Differential equations as models in science and engineering:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
[2016]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxi, 368 Seiten Diagramme |
| ISBN: | 9789814656962 9789814656979 9814656976 |
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| 245 | 1 | 0 | |a Differential equations as models in science and engineering |c Gregory Baker, the Ohio State University, USA |
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Record in the Search Index
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| adam_text | Titel: Differential equations as models in science and engineering
Autor: Baker, Gregory Richard
Jahr: 2016
Contents
Preface vii
A Note to the Student xv
1. Linear Ordinary Differential Equations 1
1.1 Growth and decay ......................................................1
1.1.1 Bacterial growth................................................2
1.1.2 From discrete to continuous....................................6
1.1.3 Conservation of quantity......................................8
1.1.4 Simple electric circuits ........................................11
1.1.5 Abstract viewpoint ............................................13
1.1.6 Exercises........................................................17
1.1.7 Additional deliberations........................................21
1.2 Forcing effects............................................................21
1.2.1 Constant inflow as an input....................................22
1.2.2 Periodic inflow as an input....................................27
1.2.3 Discontinuous inflow as an input..............................31
1.2.4 Abstract viewpoint ............................................34
1.2.5 Exercises........................................................38
1.2.6 General forcing terms..........................................43
1.3 Coefficients with time variation........................................46
1.3.1 Variable river flow..............................................46
1.3.2 Abstract viewpoint ............................................49
1.3.3 Exercises........................................................33
1.3.4 Summary........................................................34
1.3.5 Flowchart: Linear, first-order differential
equations........................................................36
1.4 Second-order equations: Growth and decay ..........................36
1.4.1 A simple chain of chemical reactions..........................57
1.4.2 Chained chemical reactions with forcing......................63
1.4.3 Abstract viewpoint ......................
1.4.4 Exercises......................70
1.4.5 Time-varying coefficients in the differential
equation ............................73
1.5 Second-order equations: Oscillations.................78
1.5.1 Exponentials with complex arguments........................78
1.5.2 Application to differential equations..........................81
1.5.3 The LCR circuit................................................83
1 5.4 Abstract viewpoint ............................................89
1.5.5 Exercises............................91
1.5.6 Higher-order differential equations............................94
1.6 Forcing terms: Resonances..............................................95
1.6.1 LCR circuit with constant applied voltage ..................96
1.6.2 LCR circuit with alternating applied voltage................97
1.6.3 Complex solutions.......................191
1.6.4 Resonance...........................192
1.6.5 Abstract view.........................194
1.6.6 Exercises............................107
1.6.7 General forcing terms....................111
1.6.8 Summary............................115
1.6.9 Flowchart: Linear, second-order differential
equations............................117
2. Periodic Behavior 119
2.1 Periodic functions............................119
2.1.1 Mathematical expression...................119
2.1.2 Periodic forcing of an LCR circuit..............122
2.1.3 Abstract view.........................125
2.1.4 Exercises............................129
2.1.5 Periodic complex functions..................131
2.2 The Fourier series............................132
2.2.1 Construction of a Fourier series ...............134
2.2.2 Calculation of the Fourier coefficients............140
2.2.3 Abstract view..............................................143
2.2.4 Exercises..........................................152
2.2.5 Complex Fourier coefficients.................153
2.3 Symmetry in the Fourier series..............................155
2.3.1 Even and odd functions..............................155
2.3.2 Fourier coefficients for even and odd periodic
functions..................157
2.3.3 Abstract view......................160
2.3.4 Exercises..............161
2.3.5 Other symmetries......................163
3. Boundary Value Problems 167
3.1 Spatially varying steady states ....................167
3.1.1 Steady state transport.....................168
3.1.2 Diffusion............................170
3.1.3 Abstract view .........................176
3.1.4 Exercises............................178
3.2 Bifurcation ...............................180
3.2.1 Column buckling........................180
3.2.2 Abstract viewpoint ......................184
3.2.3 Summary............................186
3.2.4 Exercises............................188
3.3 Forcing effects..............................190
3.3.1 Cooling fins...........................191
3.3.2 Heated plate; homogeneous boundary conditions......191
3.3.3 Heated plate; inhomogeneous boundary
conditions ...........................196
3.3.4 Abstract viewpoint ......................199
3.3.5 Exercises............................203
3.3.6 Flowchart: Linear, second-order boundary-value
problems............................205
4. Linear Partial Differential Equations 207
4.1 Diffusion: Part I ............................207
4.1.1 Transport equations......................208
4.1.2 Initial and boundary conditions ...............210
4.1.3 Exponential solutions.....................213
4.1.4 Separation of variables ....................214
4.1.5 Abstract view .........................224
4.1.6 Exercises............................226
4.2 Diffusion: Part II............................229
4.2.1 Inhomogeneous boundary conditions.............229
4.2.2 Homogeneous solution.....................231
4.2.3 Time-dependent boundary conditions............235
4.2.4 Abstract view.........................238
4.2.5 Exercises............................241
4.3 Propagation...............................244
4.3.1 Transmission line .......................24o
4.3.2 Initial and boundary conditions ...............246
4.3.3 The homogeneous solution..................247
4.3.4 Inhomogeneous boundary conditions.............254
4.3.5 No resistance..........................257
4.3.6 Abstract view .........................258
4.3.7 Exercises......................261
4 3.8 Inhomogeneous partial diderential equations........263
4.4 Laplace s equation.....................264
4.4.1 Heat transport in two dimensions ..............265
4.4.2 Steady state solution as a particular solution........268
4.4.3 Electrostatic potential.....................275
4.4.4 Abstract view.........................279
4.4.5 Exercises............................281
4.4.6 Heat transport in two dimensions - continued .......283
5. Systems of Differential Equations 287
5.1 First-order equations..........................287
5.1.1 Population dynamics .....................287
5.1.2 Abstract view.........................295
5.1.3 Exercises............................299
5.2 Homogeneous linear equations.....................303
5.2.1 Basic concepts.........................304
5.2.2 Chemical reactions.......................305
5.2.3 The LCR circuit........................310
5.2.4 Abstract viewpoint ......................313
5.2.5 Exercises............................318
5.2.6 Higher dimensional systems..................320
5.3 Inhomogeneous linear equations....................322
5.3.1 LCR circuit with constant applied voltage .........323
5.3.2 LCR circuit with alternating applied voltage........324
5.3.3 Stability ............................325
5.3.4 Abstract view.......................327
5.3.5 Exercises..................................................330
5.3.6 General forcing term................................331
5.4 Nonlinear autonomous equations............................333
5.4.1 Predator-prey model............................333
5.4.2 Abstract view........................340
5.4.3 Exercises...............343
Appendix A The Exponential Function 345
A.l A review of its properties ........345
Appendix B The Taylor Series 347
B.l Aderivationofthe Taylor series..........347
B.2 Accuracy of the truncated Taylor series . . .............349
B.d standard examples ..................................351
Appendix C Systems of Linear Equations 353
C.l Algebraic equations...........................353
C.2 Gaussian elimination..........................354
C.3 Matrix form...............................355
C.4 Eigenvalues and eigenvectors .....................356
Appendix D Complex Variables 359
D.1 Basic properties.............................359
D.2 Connections with trigonometric functions ..............363
Index 365
|
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| spelling | Baker, Gregory Richard Verfasser aut Differential equations as models in science and engineering Gregory Baker, the Ohio State University, USA New Jersey World Scientific [2016] © 2016 xxi, 368 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Ingenieurwissenschaften Mathematisches Modell Naturwissenschaft Differential equations / Textbooks Differential equations / Textbooks / Numerical solutions Science / Textbooks / Mathematical models Engineering / Textbooks / Mathematical models Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialgleichung (DE-588)4012249-9 s Mathematische Modellierung (DE-588)7651795-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029048996&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baker, Gregory Richard Differential equations as models in science and engineering Ingenieurwissenschaften Mathematisches Modell Naturwissenschaft Differential equations / Textbooks Differential equations / Textbooks / Numerical solutions Science / Textbooks / Mathematical models Engineering / Textbooks / Mathematical models Differentialgleichung (DE-588)4012249-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)7651795-0 (DE-588)4123623-3 |
| title | Differential equations as models in science and engineering |
| title_auth | Differential equations as models in science and engineering |
| title_exact_search | Differential equations as models in science and engineering |
| title_full | Differential equations as models in science and engineering Gregory Baker, the Ohio State University, USA |
| title_fullStr | Differential equations as models in science and engineering Gregory Baker, the Ohio State University, USA |
| title_full_unstemmed | Differential equations as models in science and engineering Gregory Baker, the Ohio State University, USA |
| title_short | Differential equations as models in science and engineering |
| title_sort | differential equations as models in science and engineering |
| topic | Ingenieurwissenschaften Mathematisches Modell Naturwissenschaft Differential equations / Textbooks Differential equations / Textbooks / Numerical solutions Science / Textbooks / Mathematical models Engineering / Textbooks / Mathematical models Differentialgleichung (DE-588)4012249-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Ingenieurwissenschaften Mathematisches Modell Naturwissenschaft Differential equations / Textbooks Differential equations / Textbooks / Numerical solutions Science / Textbooks / Mathematical models Engineering / Textbooks / Mathematical models Differentialgleichung Mathematische Modellierung Lehrbuch |
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