An introduction to differential equations: 1 Deterministic modeling, methods and analysis
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2012
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 523 S. graph. Darst. |
| ISBN: | 9789814368896 9789814368902 981436889X 9814368903 |
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| 245 | 1 | 0 | |a An introduction to differential equations |n 1 |p Deterministic modeling, methods and analysis |c Anil G. Ladde ; G. S. Ladde |
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Record in the Search Index
| _version_ | 1804149454345863168 |
|---|---|
| adam_text | Titel: Bd. 1. An introduction to differential equations. Deterministic modeling, methods and analysis
Autor: Ladde, Anil G
Jahr: 2012
Contents
Preface vii
1. Elements of Matrices, Determinants, and Calculus 1
1.1 Introduction.............................. 1
1.2 Problem-Solving Process....................... 1
1.2.1 Problem analysis........................ 2
1.2.2 Solution (proof) strategies.................. 3
1.3 Algebra of Matrices.......................... 11
1.4 Determinants ............................. 31
1.5 Matrix Calculus............................ 52
1.6 Notes and Comments......................... 89
2. First-Order Differential Equations 91
2.1 Introduction.............................. 91
2.2 Mathematical Modeling........................ 92
2.3 Integrable Equations......................... 100
2.3.1 General problem........................ 101
2.3.2 Procedure for finding a general solution........... 101
2.3.3 Initial value problem ..................... 102
2.3.4 Procedure for solving the rVP................ 103
2.4 Linear Homogeneous Equations................... 109
2.4.1 General problem........................ 109
2.4.2 Procedure for finding a general solution........... 110
2.4.3 Initial value problem ..................... 114
2.4.4 Procedure for solving the IVP................ 115
2.5 Linear Nonhomogeneous Equations................. 121
2.5.1 General problem........................ 122
2.5.2 Procedure for finding a general solution........... 122
2.5.3 Initial value problem ..................... 128
2.5.4 Procedure for solving the IVP................ 128
2.6 Fundamental Conceptual Algorithms and Analysis ........ 142
2.7 Notes and Comments......................... 163
xvi An Introduction to Differential Equations: Vol. 1
3. First-Order Nonlinear Differential Equations 165
3.1 Introduction.............................. 165
3.2 Mathematical Modeling........................ 166
3.3 Energy Function Method....................... 186
3.3.1 General problem........................ 186
3.3.2 Procedure for finding a general solution
representation......................... 187
3.4 Integrable Reduced Equations.................... 189
3.4.1 General problem........................ 189
3.4.2 Procedure for finding a general solution
representation......................... 189
3.5 Linear Nonhomogeneous Reduced Equations............ 200
3.5.1 General problem........................ 201
3.5.2 Procedure for finding a general solution representation . . 201
3.6 Variable Separable Equations .................... 208
3.6.1 General problem........................ 209
3.6.2 Procedure for finding a general solution........... 209
3.7 Homogeneous Equations....................... 221
3.7.1 General problem........................ 222
3.7.2 Procedure for finding a general solution........... 222
3.8 Bernoulli Equations.......................... 233
3.8.1 General problem........................ 233
3.8.2 Procedure for finding a general solution........... 233
3.9 Essentially Time-Invariant Equations................ 245
3.9.1 General problem........................ 245
3.9.2 Procedure for finding a general solution........... 245
3.10 Notes and Comments......................... 251
4. First-Order Systems of Linear Differential Equations 253
4.1 Introduction.............................. 253
4.2 Mathematical Modeling........................ 254
4.3 Linear Homogeneous Systems.................... 285
4.3.1 General problem........................ 286
4.3.2 Procedure for finding a general solution........... 287
4.3.3 Initial value problem ..................... 294
4.3.4 Procedure for the solving rVP................ 295
4.4 Procedure for Finding the Fundamental Matrix Solution..... 307
4.5 General Linear Homogeneous Systems ............... 340
4.5.1 General problem........................ 341
4.5.2 Procedure for finding a general solution........... 341
4.5.3 Initial value problem ..................... 354
4.5.4 Procedure for solving the IVP................ 354
Contents xvii
4.6 Linear Nonhomogeneous Systems.................. 361
4.6.1 General problem........................ 361
4.6.2 Procedure for finding a general solution........... 361
4.6.3 Initial value problem ..................... 378
4.6.4 Procedure for solving the IVP................ 378
4.7 Fundamental Conceptual Algorithm Analysis............ 381
4.8 Notes and Comments......................... 402
5. Higher-Order Linear Differential Equations 405
5.1 Introduction.............................. 405
5.2 Mathematical Modeling........................ 405
5.3 Linear Homogeneous Equations................... 415
5.3.1 General problem........................ 415
5.3.2 Procedure for finding a general solution........... 416
5.3.3 Initial value problem ..................... 418
5.3.4 Procedure for solving the IVP................ 420
5.4 Companion System.......................... 428
5.5 Higher-Order Linear Nonhomogeneous Equations......... 436
5.6 The Laplace Transform........................ 440
5.7 Applications of the Laplace Transform............... 448
5.8 Notes and Comments......................... 455
6. Topics in Differential Equations 457
6.1 Introduction.............................. 457
6.2 Fundamental Conceptual Algorithms and Analysis ........ 458
6.3 Method of Variation of Parameters................. 468
6.4 Generalized Method of Variation of Parameters.......... 473
6.5 Differential Inequalities and Comparison Theorems........ 477
6.6 Energy/Lyapunov Function and Comparison Theorems...... 481
6.7 Variational Comparison Method................... 489
6.8 Linear Hybrid Systems........................ 494
6.8.1 General problem........................ 499
6.9 Linear Hereditary Systems...................... 501
6.9.1 General problem........................ 502
6.10 Qualitative Properties of the Solution Process........... 505
6.11 Linear Stochastic Systems...................... 507
6.12 Notes and Comments......................... 510
Bibliography 513
Index 521
|
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| isbn | 9789814368896 9789814368902 981436889X 9814368903 |
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| spelling | Ladde, Anil G. Verfasser (DE-588)1026103401 aut An introduction to differential equations 1 Deterministic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde Singapore [u.a.] World Scientific 2012 XVII, 523 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ladde, Gangaram S. 1940- Verfasser (DE-588)1026102693 aut (DE-604)BV039940165 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025256860&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 1 Deterministic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde |
| title_fullStr | An introduction to differential equations 1 Deterministic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde |
| title_full_unstemmed | An introduction to differential equations 1 Deterministic modeling, methods and analysis Anil G. Ladde ; G. S. Ladde |
| title_short | An introduction to differential equations |
| title_sort | an introduction to differential equations deterministic modeling methods and analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025256860&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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