Computational and applied mathematics for engineering analysis:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Southampton u.a.
Computational Mechanics Publ. u.a.
1987
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 380 S. graph. Darst. |
| ISBN: | 0905451430 3540175059 0387175059 093121517X |
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MARC
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| 100 | 1 | |a Cakmak, Ahmet S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Computational and applied mathematics for engineering analysis |c A. S. Cakmak ; J. F. Botha and W. G. Gray |
| 264 | 1 | |a Southampton u.a. |b Computational Mechanics Publ. u.a. |c 1987 | |
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| 650 | 4 | |a Mathématiques de l'ingénieur | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1 SERIES 1
1.1. Introduction 1
1.2. Convergent Series 1
1. Introduction and Definitions 1
2. Tests for Convergence 4
3. Uniform Convergence 8
4. Power Series 9
1.3. Asymptotic Series 13
1. Introduction and Definitions 13
2. Asymptotic Power Series 13
1.4. Asymptotic Evaluation of Integrals 16
1. Taylor Series 16
2. Integration by Parts 17
3. Laplace s Method 18
1.5. References 22
1.6. Problems 23
Chapter 2 EVALUATION OF LINE INTEGRALS ... 26
2.1. Introduction 26
2.2. The Riemann Integral 26
2.3. The Line Integral in the Complex Plane 27
2.4. Analytic Functions of a Complex Variable 28
1. Definitions 28
2. Power Series Representation 31
3. Singular Points 33
2.5. Calculus of Residues 37
2.6. Evaluation of Real Integrals 41
1. Finite Integrals 42
2. Infinite Integrals 43
3. Fourier Integrals 46
4. Integrals Involving Branch Cuts 47
5. Contours Enclosing an Infinite Number of Singularities . . 51
6. Contours with Singularities on the Path 52
7. Circular Contour Theorems 55
2.7. Method of Steepest Descent 56
2.8. References 65
2.9. Problems 65
vi Contents
Chapter 3 LINEAR ALGEBRA 69 ,
3.1. Introduction 69
3.2. Definitions 69
3.3. Systems of Linear Equations 73
3.4. Vector Spaces 77 j
3.5. Spectral Representation — Characteristic Value Problems . . 81
3.6. Solution of a System of Linear Equations 96
3.7. References 97
3.8. Problems 97
Chapter4 TENSOR CALCULUS 101
4.1. Introduction 101
4.2. Definition of Tensor Qualities 102
4.3. Generalized Curvilinear Coordinate Systems 107
1. Geometry 107
2. Generalized Base Vectors 108
3. Representation of Tensor Qualities 112
4. Elements of Length, Area and Volume 119
4.4. Tensor Fields 121
1. Differentiation 121
2. The Differential Vector Operator Del V 129
3. Curvature of Space: The Riemann Christoffel Tensor ... 133
4.5. References 135
4.6. Problems 135
Chapter5 CALCULUS OF VARIATIONS
AND INTRODUCTION TO INTEGRAL
EQUATIONS 140
5.1. Introduction 140
5.2. Calculus of Variations 140
5.3. Integral Equations 151
1. Classification 151
2. Volterra Equation 152
3. Fredholm Equation 155
4. Characteristic Values and Functions 159
5. Hilbert Schmidt Theory 161 ;
5.4. References 164
5.5. Problems 165
Chapter6 LINEAR ORDINARY DIFFERENTIAL
EQUATIONS 167
6.1. Introduction 167
6.2. Properties of the General Solution 167
6.3. Systems of Differential Equations 173
1. Definitions 173
2. Systems with Constant Coefficients 173
Contents vii
3. The Inhomogeneous System of Equations 177
6.4. Differential Equations with Variable Coefficients 181
1. Definitions 181
2. The Method of Frobenius 183
3. The Legendre s Equation 190
4. The Bessel Equation 192
6.5. Transform Methods 195
1. The Laplace Transform 195
2. Explicit Expressions 197
3. Inverse Transforms 201
4. Application of the Laplace Transform 202
5. The Fourier Transform 205
6. The Hankel Transform 207
6.6. Boundary Value Problems 208
1. Definitions 208
2. The Green s Function Method 210
3. The Eigenfunction Method 217
6.7. Sturm Liouville Theory 225
6.8. References 229
6.9 Problems 229
Chapter 7 A PPR OXIMA TE TECHNIQ UES FOR THE
SOL UTION OF ORDINAR Y DIFFERENTIAL
EQ UA TIONS: PER TURBA TION METHODS . 235
7.1. Introduction 235
7.2. Solutions of Irregular Singular Points 235
7.3. Perturbation Methods 240
7.4. The Boundary Layer Method 243
7.5. The WKB Method 248
7.6. Multiple Scales Analysis 253
1. Many Variable Form 253
2. Two Variable Form 256
3. Non linear Scales — The Generalized Method 258
4. Boundary Layer and WKB as Special Cases 263
7.7. References 266
7.8. Problems 266
Chapter8 PARTIAL DIFFERENTIAL EQUATIONS . . 269
8.1. Introduction 269
8.2. The First Order Quasi Linear Partial Differential Equation . 270
8.3. The Second Order Equation 275
8.4. Singular Solutions 280
8.5. Partial Differential Equations of Mathematical Physics ... 281
1. General 281
2. Elliptic Equations 282
3. Parabolic Equations 287
viii Contents
4. Hyperbolic Equations 294
8.6. The Green s Function 300
8.7. References 305
8.8. Problems 305
Chapter 9 NUMERICAL METHODS 311
9.1. Introduction 311
9.2. Approximation of the Differential Operator:
The Finite Difference Approach 312
1. Ordinary Differential Equations: The Initial Value Problem . 317
2. Ordinary Differential Equations:
The Boundary Value Problem 326
3. Partial Differential Equations 333
9.3. Approximation of Differential Equation Solutions:
The Finite Element Approach 342
1. The Subdomain Method 344
2. The Galerkin Method 348
3. The Boundary Element Method 362
9.4. Consistency, Stability and Convergence 366
9.5. References 372
9.6. Problems 373
|
| any_adam_object | 1 |
| author | Cakmak, Ahmet S. Botha, Joseph F. Gray, William G. |
| author_facet | Cakmak, Ahmet S. Botha, Joseph F. Gray, William G. |
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| dewey-full | 519.4/02462 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4/02462 |
| dewey-search | 519.4/02462 |
| dewey-sort | 3519.4 42462 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:02Z |
| institution | BVB |
| isbn | 0905451430 3540175059 0387175059 093121517X |
| language | English |
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| physical | VIII, 380 S. graph. Darst. |
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| publisher | Computational Mechanics Publ. u.a. |
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| spelling | Cakmak, Ahmet S. Verfasser aut Computational and applied mathematics for engineering analysis A. S. Cakmak ; J. F. Botha and W. G. Gray Southampton u.a. Computational Mechanics Publ. u.a. 1987 VIII, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques de l'ingénieur Mathématiques de l'ingénieur - Problèmes et exercices Engineering mathematics Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Mathematik (DE-588)4037944-9 s Ingenieurwissenschaften (DE-588)4137304-2 s Botha, Joseph F. Verfasser aut Gray, William G. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001448270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cakmak, Ahmet S. Botha, Joseph F. Gray, William G. Computational and applied mathematics for engineering analysis Mathématiques de l'ingénieur Mathématiques de l'ingénieur - Problèmes et exercices Engineering mathematics Numerische Mathematik (DE-588)4042805-9 gnd Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4037944-9 (DE-588)4137304-2 |
| title | Computational and applied mathematics for engineering analysis |
| title_auth | Computational and applied mathematics for engineering analysis |
| title_exact_search | Computational and applied mathematics for engineering analysis |
| title_full | Computational and applied mathematics for engineering analysis A. S. Cakmak ; J. F. Botha and W. G. Gray |
| title_fullStr | Computational and applied mathematics for engineering analysis A. S. Cakmak ; J. F. Botha and W. G. Gray |
| title_full_unstemmed | Computational and applied mathematics for engineering analysis A. S. Cakmak ; J. F. Botha and W. G. Gray |
| title_short | Computational and applied mathematics for engineering analysis |
| title_sort | computational and applied mathematics for engineering analysis |
| topic | Mathématiques de l'ingénieur Mathématiques de l'ingénieur - Problèmes et exercices Engineering mathematics Numerische Mathematik (DE-588)4042805-9 gnd Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Mathématiques de l'ingénieur Mathématiques de l'ingénieur - Problèmes et exercices Engineering mathematics Numerische Mathematik Mathematik Ingenieurwissenschaften |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001448270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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