.6 Oscillators Coupled by Weak Nonlinearity 732
13.7 References and Bibliography 745
14 Perturbation Methods 747
G. F. Carrier
14.1 Introduction 747
14.2 Perturbation Methods for Ordinary Differential Equations 748
14.3 Partial Differential Equations 756
14.4 Multiscaling Methods 764
14.5 Boundary Layers 780
14.6 Remarks 813
14.7 References 814
15 Wave Propagation 815
Wilbert Lick
15.0 Introduction 815
15.1 General Definitions and Classification of Waves 816
15.2 Physical Systems and Their Classification 821
15.3 Simple Waves: Nondispersive, Nondiffusive 829
15.4 Dispersive Waves 848
15.5 Diffusive Waves 862
15.6 References and Bibliography 875
I
xii Contents
16 Matrices and Linear Algebra 878
Tse Sun Chow
16.1 Preliminary Considerations 878
16.2 Determinants 882
16.3 Vector Spaces and Linear Transformation 885
16.4 Matrices 889
16.5 Linear System of Equations 892
16.6 Eigenvalues and the Jordan Normal Form 897
16.7 Estimates and Determination of Eigenvalues 906
16.8 Norms 908
16.9 Hermitian Forms and Matrices 911
16.10 Matrices with Real Elements 913
16.11 Generalized Inverse 916
16.12 Commuting Matrices 917
16.13 Compound Matrices 920
16.14 Handling Large Sparse Matrices 921
16.15 References 925
17 Functional Approximation 928
Robin Esch
17.0 Introduction 928
17.1 Norms and Related Measures of Error 931
17.2 Relationship between Approximation on a Continuum and
on a Discrete Point Set 935
17.3 Existence of Best Approximations 937
17.4 L2 or Least Mean Square Approximation 938
17.5 Theory of Chebyshev Approximation 950
17.6 Chebyshev Approximation Methods Based on Characterization
Properties 958
17.7 Use of Linear Programming in Chebyshev Approximation 967
17.8 Li Approximation 974
17.9 Piecewise Approximation without Continuity at the Joints 977
17.10 Approximation by Splines and Related Smooth Piecewise
Functions 981
17.11 References 985
18 Numerical Analysis 988
A. C. R. Newbery
18.0 Introduction 988
18.1 General Information on Error Analysis 988
18.2 Linear Equation Systems 992
18.3 Eigenvalue and Lambda Matrix Problems 999
18.4 Approximation and Interpolation 1003
18.5 Quadrature and Integral Equations 1015
i
Contents xiii
18.6 Ordinary Differential Equations 1022
18.7 Nonlinear Functions of One Variable 1027
18.8 Nonlinear Equation Systems and Optimization 1032
18.9 Miscellaneous Topics 1037
18.10 References and Bibliography 1040
19 Mathematical Models and Their Formulation 1044
Frederic Y. M. Wan
19.1 Mathematical Modeling 1044
19.2 Groping in the Dark 1049
19.3 From the Simple to the Elaborate 1060
19.4 Try a Different Formulation 1081
19.5 Linearize with Care 1102
19.6 Stepping Beyond Reality 1116
19.7 Why Reinvent the Wheel? 1123
19.8 Better Robust Than Realistic 1135
19.9 References 1136
20 Optimization Techniques 1140
Juris Vagners
20.1 Introduction 1140
20.2 Parameter Optimization 1147
20.3 Dynamic Optimization, Neccessary Conditions 1158
20.4 Extremal Fields, Sufficiency Conditions 1186
20.5 Computational Techniques 1196
20.6 Elements of Game Theory 1208
20.7 References 1213
21 Probability and Statistics 1217
L. Fisher
21.0 Introduction 1217
21.1 Probability Spaces 1217
21.2 Random Vectors and Random Variables 1220
21.3 Descriptive Statistics 1233
21.4 Statistical Inference 1233
21.5 The General Linear Model 1243
21.6 Some Other Techniques of Multivariate Analysis 1248
21.7 Parametric, Nonparametric, and Distribution Free
Statistical Tests 1253
21.8 Bayesian Statistics and Decision Theory 1262
21.9 Concluding Remarks 1269
21.10 References 1270
Index 1275
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| physical | XIII, 1265 S. |
| publishDate | 1983 |
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| spelling | Handbook of applied mathematics Selected results and methods Hrsg. von Carl E. Pearson* 2. ed. New York Van Nostrand Reinhold 1983 XIII, 1265 S. txt rdacontent n rdamedia nc rdacarrier Mathematik (DE-588)4037944-9 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 s DE-604 Mathematik (DE-588)4037944-9 s 1\p DE-604 Pearson, Carl E. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004003486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Handbook of applied mathematics Selected results and methods Mathematik (DE-588)4037944-9 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4142443-8 |
| title | Handbook of applied mathematics Selected results and methods |
| title_auth | Handbook of applied mathematics Selected results and methods |
| title_exact_search | Handbook of applied mathematics Selected results and methods |
| title_full | Handbook of applied mathematics Selected results and methods Hrsg. von Carl E. Pearson* |
| title_fullStr | Handbook of applied mathematics Selected results and methods Hrsg. von Carl E. Pearson* |
| title_full_unstemmed | Handbook of applied mathematics Selected results and methods Hrsg. von Carl E. Pearson* |
| title_short | Handbook of applied mathematics |
| title_sort | handbook of applied mathematics selected results and methods |
| title_sub | Selected results and methods |
| topic | Mathematik (DE-588)4037944-9 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| topic_facet | Mathematik Angewandte Mathematik |
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