An introduction to differential equations: 2 Stochastic modeling, methods and analysis
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2013
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 619 S. graph. Darst. |
| ISBN: | 9789814390071 9789814390064 |
Internformat
MARC
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| 020 | |a 9789814390064 |9 978-981-4390-06-4 | ||
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| 245 | 1 | 0 | |a An introduction to differential equations |n 2 |p Stochastic modeling, methods and analysis |c Anil G. Ladde ; G. S. Ladde |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2013 | |
| 300 | |a XIII, 619 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804149457820844032 |
|---|---|
| adam_text | Titel: Bd. 2. An introduction to differential equations. Stochastic modeling, methods and analysis
Autor: Ladde, Anil G
Jahr: 2013
Contents
Preface v
Acknowledgeuient and Dedication ix
lements of Stochastic Processes and I to Doob Stochastic Calculus 1
.1 Probabilistic Preliminaries...................... 1
.2 Stochastic Random Function .................... 17
.3 Ito Doob Stochastic Calculus .................... 36
.1 Method of Substitution........................ 53
.5 Method of Integration by Parts ................... 58
.6 Notes and Comments......................... 63
2. First-Order Deferential Equations 65
2.1 Mathematical Modeling........................ 06
2.2 integrable Equations......................... 90
2.2.1 General Problem........................ 90
2.2.2 Procedure for Finding a General Solution.......... 92
2.2.3 Initial Value Problem..................... 95
2.2.1 Procedure for Solving the IVP................ 96
2.3 Linear Homogeneous Equations................... 1112
2.3.1 General Problem........................ 103
2.3.2 Procedure for Finding a General Solution.......... 104
2.3.3 Initial Value Problem..................... 116
2.3.1 Procedure for Solving the IVP................ lis
2.1 Linear Nonhomogeneous Equations................. 125
2.1.1 General Problem........................ 126
2.1.2 Procedure for Finding a General Solution.......... 26
2.4.3 Initial Value Problem..................... 137
2.1.1 Procedure for Solving the IVP................ 137
2.5 Fundamental Conceptual Algorithm and Analysis......... 151
2.6 Notes and Comments......................... 172
xii An Introduction to Differential Equations: Vol. 2
3. First-Order Nonlinear Differential Equations 175
3.1 Mathematical Modeling........................ 176
3.2 Method of Energy Functions..................... 198
3.2.1 General Problem........................ 199
3.2.2 Procedure for Finding a General Solution
Representation......................... 200
3.3 Integrable Reduced Equations.................... 202
3.3.1 General Problem........................ 202
3.3.2 Procedure for Finding a General Solution
Representation......................... 203
3.4 Linear Nonhomogeneous Reduced Equations ........... 227
3.4.1 General Problem........................ 227
3.4.2 Procedure for Finding a General Solution
Representation......................... 228
3.5 Variable Separable Equations .................... 252
3.5.1 General Problem........................ 252
3.5.2 Procedure for Finding a General Solution Representation . 252
3.6 Homogeneous Equations....................... 267
3.6.1 General Problem........................ 267
3.6.2 Procedure for Finding a General Solution
Representation......................... 268
3.7 Bernoulli Equations.......................... 287
3.7.1 General Problem........................ 287
3.7.2 Procedure for Finding a General Solution
Representation......................... 287
3.8 Essentially Time-Invariant Equations................ 303
3.8.1 General Problem........................ 303
3.8.2 Procedure for Finding a General Solution
Representation......................... 304
3.9 Notes and Comments......................... 313
4. First-Order Systems of Linear Differential Equations 315
4.1 Mathematical Modeling....................... 32g
4.2 Linear Homogeneous Systems................. 341
4.2.1 General Problem.................... 34^
4.2.2 Procedure for Finding a General Solution.......... 343
4.2.3 Initial Value Problem.................. 35O
4.2.4 Procedure for Solving the IVP............. 353
4.3 Procedure for Finding the Fundamental Matrix Solution..... 375
4.4 General Homogeneous Systems.................. 40i
4.4.1 General Problem.............. 402
4.4.2 Procedure for Finding a General Solution.......... 402
Contents xiii
4.4.3 Initial Value Problem..................... 414
4.4.4 Procedure for solving the IVP................ 414
4.5 Linear Nonhomogeneous Systems.................. 423
4.5.1 General Problem........................ 423
4.5.2 Procedure for Finding a General Solution.......... 423
4.5.3 Initial Value Problem..................... 446
4.5.4 Procedure for Solving the IVP................ 446
4.6 Fundamental Conceptual Algorithms and Analysis ........ 453
4.7 Notes and Comments......................... 474
5. Higher-Order Differential Equations 477
5.1 Mathematical Modeling........................ 477
5.2 Linear Homogeneous Equations................... 481
5.2.1 General Problem........................ 481
5.2.2 Feasibility of Finding a General Solution.......... 486
5.3 Companion Systems.......................... 487
5.3.1 Procedure for Finding the General Solution......... 491
5.4 Linear Nonhomogeneous Equations................. 506
5.4.1 General Problem........................ 506
5.4.2 Procedure for Finding the General Solution......... 507
5.5 The Laplace Transform........................ 509
5.6 Applications of the Laplace Transform............... 521
5.7 Notes and Comments......................... 525
6. Topics in Differential Equations 527
6.1 Fundamental Conceptual Algorithms and Analysis ........ 528
6.2 Method of Variation of Parameters................. 541
6.3 Method of Generalized Variation of Parameters.......... 552
6.4 Differential Inequalities and Comparison Theorem......... 557
6.5 Comparison Theorems........................ 562
6.6 Variational Comparison Method................... 568
6.7 Linear Hybrid Systems........................ 574
6.8 Stochastic Hereditary Systems.................... 580
6.9 Qualitative Properties of Solution Processes............ 586
6.10 Critical Point Theory: Stochastic Versus Deterministic...... 589
6.11 Statistical Properties and Effects of Random Perturbations .... 592
6.12 Notes and Comments......................... 601
Bibliography 603
Index 613
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:23:20Z |
| institution | BVB |
| isbn | 9789814390071 9789814390064 |
| language | English |
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| physical | XIII, 619 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
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| publisher | World Scientific |
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| spelling | Ladde, Anil G. Verfasser (DE-588)1026103401 aut An introduction to differential equations 2 Stochastic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde Singapore [u.a.] World Scientific 2013 XIII, 619 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ladde, Gangaram S. 1940- Verfasser (DE-588)1026102693 aut (DE-604)BV039940165 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025259166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ladde, Anil G. Ladde, Gangaram S. 1940- An introduction to differential equations |
| title | An introduction to differential equations |
| title_auth | An introduction to differential equations |
| title_exact_search | An introduction to differential equations |
| title_full | An introduction to differential equations 2 Stochastic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde |
| title_fullStr | An introduction to differential equations 2 Stochastic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde |
| title_full_unstemmed | An introduction to differential equations 2 Stochastic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde |
| title_short | An introduction to differential equations |
| title_sort | an introduction to differential equations stochastic modeling methods and analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025259166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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