Advanced mathematical methods for engineering and science students:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Pr.
1990
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 255 S. graph. Darst. |
| ISBN: | 0521363128 052136860X |
Staff View
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| 100 | 1 | |a Stephenson, Geoffrey |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Advanced mathematical methods for engineering and science students |c G. Stephenson and P. M. Radmore |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Pr. |c 1990 | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Notes to the reader xi
1 Suffix notation and tensor algebra 1
1.1 Summation convention 1
1.2 Free and dummy indices 3
1.3 Special symbols 4
1.4 Vector identities 6
1.5 Vector operators 8
1.6 Orthogonal coordinate systems 9
1.7 General coordinate transformations 13
1.8 Contravariant vectors 15
1.9 Kronecker delta symbol 15
1.10 Scalars and covariant vectors 16
1.11 Tensors of higher rank 18
Problems 1 19
2 Special functions 22
2.1 Origins 22
2.2 The gamma function 23
2.3 The exponential integral and related functions 28
2.4 The error function 28
2.5 The Bessel function 31
2.6 The Bessel function Yv 36
2.7 Generating function 39
2.8 Modified Bessel functions 42
2.9 Summary of the main properties of special functions 44
Problems 2 50
3 Non linear ordinary differential equations S3
3.1 Introduction 53
3.2 Equations with separable variables 54
v
vi Contents
3.3 Equations reducible to linear form 57
3.4 Bernoulli s equation 59
3.5 Riccati s equation 61
3.6 Special forms of Riccati s equation 63
3.7 The Lane Emden equation 65
3.8 The non linear pendulum 66
3.9 Duffing s equation 68
Problems 3 73
4 Approximate solutions of ordinary differential equations 75
4.1 Power series 75
4.2 Frobenius series 78
4.3 Picard iterative method 79
4.4 Perturbation series 82
4.5 Normal form 83
4.6 The W.K.B. (Wentzel Kramers Brillouin) approximation 84
4.7 Eigenvalue problems 88
4.8 The Liouville Green technique 90
Problems 4 96
5 Contour integration 98
5.1 Functions of a complex variable 98
5.2 Exponential and logarithmic functions 101
5.3 The derivative of a complex function 103
5.4 The Cauchy Riemann equations 105
5.5 Derivatives of multi valued functions 108
5.6 Complex integration 109
5.7 Cauchy s Theorem (First Integral Theorem) 112
5.8 Cauchy Integral Formula (Second Integral Theorem) 116
5.9 Derivatives of an analytic function 118
5.10 Taylor and Laurent series 120
5.11 Singularities and residues 125
5.12 Cauchy Residue Theorem 131
Problems 5 134
6 Applications of contour integration 137
6.1 Introduction 137
6.2 Calculation of real integrals 137
6.3 An alternative contour 144
6.4 Poles on the real axis: the principal value of integrals 146
6.5 Branch points and integrals of many valued functions 150
6.6 Summation of series 154
Problems 6 158
7 Laplace and Fourier transforms 161
7.1 Introduction 161
Contents vii
7.2 The Laplace transform 162
7.3 Three basic theorems 163
7.4 The calculation of an integral 166
7.5 Laplace transform of an error function 167
7.6 Transforms of the Heaviside step function and the Dirac
delta function 169
7.7 Transforms of derivatives 171
7.8 Inversion 173
7.9 Inversions of functions with branch points 179
7.10 Solution of ordinary differential equations 181
7.11 Solution of a Volterra integral equation 182
7.12 The Fourier transform 183
Problems 7 188
8 Partial differential equations 190
8.1 Introduction 190
8.2 Principle of Superposition 190
8.3 Some important equations 191
8.4 Linear second order equations in two independent variables 193
8.5 Boundary conditions 194
8.6 Method of characteristics 195
8.7 Separation of variables 205
8.8 Integral transform techniques 214
Problems 8 218
9 Calculus of variations 224
9.1 Introduction 224
9.2 Euler s equation 225
9.3 Alternative forms of Euler s equation 229
9.4 Extremal curves with discontinuous derivatives 233
9.5 Several dependent variables 233
9.6 Lagrange s equations of dynamics 234
9.7 Integrals involving derivatives higher than the first 237
9.8 Problems with constraints 238
9.9 Direct methods and eigenvalue problems 240
Problems 9 246
Answers to problems 248
Index 253
|
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| ctrlnum | (OCoLC)611680229 (DE-599)BVBBV002753293 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T15:49:07Z |
| institution | BVB |
| isbn | 0521363128 052136860X |
| language | English |
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| physical | XI, 255 S. graph. Darst. |
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| spelling | Stephenson, Geoffrey Verfasser aut Advanced mathematical methods for engineering and science students G. Stephenson and P. M. Radmore 1. publ. Cambridge [u.a.] Cambridge Univ. Pr. 1990 XI, 255 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques ram Natuurkunde gtt Technische wetenschappen gtt Toepassingen gtt Wiskunde gtt Mathematik Physik Mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematik (DE-588)4037944-9 s DE-604 Radmore, Paul M. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001760093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stephenson, Geoffrey Radmore, Paul M. Advanced mathematical methods for engineering and science students Mathématiques ram Natuurkunde gtt Technische wetenschappen gtt Toepassingen gtt Wiskunde gtt Mathematik Physik Mathematics Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4151278-9 |
| title | Advanced mathematical methods for engineering and science students |
| title_auth | Advanced mathematical methods for engineering and science students |
| title_exact_search | Advanced mathematical methods for engineering and science students |
| title_full | Advanced mathematical methods for engineering and science students G. Stephenson and P. M. Radmore |
| title_fullStr | Advanced mathematical methods for engineering and science students G. Stephenson and P. M. Radmore |
| title_full_unstemmed | Advanced mathematical methods for engineering and science students G. Stephenson and P. M. Radmore |
| title_short | Advanced mathematical methods for engineering and science students |
| title_sort | advanced mathematical methods for engineering and science students |
| topic | Mathématiques ram Natuurkunde gtt Technische wetenschappen gtt Toepassingen gtt Wiskunde gtt Mathematik Physik Mathematics Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathématiques Natuurkunde Technische wetenschappen Toepassingen Wiskunde Mathematik Physik Mathematics Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001760093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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