Elementary differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
CRC Press, Taylor & Francis Group
2019
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| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 536 Seiten Illustrationen, Diagramme |
| ISBN: | 9781498776080 |
Staff View
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| adam_text | Contents Preface xi 1 Introduction 1 1.1 Historical Prologue...................................................................... 1 1.2 Definitions and Terminology...................................................... 5 1.3 Solutions and Problems.............................................................. 17 1.4 A Nobel Prize Winning Application.......................................... 27 2 The Initial Value Problem y/ = f(x,y); y(c) = d 33 2.1 Direction Fields............................................................................. 34 2.2 Fundamental Theorems.............................................................. 42 2.3 Solution of Simple First-OrderDifferential Equations 54 .... 2.3.1 Solution of y = g(x).......................................................... 54 2.3.2 Solution of the Separable Equation y — g(x)/h(y) ... 57 2.3.3 Solution of the Linear Equation y = a(x)y + b(x) ... 64 2.4 Numerical Solution...................................................................... 73 2.4.1 Euler’s Method.................................................................. 77 2.4.2 Pitfalls of Numerical Methods........................................... 82 3 Applications of the Initial Value Problem У՛ ~ f(x։y); y(c) = d 3.1 Calculus Revisited 93 ...................................................................... 93 3.2 Learning Theory Models................................................................... 104 3.3 Population Models...........................................................................106 3.4 Simple Epidemic
Models.............................................................. 113 3.5 Falling Bodies...................................................................................118 vii
VIU 3.6 Mixture Problems ...........................................................................121 3.7 Curves of Pursuit...............................................................................128 3.8 Chemical Reactions...................................................................... 4 N-th Order Linear Differential Equations 132 143 4.1 Basic Theory...................................................................................... 144 4.2 Roots of Polynomials.................................................................. 165 4.3 Homogeneous Linear Equations with Constant Coefficients . . 177 4.4 Nonhomogeneous Linear Equations with Constant Coefficients 188 4.5 Initial Value Problems.................................................................. 195 5 The Laplace Transform Method 5.1 The Laplace Transform and Its Properties............................... 199 199 5.2 Using the Laplace Transform and Its Inverse to Solve Initial Value Problems....................................................... 216 5.3 Convolution and the Laplace Transform........................................224 5.4 The Unit Function and Time-Delay Function................................230 5.5 Impulse Function.............................................................................. 239 6 Applications of Linear Differential Equations with Constant Coefficients 247 6.1 Second-Order Differential Equations................................................247 6.1.1 Free Motion ...........................................................................253 6.1.1.1 Free Undamped
Motion............................................254 6.1.1.2 Free Damped Motion............................................... 255 6.1.2 Forced Motion .......................................................................264 6.1.2.1 Undamped Forced Motion........................................264 6.1.2.2 Damped Forced Motion............................................265 6.2 Higher Order Differential Equations................................................269
ix 7 Systems of First-Order Differential Equations 7.1 Properties of Systems of Differential Equations 285 ................ 285 7.2 Writing Systems as Equivalent First-Order Systems . . . 8 Linear Systems of First-Order Differential Equations 297 305 8.1 Matrices and Vectors..................................................................... 305 8.2 Eigenvalues and Eigenvectors.........................................................317 8.3 Linear Systems with Constant Coefficients............................ 330 9 Applications of Linear Systems with Constant Coefficients 347 9.1 Coupled Spring-Mass Systems.........................................................347 9.2 Pendulum Systems......................................................................... 353 9.3 The Path of an Electron................................................................. 355 9.4 Mixture Problems............................................................................. 360 10 Applications of Systems of Equations 369 10.1 Richardson’s Arms Race Model.....................................................369 10.2 Phase-Plane Portraits..................................................................... 378 10.3 Modified Richardson’s Arms Race Models................................. 394 10.4 Lanchester’s Combat Models......................................................... 405 10.5 Models for Interacting Species..................................................... 412 10.6 Epidemics......................................................................................... 430 10.7
Pendulums..................................................................................... 440 10.8 Duffing’s Equation......................................................................... 449 10.9 Van der Pol’s Equation................................................................. 450 10.10 Mixture Problems......................................................................... 451 10.11 The Restricted Three-Body Problem......................................... 454 Appendix A Numerical Solution of the Initial Value Problem у = f(x,y); y(c) = d 459
x Answers to Selected Exercises 489 References 523 Index 527
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:19:59Z |
| institution | BVB |
| isbn | 9781498776080 |
| language | English |
| lccn | 017061579 |
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| physical | xvii, 536 Seiten Illustrationen, Diagramme |
| publishDate | 2019 |
| publishDateSearch | 2019 |
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| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| spelling | Roberts, Charles E. 1942- (DE-588)172346991 aut Elementary differential equations Charles Roberts Second edition Boca Raton CRC Press, Taylor & Francis Group 2019 xvii, 536 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Differential equations Textbooks Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 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=030890787&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roberts, Charles E. 1942- Elementary differential equations Differential equations Textbooks Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Elementary differential equations |
| title_auth | Elementary differential equations |
| title_exact_search | Elementary differential equations |
| title_full | Elementary differential equations Charles Roberts |
| title_fullStr | Elementary differential equations Charles Roberts |
| title_full_unstemmed | Elementary differential equations Charles Roberts |
| title_short | Elementary differential equations |
| title_sort | elementary differential equations |
| topic | Differential equations Textbooks Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differential equations Textbooks Differentialgleichung |
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