Mathematical analysis in engineering: how to use the basic tools
"This user-friendly text shows how to use mathematics to formulate, solve, and analyze physical problems." "Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at center stag...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Press
1995
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "This user-friendly text shows how to use mathematics to formulate, solve, and analyze physical problems." "Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at center stage; that is, it starts with the problem, finds the mathematics that suits it, and ends with a mathematical analysis of the physics. The emphasis throughout is on engineering applications rather than mathematical formalities." "Physical examples are selected primarily from applied mechanics, a field central to many branches of engineering and applied science, and they range from the simple to the more sophisticated. Among mathematical topics included in the book are Fourier series, separation of variables, Bessel functions, Fourier and Laplace transforms, Green's functions, and complex function theories. Also covered are advanced topics such as Riemann-Hilbert techniques, perturbation methods, and practical topics such as symbolic computation."--BOOK JACKET. |
| Physical Description: | XVII, 461 S. graph. Darst. |
| ISBN: | 0521460530 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface page xiii
Acknowledgments xvii
1 Formulation of physical problems 1
1.1 Transverse vibration of a taut string 1
1.2 Longitudinal vibration of an elastic rod 4
1.3 Traffic flow on a freeway 6
1.4 Seepage flow through a porous medium 7
1.5 Diffusion in a stationary medium 10
1.6 Shallow water waves and linearization 12
1.6.1 Nonlinear governing equations 12
1.6.2 Linearization for small amplitude 15
2 Classification of equations with two independent
variables 20
2.1 A first order equation 20
2.2 System of first order equations 22
2.3 Linear second order equations 25
2.3.1 Constant coefficients 25
2.3.2 Variable coefficients 28
3 One dimensional waves 33
3.1 Waves due to initial disturbances 33
3.2 Reflection from the fixed end of a string 38
3.3 Specification of initial and boundary data 40
3.4 Forced waves in a long string 41
3.5 Uniqueness of the Cauchy problem 44
3.6 Traffic flow a taste of nonlinearity 45
3.7 Green light at the head of traffic 46
3.8 Traffic congestion and jam 50
vii
viii Contents
4 Finite domains and separation of variables 57
4.1 Separation of variables 57
4.2 One dimensional diffusion 63
4.3 Eigenfunctions and base vectors 65
4.4 Partially insulated slab 66
4.5 Sturm Liouville problems 71
4.6 Steady forcing 75
4.7 Transient forcing 76
4.8 Two dimensional diffusion 78
4.9 Cylindrical polar coordinates 80
4.10 Steady heat conduction in a circle 82
5 Elements of Fourier series 91
5.1 General Fourier series 91
5.2 Trigonometric Fourier series 93
5.2.1 Full Fourier series 93
5.2.2 Fourier cosine and sine series 95
5.2.3 Other intervals 96
5.3 Exponential Fourier series 98
5.4 Convergence of Fourier series 99
6 Introduction to Green s functions 105
6.1 The 6 function 105
6.2 Static deflection of a string under a concentrated load 108
6.3 String under a simple harmonic point load 110
6.4 Sturm Liouville boundary value problem 112
6.5 Bending of an elastic beam on an elastic foundation 114
6.5.1 Formulation of the beam problem 114
6.5.2 Beam under a sinusoidal concentrated load 117
6.6 Fundamental solutions 121
6.7 Green s function in a finite domain 124
6.8 Adjoint operator and Green s function 125
7 Unbounded domains and Fourier transforms 132
7.1 Exponential Fourier transform 132
7.1.1 From Fourier series to Fourier transform 132
7.1.2 Transforms of derivatives 134
7.1.3 Convolution theorem 134
7.2 One dimensional diffusion 135
7.2.1 General solution in integral form 135
7.2.2 A localized source 137
7.2.3 Discontinuous initial temperature 139
Contents ix
7.3 Forced waves in one dimension 141
7.4 Seepage flow into a line drain 143
7.5 Surface load on an elastic ground 145
7.5.1 Field equations for plane elasticity 145
7.5.2 Half plane under surface load 147
7.5.3 Response to a line load 149
7.6 Fourier sine and cosine transforms 153
7.7 Diffusion in a semi infinite domain 154
7.8 Potential problem in a semi infinite strip 159
8 Bessel functions and circular boundaries 165
8.1 Circular region and Bessel s equation 165
8.2 Bessel function of the first kind 167
8.3 Bessel function of the second kind for integer order 171
8.4 Some properties of Bessel functions 174
8.4.1 Recurrence relations 175
8.4.2 Behavior for small argument 176
8.4.3 Behavior for large argument 176
8.4.4 Wronskians 178
8.4.5 Partial wave expansion 179
8.5 Oscillations in a circular region 180
8.5.1 Radial eigenfunctions and natural modes 180
8.5.2 Orthogonality of natural modes 182
8.5.3 Transient oscillations in a circular pond 184
8.6 Hankel functions and wave propagation 185
8.6.1 Wave radiation from a circular cylinder 186
8.6.2 Scattering of plane waves by a circular cylinder 190
8.7 Modified Bessel functions 192
8.8 Bessel functions with complex argument 194
8.9 Pipe flow through a vertical thermal gradient 195
8.9.1 Formulation 195
8.9.2 Solution for rising ambient temperature 199
8.10 Differential equations reducible to Bessel form 201
9 Complex variables 210
9.1 Complex numbers 210
9.2 Complex functions 212
9.3 Branch cuts and Riemann surfaces 215
9.4 Analytic functions 220
9.5 Plane seepage flows in porous media 223
9.6 Plane flow of a perfect fluid 225
x Contents
9.7 Simple irrotational flows 227
9.8 Cauchy s theorem 229
9.9 Cauchy s integral formula and inequality 235
9.10 Liouville s theorem 237
9.11 Singularities 238
9.12 Evaluation of integrals by Cauchy s theorems 239
9.13 Jordan s lemma 246
9.14 Forced harmonic waves and the radiation condition 247
9.15 Taylor and Laurent series 250
9.16 More on contour integration 254
10 Laplace transform and initial value problems 260
10.1 The Laplace transform 260
10.2 Derivatives and the convolution theorem 263
10.3 Coupled pendula 265
10.4 One dimensional diffusion in a strip 267
10.5 A string oscillator system 269
10.6 Diffusion by sudden heating at the boundary 272
10.7 Sound diffraction near a shadow edge 275
10.8 Temperature in a layer of accumulating snow 280
11 Conformal mapping and hydrodynamics 289
11.1 What is conformal mapping? 289
11.2 Relevance to plane potential flows 290
11.3 Schwarz Christoffel transformation 291
11.4 An infinite channel 295
11.4.1 Mapping onto a half plane 295
11.4.2 Source in an infinite channel 296
11.5 A semi infinite channel 298
11.6 An estuary 301
11.7 Seepage flow under an impervious dam 302
11.8 Water table above an underground line source 307
12 Riemann—Hilbert problems in hydrodynamics
and elasticity 318
12.1 Riemann Hilbert problem and Plemelj s formulas 318
12.2 Solution to the Ricmann Hilbert problem 320
12.3 Linearized theory of cavity flow 322
12.4 Schwarz s principle of reflection 327
12.5 *Complex formulation of plane elasticity 330
12.5.1 Airy s stress function 330
12.5.2 Stress components 331
Contents xi
12.5.3 Displacement components 332
12.5.4 Half plane problems 333
12.6 *A strip footing on the ground surface 335
12.6.1 General solution to the boundary value problem 335
12.6.2 Vertically pressed flat footing 336
13 Perturbation methods — the art of
approximation 343
13.1 Introduction 343
13.2 Algebraic equations 345
13.2.1 Regular perturbations 345
13.2.2 Singular perturbations 347
13.3 Parallel flow with heat dissipation 349
13.4 Freezing of water surface 352
13.5 Method of multiple scales for an oscillator 358
13.5.1 Weakly damped harmonic oscillator 358
13.5.2 Elastic spring with weak nonlinearity 363
13.6 Theory of homogenization 367
13.6.1 Differential equation with periodic coefficient 367
13.6.2 *Darcy s law in seepage flow 370
13.7 *Envelope of a propagating wave 376
13.8 Boundary layer technique 381
13.9 Seepage flow in an aquifer with slowly varying depth 384
13.10 Water table near a cracked sheet pile 390
13.11 * Vibration of a soil layer 395
13.11.1 Formulation 395
13.11.2 The outer solution 397
13.11.3 The boundary layer correction 399
14 Computer algebra for perturbation analysis 408
14.1 Getting started 408
14.2 Algebraic and trigonometric operations 409
14.2.1 Elementary operations 409
14.2.2 Functions 411
14.2.3 Algebraic reductions 412
14.2.4 Trigonometric reductions 413
14.2.5 Substitutions and manipulations 414
14.3 Exact and perturbation methods for algebraic equations 417
14.4 Calculus 121
14.4.1 Differentiation 421
14.4.2 Integration 423
xii Contents
14.5 Ordinary differential equations 426
14.6 Pipe flow in a vertical thermal gradient 427
14.7 Duffing problem by multiple scales 435
14.8 Evolution of wave envelope on a nonlinear string 441
Appendices 447
Bibliography 453
Index 457
|
| any_adam_object | 1 |
| author | Mei, Chiang C. |
| author_facet | Mei, Chiang C. |
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| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620/.00151 |
| dewey-search | 620/.00151 |
| dewey-sort | 3620 3151 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T18:02:31Z |
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| isbn | 0521460530 |
| language | English |
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| spelling | Mei, Chiang C. Verfasser aut Mathematical analysis in engineering how to use the basic tools Chiang C. Mei 1. publ. Cambridge u.a. Cambridge Univ. Press 1995 XVII, 461 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier "This user-friendly text shows how to use mathematics to formulate, solve, and analyze physical problems." "Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at center stage; that is, it starts with the problem, finds the mathematics that suits it, and ends with a mathematical analysis of the physics. The emphasis throughout is on engineering applications rather than mathematical formalities." "Physical examples are selected primarily from applied mechanics, a field central to many branches of engineering and applied science, and they range from the simple to the more sophisticated. Among mathematical topics included in the book are Fourier series, separation of variables, Bessel functions, Fourier and Laplace transforms, Green's functions, and complex function theories. Also covered are advanced topics such as Riemann-Hilbert techniques, perturbation methods, and practical topics such as symbolic computation."--BOOK JACKET. Ciencias da engenharia larpcal Matematica aplicada larpcal Engineering mathematics Analysis (DE-588)4001865-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Ingenieur (DE-588)4026955-3 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Mathematik (DE-588)4037944-9 s Ingenieur (DE-588)4026955-3 s Ingenieurwissenschaften (DE-588)4137304-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007369868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mei, Chiang C. Mathematical analysis in engineering how to use the basic tools Ciencias da engenharia larpcal Matematica aplicada larpcal Engineering mathematics Analysis (DE-588)4001865-9 gnd Mathematik (DE-588)4037944-9 gnd Ingenieur (DE-588)4026955-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4037944-9 (DE-588)4026955-3 (DE-588)4137304-2 |
| title | Mathematical analysis in engineering how to use the basic tools |
| title_auth | Mathematical analysis in engineering how to use the basic tools |
| title_exact_search | Mathematical analysis in engineering how to use the basic tools |
| title_full | Mathematical analysis in engineering how to use the basic tools Chiang C. Mei |
| title_fullStr | Mathematical analysis in engineering how to use the basic tools Chiang C. Mei |
| title_full_unstemmed | Mathematical analysis in engineering how to use the basic tools Chiang C. Mei |
| title_short | Mathematical analysis in engineering |
| title_sort | mathematical analysis in engineering how to use the basic tools |
| title_sub | how to use the basic tools |
| topic | Ciencias da engenharia larpcal Matematica aplicada larpcal Engineering mathematics Analysis (DE-588)4001865-9 gnd Mathematik (DE-588)4037944-9 gnd Ingenieur (DE-588)4026955-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Ciencias da engenharia Matematica aplicada Engineering mathematics Analysis Mathematik Ingenieur Ingenieurwissenschaften |
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