Mathematics for scientists and engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Englewood Cliffs, NJ
Prentice Hall
1992
|
| Ausgabe: | 2. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 783 S. |
| ISBN: | 0135631564 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
PREFACE xi
CHAPTER 1 VECTOR ANALYSIS 1
1.1 Vector Arithmetic 1
1.2 Geometry of Lines and Planes 9
1.3 Non Cartesian Coordinate Systems 15
1.4 Operations with V 22
1.5 Generalized Coordinates 34
Problems 43
CHAPTER 2 COMPLEX ANALYSIS 46
2.1 Complex Numbers 46
2.2 Functions of a Complex Variable 51
2.3 Evaluation of Integrals: Part I 54
2.4 Series Representations of Functions 64
2.5 Evaluation of Integrals: Part II 75
2.6 Multivalued Functions, Branch Points, and Cuts 80
2.7 Evaluation of Integrals: Part III 83
2.8 Evaluation of Integrals: Part IV 92
2.9 Conformal Mapping 102
2.10 Singularities of Functions Defined by Integrals 109
2.11 Dispersion Relations 112
Problems 120
vi!
CHAPTER 3 INFINITE SERIES 123
3.1 Convergence Tests 124
3.2 Arithmetic Combinations of Power Series 140
3.3 Summing a Power Series 141
3.4 Other Processes Using Series 150
3.5 Bernoulli and Euler Series 151
Problems 163
CHAPTER 4 FOURIER SERIES AND INTEGRAL
TRANSFORMS 166
4.1 Fourier Series 166
4.2 Fourier Transforms 179
4.3 Laplace Transforms 189
4.4 Other Integral Transforms 197
Problems 198
CHAPTER 5 ORDINARY DIFFERENTIAL EQUATIONS 201
5.1 First Order Differential Equations 201
5.2 Higher Order Differential Equations with Constant
Coefficients 211
5.3 Higher Order Differential Equations with Nonconstant
Coefficients 241
Problems 260
CHAPTER 6 SPECIAL FUNCTIONS 264
6.1 Functions Defined by Integrals 264
6.2 Sturm Liouville Theory 280
6.3 Legendre Functions 288
6.4 Gegenbauer Functions 317
6.5 Laguerre Functions 320
6.6 Hermite Functions 330
6.7 Bessel Functions 337
6.8 Hypergeometric Functions 353
6.9 Properties of the Dirac 5 Symbol 365
6.10 Summary 367
Problems 387
Contents
CHAPTER 7 CALCULUS OF VARIATIONS 393
7.1 Statement of the Problem and Formulation of the Solution 393
7.2 Isoperimetric Constraints and Lagrange Multipliers 400
7.3 Several Variables, Principle of Least Action, and Lagrange s
Equations 403
7.4 Several Independent Variables 408
7.5 Rayleigh Ritz Variational Method 409
7.6 Estimating the Solution to a Differential Equation 414
Problems 418
CHAPTER 8 DETERMINANTS AND MATRICES 420
8.1 Determinants 420
8.2 Arithmetic of Matrices 433
8.3 Functions of Matrices 447
8.4 Matrices with Special Properties 448
8.5 Eigenvalue Equations and Similarity Transformations 454
Problems 473
CHAPTER 9 TENSOR ANALYSIS 478
9.1 Definitions and Tensor Algebra 478
9.2 Riemannian Geometry and the Equation of a Geodesic 484
9.3 Applications to Relativity 503
9.4 Maxwell s Equations and Quaternions 510
Problems 512
CHAPTER 10 INTRODUCTION TO GROUP THEORY 515
10.1 Abstract Theory of Finite Groups 515
10.2 Theory and Application of Continuous Groups 543
Problems 581
CHAPTER 11 PARTIAL DIFFERENTIAL EQUATIONS 586
11.1 Separation of Variables 587
11.2 Integral Transform Methods 596
11.3 Green s Function Methods 600
Problems 620
Contents
CHAPTER 12 INTEGRAL EQUATIONS 624
12.1 Fredholm and Volterra Equations and Differential
Equations 624
12.2 Methods of Solution for Fredholm Equations 627
12.3 Volterra Equations 649
12.4 Singular Integral Equations for Scientific Problems 656
Problems 664
CHAPTER 13 NUMERICAL METHODS 668
13.1 Interpolation 668
13.2 Least Squares Curve Fitting 677
13.3 Numerical Integration 686
13.4 Numerical Solutions to Differential Equations 709
13.5 Numerical Solutions to Integral Equations 740
13.6 Zeros of a Function 759
Problems 770
INDEX 775
Contents
|
| adam_txt |
CONTENTS
PREFACE xi
CHAPTER 1 VECTOR ANALYSIS 1
1.1 Vector Arithmetic 1
1.2 Geometry of Lines and Planes 9
1.3 Non Cartesian Coordinate Systems 15
1.4 Operations with V 22
1.5 Generalized Coordinates 34
Problems 43
CHAPTER 2 COMPLEX ANALYSIS 46
2.1 Complex Numbers 46
2.2 Functions of a Complex Variable 51
2.3 Evaluation of Integrals: Part I 54
2.4 Series Representations of Functions 64
2.5 Evaluation of Integrals: Part II 75
2.6 Multivalued Functions, Branch Points, and Cuts 80
2.7 Evaluation of Integrals: Part III 83
2.8 Evaluation of Integrals: Part IV 92
2.9 Conformal Mapping 102
2.10 Singularities of Functions Defined by Integrals 109
2.11 Dispersion Relations 112
Problems 120
vi!
CHAPTER 3 INFINITE SERIES 123
3.1 Convergence Tests 124
3.2 Arithmetic Combinations of Power Series 140
3.3 Summing a Power Series 141
3.4 Other Processes Using Series 150
3.5 Bernoulli and Euler Series 151
Problems 163
CHAPTER 4 FOURIER SERIES AND INTEGRAL
TRANSFORMS 166
4.1 Fourier Series 166
4.2 Fourier Transforms 179
4.3 Laplace Transforms 189
4.4 Other Integral Transforms 197
Problems 198
CHAPTER 5 ORDINARY DIFFERENTIAL EQUATIONS 201
5.1 First Order Differential Equations 201
5.2 Higher Order Differential Equations with Constant
Coefficients 211
5.3 Higher Order Differential Equations with Nonconstant
Coefficients 241
Problems 260
CHAPTER 6 SPECIAL FUNCTIONS 264
6.1 Functions Defined by Integrals 264
6.2 Sturm Liouville Theory 280
6.3 Legendre Functions 288
6.4 Gegenbauer Functions 317
6.5 Laguerre Functions 320
6.6 Hermite Functions 330
6.7 Bessel Functions 337
6.8 Hypergeometric Functions 353
6.9 Properties of the Dirac 5 Symbol 365
6.10 Summary 367
Problems 387
Contents
CHAPTER 7 CALCULUS OF VARIATIONS 393
7.1 Statement of the Problem and Formulation of the Solution 393
7.2 Isoperimetric Constraints and Lagrange Multipliers 400
7.3 Several Variables, Principle of Least Action, and Lagrange's
Equations 403
7.4 Several Independent Variables 408
7.5 Rayleigh Ritz Variational Method 409
7.6 Estimating the Solution to a Differential Equation 414
Problems 418
CHAPTER 8 DETERMINANTS AND MATRICES 420
8.1 Determinants 420
8.2 Arithmetic of Matrices 433
8.3 Functions of Matrices 447
8.4 Matrices with Special Properties 448
8.5 Eigenvalue Equations and Similarity Transformations 454
Problems 473
CHAPTER 9 TENSOR ANALYSIS 478
9.1 Definitions and Tensor Algebra 478
9.2 Riemannian Geometry and the Equation of a Geodesic 484
9.3 Applications to Relativity 503
9.4 Maxwell's Equations and Quaternions 510
Problems 512
CHAPTER 10 INTRODUCTION TO GROUP THEORY 515
10.1 Abstract Theory of Finite Groups 515
10.2 Theory and Application of Continuous Groups 543
Problems 581
CHAPTER 11 PARTIAL DIFFERENTIAL EQUATIONS 586
11.1 Separation of Variables 587
11.2 Integral Transform Methods 596
11.3 Green's Function Methods 600
Problems 620
Contents
CHAPTER 12 INTEGRAL EQUATIONS 624
12.1 Fredholm and Volterra Equations and Differential
Equations 624
12.2 Methods of Solution for Fredholm Equations 627
12.3 Volterra Equations 649
12.4 Singular Integral Equations for Scientific Problems 656
Problems 664
CHAPTER 13 NUMERICAL METHODS 668
13.1 Interpolation 668
13.2 Least Squares Curve Fitting 677
13.3 Numerical Integration 686
13.4 Numerical Solutions to Differential Equations 709
13.5 Numerical Solutions to Integral Equations 740
13.6 Zeros of a Function 759
Problems 770
INDEX 775
Contents |
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| title_fullStr | Mathematics for scientists and engineers Harold Cohen |
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