Analytical and computational methods of advanced engineering mathematics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Schriftenreihe: | Texts in applied mathematics
28 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 729 S. Ill., graph. Darst. |
| ISBN: | 0387982655 |
Internformat
MARC
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| 100 | 1 | |a Gustafson, Grant B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analytical and computational methods of advanced engineering mathematics |c Grant B. Gustafson ; Calvin H. Wilcox |
| 246 | 1 | 3 | |a Advanced engineering mathematics |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1998 | |
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Datensatz im Suchindex
| _version_ | 1804126881068351488 |
|---|---|
| adam_text | Contents
Preface v
Introduction xv
1 Numerical Analysis 1
1.1 The Nature of Numerical Analysis 1
1.2 Polynomial Interpolation 2
1.3 Numerical Integration and Differentiation 22
1.4 Solution of Equations 41
1.5 Inverse Functions 55
1.6 Implicit Functions 64
1.7 Numerical Summation of Infinite Series 70
2 Ordinary Differential Equations of First Order 76
2.1 The Nature of Differential Equations 77
2.2 Separable Equations 83
2.3 Linear First Order Equations 92
2.4 Exact Equations 98
2.5 Applications to Some Second Order Equations 106
2.6 The Initial Value Problem 123
2.7 Numerical Methods for the Initial Value Problem 127
xii Contents
3 Ordinary Differential Equations of Higher Order 138
3.1 Examples from Engineering and Physics 139
3.2 Linear Second Order Equations — Structure of Solutions 155
3.3 Linear Second Order Equations with Constant Coefficients 164
3.4 Linear Second Order Equations with Analytic Coefficients 182
3.5 Numerical Methods for Second Order Equations 204
3.6 Linear Equations of Order n 2 211
4 The Laplace Transform 218
4.1 The Nature of the Laplace Transform 220
4.2 The Laplace Transforms of Some Elementary Functions 224
4.3 Operational Rules for the Laplace Transform 231
4.4 Applications to Differential Equations 249
4.5 Applications to Systems of Differential Equations 263
5 Linear Algebra 276
5.1 Systems of Linear Equations 277
5.2 The Gauss Elimination Method 284
5.3 Vector Spaces 294
5.4 Matrices and Matrix Algebra 305
5.5 The Fundamental Theorem of Linear Algebra 314
5.6 Determinants and Cramer s Rule 326
5.7 Eigenvalues and Eigenvectors 345
6 Vector Analysis 364
6.1 Vector Algebra 366
6.2 Vector Calculus of Curves in Space 381
6.3 Vector Calculus of Surfaces in Space 392
6.4 Calculus of Scalar and Vector Fields 403
6.5 Integral Theorems of Vector Calculus 417
6.6 X Ray Diffraction and Crystal Structure 431
7 Partial Differential Equations of Mathematical Physics 440
7.1 Vibrating Strings: D Alembert s Wave Equation 442
7.2 Heat Diffusion in Rods: Fourier s Heat Equation 451
7.3 Heat Diffusion in Plates 456
7.4 Steady State Heat Diffusion in Plates: The Laplace Equation 461
7.5 Vibrations of Drums 463
Contents xiii
7.6 Heat Diffusion in Solids 468
7.7 Steady State Heat Diffusion in Solids 470
8 Fourier Analysis and Sturm Liouville Theory 472
Part I Fourier Series 474
8.1 Dirichlet Boundary Conditions and Fourier Sine Series 474
8.2 Orthogonality and Fourier Coefficients 479
8.3 Convergence of Fourier Sine Series 480
8.4 Neumann Boundary Conditions and Fourier Cosine Series 486
8.5 Periodic Boundary Conditions and the Complete Fourier Series .... 492
8.6 Proofs of the Convergence Theorems (Optional) 501
Part II Fourier Integrals 511
8.7 Heat Diffusion in an Infinite Rod 512
8.8 Orthogonality Calculation 514
8.9 The Fourier Integral 516
8.10 Fourier Sine and Cosine Integrals 529
Part III Sturm Liouville Theory 533
8.11 Heat Diffusion in Nonhomogeneous Rods 533
8.12 Sturm Liouville Problems: Basic Theory 534
8.13 Construction of Eigenvalues and Eigenfunctions 539
8.14 Singular Sturm Liouville Problems 548
9 Boundary Value Problems of Mathematical Physics 556
9.1 Heat Diffusion in One Dimension 557
9.2 Vibration of Strings and Traveling Waves 579
9.3 Steady State Diffusion of Heat in Plates 598
9.4 Transient Diffusion of Heat in Plates 630
9.5 Vibrations of Drums 638
9.6 Steady State Diffusion of Heat in Solids 643
9.7 The Laplace Transform Method 653
Appendix: Answers and Hints to Selected Exercises 662
References 709
Index 711
|
| any_adam_object | 1 |
| author | Gustafson, Grant B. Wilcox, Calvin H. |
| author_facet | Gustafson, Grant B. Wilcox, Calvin H. |
| author_role | aut aut |
| author_sort | Gustafson, Grant B. |
| author_variant | g b g gb gbg c h w ch chw |
| building | Verbundindex |
| bvnumber | BV012262450 |
| classification_rvk | SK 110 SK 950 ZG 9120 |
| ctrlnum | (OCoLC)845032645 (DE-599)BVBBV012262450 |
| dewey-full | 620.00151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.00151 |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Technik Mathematik |
| format | Book |
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| id | DE-604.BV012262450 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:24:29Z |
| institution | BVB |
| isbn | 0387982655 |
| language | English |
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| physical | XXII, 729 S. Ill., graph. Darst. |
| publishDate | 1998 |
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| publisher | Springer |
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| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Gustafson, Grant B. Verfasser aut Analytical and computational methods of advanced engineering mathematics Grant B. Gustafson ; Calvin H. Wilcox Advanced engineering mathematics New York [u.a.] Springer 1998 XXII, 729 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 28 Engineering mathematics Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Vektoranalysis (DE-588)4191992-0 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content (DE-588)4144384-6 Beispielsammlung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Ingenieurwissenschaften (DE-588)4137304-2 s Mathematik (DE-588)4037944-9 s DE-604 Numerische Mathematik (DE-588)4042805-9 s Differentialgleichung (DE-588)4012249-9 s Vektoranalysis (DE-588)4191992-0 s Harmonische Analyse (DE-588)4023453-8 s Wilcox, Calvin H. Verfasser aut Texts in applied mathematics 28 (DE-604)BV002476038 28 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008310222&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gustafson, Grant B. Wilcox, Calvin H. Analytical and computational methods of advanced engineering mathematics Texts in applied mathematics Engineering mathematics Numerische Mathematik (DE-588)4042805-9 gnd Harmonische Analyse (DE-588)4023453-8 gnd Vektoranalysis (DE-588)4191992-0 gnd Mathematik (DE-588)4037944-9 gnd Differentialgleichung (DE-588)4012249-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4023453-8 (DE-588)4191992-0 (DE-588)4037944-9 (DE-588)4012249-9 (DE-588)4137304-2 (DE-588)4143389-0 (DE-588)4144384-6 (DE-588)4123623-3 |
| title | Analytical and computational methods of advanced engineering mathematics |
| title_alt | Advanced engineering mathematics |
| title_auth | Analytical and computational methods of advanced engineering mathematics |
| title_exact_search | Analytical and computational methods of advanced engineering mathematics |
| title_full | Analytical and computational methods of advanced engineering mathematics Grant B. Gustafson ; Calvin H. Wilcox |
| title_fullStr | Analytical and computational methods of advanced engineering mathematics Grant B. Gustafson ; Calvin H. Wilcox |
| title_full_unstemmed | Analytical and computational methods of advanced engineering mathematics Grant B. Gustafson ; Calvin H. Wilcox |
| title_short | Analytical and computational methods of advanced engineering mathematics |
| title_sort | analytical and computational methods of advanced engineering mathematics |
| topic | Engineering mathematics Numerische Mathematik (DE-588)4042805-9 gnd Harmonische Analyse (DE-588)4023453-8 gnd Vektoranalysis (DE-588)4191992-0 gnd Mathematik (DE-588)4037944-9 gnd Differentialgleichung (DE-588)4012249-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Engineering mathematics Numerische Mathematik Harmonische Analyse Vektoranalysis Mathematik Differentialgleichung Ingenieurwissenschaften Aufgabensammlung Beispielsammlung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008310222&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
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