Linear algebra and differential equations using MATLAB:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Pacific Grove [u.a.]
Brooks/Cole
1999
|
| Series: | A Gary W. Ostedt book
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 704 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0534354254 |
Staff View
MARC
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| 245 | 1 | 0 | |a Linear algebra and differential equations using MATLAB |c Martin Golubitsky ; Michael Dellnitz |
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| 650 | 4 | |a Differential equations |x Data processing | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
PREFACE VIII
CHAPTER 1 PRELIMINARIES 1
1.1 Vectors and Matrices 1
1.2 MATLAB 4
1.3 Special Kinds of Matrices 7
1.4 The Geometry of Vector Operations 9
CHAPTER2 SOLVING LINEAR EQUATIONS 16
2.1 Systems of Linear Equations and Matrices 17
2.2 The Geometry of Low Dimensional Solutions 24
2.3 Gaussian Elimination 33
2.4 Reduction to Echelon Form 45
2.5 Linear Equations with Special Coefficients 52
2.6 *Uniqueness of Reduced Echelon Form 58
CHAPTER 3 MATRICES AND LINEARITY 61
3.1 Matrix Multiplication of Vectors 62
3.2 Matrix Mappings 67
3.3 Linearity 72
3.4 The Principle of Superposition 79
3.5 Composition and Multiplication of Matrices 83
Hi
3.6 Properties of Matrix Multiplication 88
3.7 Solving Linear Systems and Inverses 92
3.8 Determinants of 2 x 2 Matrices 101
CHAPTER4 SOLVING ORDINARY DIFFERENTIAL EQUATIONS 106
4.1 A Single Differential Equation 107
4.2 Graphing Solutions to Differential Equations 119
4.3 Phase Space Pictures and Equilibria 126
4.4 *Separation of Variables 133
4.5 Uncoupled Linear Systems of Two Equations 142
4.6 Coupled Linear Systems 149
4.7 The Initial Value Problem and Eigenvectors 153
4.8 Eigenvalues of 2 x 2 Matrices 162
4.9 Initial Value Problems Revisited 168
4.10 *Markov Chains 175
CHAPTERS VECTOR SPACES 185
5.1 Vector Spaces and Subspaces 186
5.2 Construction of Subspaces 192
5.3 Spanning Sets and MATLAB 198
5.4 Linear Dependence and Linear Independence 201
5.5 Dimension and Bases 206
5.6 The Proof of the Main Theorem 211
CHAPTER6 CLOSED FORM SOLUTIONS FOR PLANAR ODES 218
6.1 The Initial Value Problem 219
6.2 Closed Form Solutions by the Direct Method 225
6.3 Solutions Using Matrix Exponentials 234
6.4 Linear Normal Form Planar Systems 241
6.5 Similar Matrices 244
6.6 *Formulas for Matrix Exponentials 251
6.7 Second Order Equations 256
CHAPTER7 QUALITATIVE THEORY OF PLANAR ODES 263
7.1 Sinks, Saddles, and Sources 263
7.2 Phase Portraits of Sinks 270
7.3 Phase Portraits of Nonhyperbolic Systems 278
CHAPTER 8 DETERMINANTS AND EIGENVALUES 285
8.1 Determinants 285
8.2 Eigenvalues 297
8.3 * Appendix: Existence of Determinants 305
CHAPTER9 LINEAR MAPS AND CHANGES OF COORDINATES 309
9.1 Linear Mappings and Bases 309
9.2 Row Rank Equals Column Rank 316
9.3 Vectors and Matrices in Coordinates 320
9.4 Matrices of Linear Maps on a Vector Space 331
CHAPTER 10 ORTHOGONALITY 336
10.1 Orthonormal Bases 336
10.2 Least Squares Approximations 340
10.3 Least Squares Fitting of Data 347
10.4 Symmetric Matrices 356
10.5 Orthogonal Matrices and QR Decompositions 360
CHAPTER11 AUTONOMOUS PLANAR NONLINEAR SYSTEMS 368
11.1 Introduction 369
11.2 Equilibria and Linearization 375
11.3 Periodic Solutions 384
11.4 Stylized Phase Portraits 390
CHAPTER 12 BIFURCATION THEORY 394
12.1 Two Species Population Models 395
12.2 Examples of Bifurcations 402
12.3 The Continuous Flow Stirred Tank Reactor 416
12.4 The Remaining Global Bifurcations 423
12.5 *Saddle Node Bifurcations Revisited 428
12.6 *Hopf Bifurcations Revisited 434
CHAPTER 13 MATRIX NORMAL FORMS 440
13.1 Real Diagonalizable Matrices 440
13.2 Simple Complex Eigenvalues 446
13.3 Multiplicity and Generalized Eigenvectors 456
13.4 The Jordan Normal Form Theorem 462
13.5 * Appendix: Markov Matrix Theory 471
13.6 * Appendix: Proof of Jordan Normal Form 475
CHAPTER 14 HIGHER DIMENSIONAL SYSTEMS 479
14.1 Linear Systems in Jordan Normal Form 480
14.2 Qualitative Theory near Equilibria 489
14.3 MATLAB ode45 in One Dimension 495
14.4 Higher Dimensional Systems Using ode45 503
14.5 Quasiperiodic Motions and Tori 509
14.6 Chaos and the Lorenz Equation 516
CHAPTER 15 LINEAR DIFFERENTIAL EQUATIONS 524
15.1 Solving Systems in Original Coordinates 525
15.2 Higher Order Equations 537
15.3 Linear Differential Operators 544
15.4 Undetermined Coefficients 550
15.5 Periodic Forcing and Resonance 557
CHAPTER 16 LAPLACE TRANSFORMS 564
16.1 The Method of Laplace Transforms 565
16.2 Laplace Transforms and Their Computation 571
16.3 Partial Fractions 579
16.4 Discontinuous Forcing 584
16.5 RLC Circuits 590
CHAPTER17 ADDITIONAL TECHNIQUES FOR SOLVING ODES 596
17.1 Nonconstant Coefficient Linear Equations 597
17.2 Variation of Parameters for Systems 602
17.3 The Wronskian 608
17.4 Higher Order Equations 611
17.5 Simplification by Substitution 619
17.6 Exact Differential Equations 623
17.7 Hamiltonian Systems 633
CHAPTER 18 NUMERICAL SOLUTIONS OF ODES 639
18.1 A Description of Numerical Methods 640
18.2 Error Bounds for Euler s Method 652
18.3 Local and Global Error Bounds 658
18.4 Appendix: Variable Step Methods 667
matiab COMMANDS 669
ANSWERS TO SELECTED ODD NUMBERED PROBLEMS 675
INDEX 697
|
| any_adam_object | 1 |
| author | Golubitsky, Martin 1945- Dellnitz, Michael |
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| bvnumber | BV012720115 |
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| callnumber-label | QA185 |
| callnumber-raw | QA185.D37 |
| callnumber-search | QA185.D37 |
| callnumber-sort | QA 3185 D37 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 915 ST 601 |
| ctrlnum | (OCoLC)42960871 (DE-599)BVBBV012720115 |
| dewey-full | 512/.5/0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.5/0285 |
| dewey-search | 512/.5/0285 |
| dewey-sort | 3512 15 3285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:32:29Z |
| institution | BVB |
| isbn | 0534354254 |
| language | English |
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| physical | XIV, 704 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Brooks/Cole |
| record_format | marc |
| series2 | A Gary W. Ostedt book |
| spelling | Golubitsky, Martin 1945- Verfasser (DE-588)10805621X aut Linear algebra and differential equations using MATLAB Martin Golubitsky ; Michael Dellnitz Pacific Grove [u.a.] Brooks/Cole 1999 XIV, 704 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier A Gary W. Ostedt book MATLAB Algèbre linéaire - Informatique Dataprocessing gtt Gewone differentiaalvergelijkingen gtt Lineaire algebra gtt MATLAB gtt Numerieke methoden gtt Équations différentielles - Informatique Datenverarbeitung Algebras, Linear Data processing Differential equations Data processing MATLAB (DE-588)4329066-8 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s MATLAB (DE-588)4329066-8 s DE-604 Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Dellnitz, Michael Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008647458&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Golubitsky, Martin 1945- Dellnitz, Michael Linear algebra and differential equations using MATLAB MATLAB Algèbre linéaire - Informatique Dataprocessing gtt Gewone differentiaalvergelijkingen gtt Lineaire algebra gtt MATLAB gtt Numerieke methoden gtt Équations différentielles - Informatique Datenverarbeitung Algebras, Linear Data processing Differential equations Data processing MATLAB (DE-588)4329066-8 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4020929-5 (DE-588)4035811-2 |
| title | Linear algebra and differential equations using MATLAB |
| title_auth | Linear algebra and differential equations using MATLAB |
| title_exact_search | Linear algebra and differential equations using MATLAB |
| title_full | Linear algebra and differential equations using MATLAB Martin Golubitsky ; Michael Dellnitz |
| title_fullStr | Linear algebra and differential equations using MATLAB Martin Golubitsky ; Michael Dellnitz |
| title_full_unstemmed | Linear algebra and differential equations using MATLAB Martin Golubitsky ; Michael Dellnitz |
| title_short | Linear algebra and differential equations using MATLAB |
| title_sort | linear algebra and differential equations using matlab |
| topic | MATLAB Algèbre linéaire - Informatique Dataprocessing gtt Gewone differentiaalvergelijkingen gtt Lineaire algebra gtt MATLAB gtt Numerieke methoden gtt Équations différentielles - Informatique Datenverarbeitung Algebras, Linear Data processing Differential equations Data processing MATLAB (DE-588)4329066-8 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | MATLAB Algèbre linéaire - Informatique Dataprocessing Gewone differentiaalvergelijkingen Lineaire algebra Numerieke methoden Équations différentielles - Informatique Datenverarbeitung Algebras, Linear Data processing Differential equations Data processing Gewöhnliche Differentialgleichung Lineare Algebra |
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