Lectures, problems, and solutions for ordinary differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2018]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | x, 561 Seiten Diagramme |
| ISBN: | 9789813226128 9789813226135 |
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MARC
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| 245 | 1 | 0 | |a Lectures, problems, and solutions for ordinary differential equations |c Yuefan Deng, Stony Brook University, USA |
| 250 | |a Second edition | ||
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Record in the Search Index
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| adam_text | Contents
PREFACE.............................................................V
CHAPTER 1 FIRST-ORDER DIFFERENTIAL EQUATIONS...................1
1.1 Definition of Differential Equations........................1
1.2 Slope Fields and Solution Curves...........................10
1.3 Separation of Variables....................................13
1.4 First-Order Linear DEs................................... 19
1.5 The Substitution Methods...................................27
1.5.1 Polynomial Substitution.............................27
1.5.2 Homogeneous DEs.....................................29
1.5.3 Bernoulli DEs.......................................30
1.6 Riccati DEs................................................38
1.7 The Exact DEs..............................................43
1.8 Summary....................................................65
CHAPTER 2 MATHEMATICAL MODELS.................................68
2.1 Newton s Law of Cooling....................................68
2.2 Torricelli s Law for Draining..............................72
2.3 The Population Model.......................................79
2.3.1 introduction........................................79
2.3.2General Population Equation........................80
2.3.3 The Logistic Equation...............................82
2.3.4 Doomsday vs. Extinction.............................86
2.4 Acceleration-Velocity Model................................92
2.4.1 Ne wton sLa ws of Motion.........92
2.4.2 Velocity and A ccelera tion Models..................94
vii
Contents
2.4.3 Air Resistance Model...................................95
2.4.4 Gra vitational A cceieration..........................113
2.5 Windy Day Plane Landing...................................123
2.6 A Swimmer s Problem.......................................131
2.7 River Ferryboat-Docking Problem...........................136
2.8 Equation for Compound Interest............................141
CHAPTER 3 LINEAR DEs OF HIGHER ORDER............................149
3.1 Classifications of Linear DEs.............................149
3.2 Linear Independence.......................................155
3.3 Homogeneous DEs...........................................164
3.3.1 DEs with Constant Coefficients........................164
3.3.2 DEs with Variable Coefficients.......................175
3.4 Inhomogeneous Linear DEs..................................187
3.4.1 Method of Undetermined Coefficients...................187
3.4.2 Variation of Parameters...............................197
CHAPTER 4 SYSTEMS OF LINEAR DEs.................................211
4.1 Basics of System of DEs...................................211
4.2 First-Order Systems and Applications......................214
4.2.1 One Block and One Spring..............................214
4.2.2 Two Blocks and Two Springs............................216
4.2.3 Kirchhoff Circuit La ws...............................217
4.3 The Substitution Method...................................222
4.4 The Operator Method.......................................227
4.5 The Eigen-Analysis Method.................................232
4.6 Examples of Systems of DEs................................256
4.6.1 Predator-prey DEs.....................................256
4.6.2 Cascade of Tanks......................................259
CHAPTER 5 LAPLACE TRANSFORMS.....................................262
5.1 Laplace Transforms........................................262
5.2 Properties of Laplace Transforms..........................264
5.2.1 Laplace Transforms for Polynomials....................265
viii
Contents
5.2.2 The Translator Property...............................268
5.2.3 Transforms of Step and Delta Functions................272
5.2.4 The t-multiplication Property.........................276
5.2.5 Periodic Functions.................................. 279
5.2.6 Differentiation and Integration Property..............280
5.3 Inverse Laplace Transforms................................285
5.4 The Convolution of Two Functions..........................290
5.5 Applications..............................................295
APPENDIX A SOLUTIONS TO PROBLEMS..................................315
Chapter 1 First-Order DEs.......................................315
1.1 Definition of DEs.................................... 315
1.2 Slope Fields and Solution Curves.........................320
1.3 Separation of Variables..................................321
1.4 First-Order Linear DEs...................................327
1.5Substitution Methods......................................337
1.6 Riccati DEs............................................357
1.7 The Exact DEs.......................................... 364
Chapter 2 Mathematical Models...................................376
2.1 Ne wton s La w of Cooling................................376
2.2 Torricelli s Law for Draining............................377
2.3 Population Model.........................................385
2.4 Acceleration- Velocity Model.............................393
2.5 Windy Day Plane Landing..................................413
2.6 A Swimmer s Problem......................................422
2.7River Ferryboat-Docking Problem...........................424
2.8 Equation for Compound Interest...........................427
Chapter 3 Linear DEs of Higher Order...........................435
3.1 Classification of Linear DEs.............................435
3.2 Linear Independence......................................437
3.3 Homogeneous DEs..........................................444
3.4 inhomogeneous Linear DEs.................................458
Chapter 4 Systems of Linear DEs.................................481
4.1 Basics of System of DEs..................................481
ix
Contents
4.2 First-Order Systems and Applications...................482
4.3 Substitution Method....................................487
4.4 The Operator Method....................................493
4.5 The Eigen-Analysis Method..............................501
4.6 Examples of Systems....................................509
Chapter 5 Laplace Transforms.................................510
5.2 Properties of Laplace Transforms.......................510
5.3 Inverse Laplace Transforms.............................516
5.4 The Convolution of Two Functions.......................519
5.5 A pplications..........................................521
APPENDIX B LAPLACE TRANSFORMS...................................547
Selected Laplace Transforms..................................547
Selected Properties of Laplace Transforms....................548
APPENDIX C BASIC FORMULAS.......................................551
APPENDIX D ABBREVIATIONS...................................... 553
REFERENCES......................................................557
INDEX......................................................... 559
x
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| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| spelling | Deng, Yuefan (DE-588)1027321356 aut Lectures, problems, and solutions for ordinary differential equations Yuefan Deng, Stony Brook University, USA Second edition New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2018] © 2018 x, 561 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Differential equations Differential equations, Linear Laplace transformation Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030132131&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Deng, Yuefan Lectures, problems, and solutions for ordinary differential equations Differential equations Differential equations, Linear Laplace transformation Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4143389-0 (DE-588)4123623-3 |
| title | Lectures, problems, and solutions for ordinary differential equations |
| title_auth | Lectures, problems, and solutions for ordinary differential equations |
| title_exact_search | Lectures, problems, and solutions for ordinary differential equations |
| title_full | Lectures, problems, and solutions for ordinary differential equations Yuefan Deng, Stony Brook University, USA |
| title_fullStr | Lectures, problems, and solutions for ordinary differential equations Yuefan Deng, Stony Brook University, USA |
| title_full_unstemmed | Lectures, problems, and solutions for ordinary differential equations Yuefan Deng, Stony Brook University, USA |
| title_short | Lectures, problems, and solutions for ordinary differential equations |
| title_sort | lectures problems and solutions for ordinary differential equations |
| topic | Differential equations Differential equations, Linear Laplace transformation Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differential equations Differential equations, Linear Laplace transformation Gewöhnliche Differentialgleichung Aufgabensammlung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030132131&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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