Advanced calculus for applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice-Hall
1976
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Früher u.d.T.: Hildebrand, Francis B: Advanced calculus for engineers |
| Physical Description: | XIII, 733 S. zahlr. graph. Darst. |
| ISBN: | 0130111899 |
Staff View
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| 245 | 1 | 0 | |a Advanced calculus for applications |c Francis B. Hildebrand |
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Record in the Search Index
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| adam_text | Contents
Preface xi
1
Ordinary Differential Equations 1
1.1 Introduction 1
1.2 Linear Dependence 3
1.3 Complete Solutions of Linear Equations 4
1.4 The Linear Differential Equation of First Order 6
1.5 Linear Differential Equations with Constant Coefficients 8
1.6 The Equidimensional Linear Differential Equation 12
1.7 Properties of Linear Operators 75
1.8 Simultaneous Linear Differential Equations 18
1.9 Particular Solutions by Variation of Parameters 24
1.10 Reduction of Order 28
1.11 Determination of Constants 30
1.12 Special Solvable Types of Nonlinear Equations 31
2
The Laplace Transform 53
2.1 An introductory Example 53
2.2 Definition and Existence of Laplace Transforms 55
v
• Contents
2.3 Properties of Laplace Transforms 58
2.4 The Inverse Transform 62
2.5 The Convolution 63
2.6 Singularity Functions 65
2.7 Use of Table of Transforms 67
2.8 Applications to Linear Differential Equations with
Constant Coefficients 72
2.9 The Gamma Function 76
3
Numerical Methods for Solving Ordinary Differential Equations 93
3.1 Introduction 93
3.2 Use of Taylor Series 94
3.3 The Adams Method 96
3.4 The Modified Adams Method 100
3.5 The Runge-Kutta Method 102
3.6 Picard s Method 105
3.7 Extrapolation with Differences 107
4
Series Solutions of Differential Equations: Special Functions 118
4.1 Properties of Power Series 118
4.2 Illustrative Examples 122
4.3 Singular Points of Linear Second-Order Differential
Equations 126
4.4 The Method of Frobenius 128
4.5 Treatment of Exceptional Cases 134
4.6 Example of an Exceptional Case 136
4.7 A Particular Class of Equations 138
4.8 Bessel Functions 141
4.9 Properties of Bessel Functions 147
4.10 Differential Equations Satisfied by Bessel Functions 151
4.11 Ber and Bei Functions 153
4.12 Legendre Functions 755
4.13 The Hypergeometric Function 162
4.14 Series Solutions Valid for Large Values of x 163
Contents vii
5
Boundary-Value Problems and Characteristic-Function Representations 186
5.1 Introduction 186
5.2 The Rotating String 188
5.3 The Rotating Shaft 192
5.4 Bückling of Long Columns Under Axial Loads 195
5.5 The Method of Stodola and Vianello 197
5.6 Orthogonality of Characteristic Functions 203
5.7 Expansion of Arbitrary Functions in Series of Orthogonal
Functions 207
5.8 Boundary-Value Problems Involving Nonhomogeneous
Differential Equations 211
5.9 Convergence of the Method of Stodola and Vianello 212
5.10 Fourier Sine Series and Cosine Series 214
5.11 Complete Fourier Series 219
5.12 Term-by-Term Differentiation of Fourier Series 223
5.13 Fourier-Bessel Series 226
5.14 Legendre Series 230
5.15 The Fourier Integral 234
6
Vector Analysis 269
6.1 Elementary Properties of Vectors 269
6.2 The Scalar Product of Two Vectors 271
6.3 The Vector Product of Two Vectors 273
6.4 Multiple Products 275
6.5 Differentiation of Vectors 277
6.6 Geometry of a Space Curve 278
6.7 The Gradient Vector 281
6.8 The Vector Operator V 283
6.9 Differentiation Formulas 284
6.10 Line Integrals 287
6.11 The Potential Function 291
6.12 Surface Integrals 294
6.13 Interpretation of Divergence. The Divergence Theorem 297
6.14 Green s Theorem 301
6.15 Interpretation of Curl. Laplace s Equation 302
6.16 Stokes s Theorem 303
6.17 Orthogonal Curvilinear Coordinates 306
viii Contents
6.18 Special Coordinate Systems 311
6.19 Application to Two-Dimensional Incompressible Fluid Flow 313
6.20 Compressible Ideal Fluid Flow 316
7
Topics in Higher-Dimensional Calculus 342
7.1 Partial Differentiation. Chain Rules 342
7.2 Implicit Functions. Jacobian Determinants 347
7.3 Functional Dependence 350
1A Jacobians and Curvilinear Coordinates. Change of Variables
in Integrals 352
7.5 Taylor Series 354
7.6 Maxima and Minima 356
7.7 Constraints and Lagrange Multipliers 357
7.8 Calculus of Variations 360
7.9 Differentiation of Integrals Involving a Parameter 364
7.10 Newton s Iterative Method 367
8
Partial Differential Equations 384
8.1 Definitions and Examples 384
8.2 The Quasi-Linear Equation of First Order 387
8.3 Special Devices. Initial Conditions 392
8.4 Linear and Quasi-Linear Equations of Second Order 396
8.5 Special Linear Equations of Second Order, with Constant
CoefRcients 397
8.6 Other Linear Equations 400
8.7 Characteristics of Linear First-Order Equations 403
8.8 Characteristics of Linear Second-Order Equations 408
8.9 Singular Curves on Integral Surfaces 414
8.10 Remarks on Linear Second-Order Initial-Value Problems 417
8.11 The Characteristics of a Particular Quasi-Linear Problem 417
9
Solutions of Partial Differential Equations of Mathematical Physics 439
9.1 Introduction 439
9.2 Heat Flow 441
9.3 Steady-State Temperature Distribution in a Rectangular Plate 443
9.4 Steady-State Temperature Distribution in a Circular Annulus 446
Contents ix
9.5 Poisson s Integral 450
9.6 Axisymmetrical Temperature Distribution in a Solid Sphere 451
9.7 Temperature Distribution in a Rectangular Parallelepiped 453
9.8 Ideal Fluid Flow about a Sphere 456
9.9 The Wave Equation. Vibration of a Circular Membrane 459
9.10 The Heat-Flow Equation. Heat Flow in a Rod 461
9.11 Duhamel s Superposition Integral 463
9.12 Traveling Waves 467
9.13 The Pulsating Cylinder 470
9A4 Examples of the Use of Fourier Integrals 473
9.15 Laplace Transform Methods 477
9.16 Application of the Laplace Transform to the Telegraph
Equations for a Long Line 480
9.17 Nonhomogeneous Conditions. The Method of Variation of
Parameters 484
9.18 Formulation of Problems 490
9.19 Supersonic Flow of Ideal Compressible Fluid Past an Obstacle 495
10
Functions of a Complex Variable 539
10.1 Introduction. The Complex Variable 539
10.2 Elementary Functions of a Complex Variable 541
10.3 Other Elementary Functions 544
10.4 Analytic Functions of a Complex Variable 550
10.5 Line Integrals of Complex Functions 554
10.6 Cauchy s Integral Formula 560
10.7 Taylor Series 561
10.8 Laurent Series 563
10.9 Singularities of Analytic Functions 567
10.10 Singularities at Infinity 575
10.11 Significance of Singularities 578
10.12 Residues 580
10.13 Evaluation of Real Definite Integrals 583
10.14 Theorems on Limiting Contours 589
10.15 Indented Contours 592
10.16 Integrals Involving Branch Points 595
11
Applications of Analytic Function Theory 622
11.1 Introduction 622
11.2 Inversion of Laplace Transforms 622
x Contents
11.3 Inversion of Laplace Transforms with Branch Points. The Loop
Integral 625
11.4 Conformal Mapping 628
11.5 Applications to Two-Dimensional Fluid Flow 632
11.6 Basic Flows 634
11.7 Other Applications of Conformal Mapping 638
11.8 The Schwarz-Christoffel Transformation 641
11.9 Green s Functions and the Dirichlet Problem 652
11.10 The Use of Conformal Mapping 658
11.11 Other Two-Dimensional Green s Functions 661
Answers to Problems 703
Index 721
|
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| discipline | Mathematik |
| edition | 2. ed. |
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| isbn | 0130111899 |
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| spelling | Hildebrand, Francis Begnaud 1915-2002 Verfasser (DE-588)138317267 aut Advanced calculus for applications Francis B. Hildebrand 2. ed. Englewood Cliffs, NJ Prentice-Hall 1976 XIII, 733 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Früher u.d.T.: Hildebrand, Francis B: Advanced calculus for engineers Calcul infinitésimal Mathematik Calculus Mathematics Anwendung (DE-588)4196864-5 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Vektoranalysis (DE-588)4191992-0 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Vektoranalysis (DE-588)4191992-0 s Differentialgleichung (DE-588)4012249-9 s Analysis (DE-588)4001865-9 s Anwendung (DE-588)4196864-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001499614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hildebrand, Francis Begnaud 1915-2002 Advanced calculus for applications Calcul infinitésimal Mathematik Calculus Mathematics Anwendung (DE-588)4196864-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Vektoranalysis (DE-588)4191992-0 gnd Analysis (DE-588)4001865-9 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4018935-1 (DE-588)4191992-0 (DE-588)4001865-9 (DE-588)4012249-9 |
| title | Advanced calculus for applications |
| title_auth | Advanced calculus for applications |
| title_exact_search | Advanced calculus for applications |
| title_full | Advanced calculus for applications Francis B. Hildebrand |
| title_fullStr | Advanced calculus for applications Francis B. Hildebrand |
| title_full_unstemmed | Advanced calculus for applications Francis B. Hildebrand |
| title_short | Advanced calculus for applications |
| title_sort | advanced calculus for applications |
| topic | Calcul infinitésimal Mathematik Calculus Mathematics Anwendung (DE-588)4196864-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Vektoranalysis (DE-588)4191992-0 gnd Analysis (DE-588)4001865-9 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Calcul infinitésimal Mathematik Calculus Mathematics Anwendung Funktionentheorie Vektoranalysis Analysis Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001499614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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