Introduction to differential equations:
"The pdf contains a draft title page, draft copyright page and a draft manuscript"--
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island, USA
AMS American Mathematical Society
[2022]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Pure and applied undergraduate texts
52 |
| Schlagworte: | |
| Online-Zugang: | Rezension Inhaltsverzeichnis |
| Zusammenfassung: | "The pdf contains a draft title page, draft copyright page and a draft manuscript"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiv, 388 Seiten Illustrationen |
| ISBN: | 9781470467623 |
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| 245 | 1 | 0 | |a Introduction to differential equations |c Michael E. Taylor |
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Datensatz im Suchindex
| _version_ | 1804183108534140928 |
|---|---|
| adam_text | Contents Preface ix Some basic notation Chapter 1. Single differential equations 1.1. The exponential and trigonometric functions xiii 1 3 Exercises 1.2. First order linear equations 9 13 Exercises 16 1.3. 17 Separable equations Exercises 21 1.4. Second order equations-reducible cases Exercises 21 23 1.5. Newton’s equations for motion in onedimension 23 Exercises 26 1.6. The pendulum Exercises 27 34 1.7. 35 Motion with resistance Exercises 1.8. Linearization 36 37 Exercises 1.9. Second order constant-coefficient linear equations-homogeneous 38 38 Exercises 43 1.10. Nonhomogeneous equations I-undetermined coefficients Exercises 1.11. Forced pendulum-resonance 44 48 49 v
Contents vi Exercises 1.12. Spring motion 51 52 Exercises 1.13. RLC circuits Exercises 1.14. Nonhomogeneous equations Il-variation of parameters 53 53 56 56 Exercises 58 1.15. Variable coefficient second orderequations Exercises 59 61 1.16. Bessel’s equation Exercises 1.17. Higher order linear equations Exercises 1.18. The Laplace transform Exercises 62 67 68 69 70 77 l.A. The genesis of Bessel’s equation:PDE in polar coordinates 78 l.B. Euler’s gamma function 80 l.C. Differentiating power series Chapter 2. Linear algebra 2.1. Vector spaces 82 87 88 Exercises 89 2.2. Linear transformations and matrices Exercises 90 93 2.3. Basis and dimension Exercises 94 98 2.4. Matrix representation of a linear transformation Exercises 99 101 2.5. Determinants and invertibility Exercises 102 107 2.6. Eigenvalues and eigenvectors Exercises 110 111 2.7. Generalized eigenvectors and theminimal polynomial Exercises 112 117 2.8. Triangular matrices Exercises 118 120 2.9. Inner products and norms Exercises 121 125 2.10. Norm, trace, and adjoint of a linear transformation 126
Contents vii Exercises 2.11. Self-adjoint and skew-adjoint transformations 128 129 Exercises 2.12. Unitary and orthogonal transformations Exercises 2.A. The Jordan canonical form 2.B. Schur’s upper triangular representation 2.C. The fundamental theorem of algebra 131 132 135 138 139 140 Chapter 3. Linear systems of differential equations 3.1. The matrix exponential Exercises 3.2. Exponentials and trigonometric functions 143 144 150 153 Exercises 3.3. First order systems derived from higher order equations Exercises 3.4. Nonhomogeneous equations and Duhamel’s formula Exercises 3.5. Simple electrical circuits Exercises 3.6. Second order systems Exercises 155 156 158 158 160 161 165 166 171 3.7. Curves in R3 and the Frenet-Serret equations Exercises 3.8. Variable coefficient systems Exercises 3.9. Variation of parameters and Duhamel’s formula Exercises 3.10. Power series expansions Exercises 3.11. Regular singular points Exercises 3.A. Logarithms of matrices 3.B. The matrix Laplace transform 3.C. Complex analytic functions 172 177 178 182 184 186 186 193 194 204 206 207 210 Chapter 4. Nonlinear systems of differential equations 4.1. Existence and uniqueness of solutions Exercises 4.2. Dependence of solutions on initial data andother parameters 213 215 221 224
viii Contents Exercises 4.3. Vector fields, orbits, and flows Exercises 4.4. Gradient vector fields Exercises 4.5. Newtonian equations 227 228 242 245 251 251 Exercises 4.6. Central force problems and two-body planetary motion Exercises 4.7. Variational problems and the stationary action principle 255 256 262 264 Exercises 4.8. The brachistochrone problem Exercises 4.9. The double pendulum Exercises 4.10. Momentum-quadratic Hamiltonian systems Exercises 4.11. Numerical study-difference schemes Exercises 4.12. Limit sets and periodic orbits Exercises 4.13. Predator-prey equations Exercises 4.14. Competing species equations Exercises 4.15. Chaos in multidimensional systems Exercises 4.A. The derivative in several variables 4.B. Convergence, compactness, and continuity 4.C. Critical points that are saddles 4.D. Blown up phase portrait at a critical point 4.E. Periodic solutions of x + x = εψ^χ) 4.F. A dram of potential theory 4.G. Brouwer’s fixed-point theorem 269 274 278 278 282 282 286 287 294 295 304 306 316 320 324 326 336 337 340 343 352 358 364 366 4.H. Geodesic equations on surfaces 4.1. Rigid body motion in Rn and geodesics on SO{n) 368 371 Bibliography 381 Index 385
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| adam_txt |
Contents Preface ix Some basic notation Chapter 1. Single differential equations 1.1. The exponential and trigonometric functions xiii 1 3 Exercises 1.2. First order linear equations 9 13 Exercises 16 1.3. 17 Separable equations Exercises 21 1.4. Second order equations-reducible cases Exercises 21 23 1.5. Newton’s equations for motion in onedimension 23 Exercises 26 1.6. The pendulum Exercises 27 34 1.7. 35 Motion with resistance Exercises 1.8. Linearization 36 37 Exercises 1.9. Second order constant-coefficient linear equations-homogeneous 38 38 Exercises 43 1.10. Nonhomogeneous equations I-undetermined coefficients Exercises 1.11. Forced pendulum-resonance 44 48 49 v
Contents vi Exercises 1.12. Spring motion 51 52 Exercises 1.13. RLC circuits Exercises 1.14. Nonhomogeneous equations Il-variation of parameters 53 53 56 56 Exercises 58 1.15. Variable coefficient second orderequations Exercises 59 61 1.16. Bessel’s equation Exercises 1.17. Higher order linear equations Exercises 1.18. The Laplace transform Exercises 62 67 68 69 70 77 l.A. The genesis of Bessel’s equation:PDE in polar coordinates 78 l.B. Euler’s gamma function 80 l.C. Differentiating power series Chapter 2. Linear algebra 2.1. Vector spaces 82 87 88 Exercises 89 2.2. Linear transformations and matrices Exercises 90 93 2.3. Basis and dimension Exercises 94 98 2.4. Matrix representation of a linear transformation Exercises 99 101 2.5. Determinants and invertibility Exercises 102 107 2.6. Eigenvalues and eigenvectors Exercises 110 111 2.7. Generalized eigenvectors and theminimal polynomial Exercises 112 117 2.8. Triangular matrices Exercises 118 120 2.9. Inner products and norms Exercises 121 125 2.10. Norm, trace, and adjoint of a linear transformation 126
Contents vii Exercises 2.11. Self-adjoint and skew-adjoint transformations 128 129 Exercises 2.12. Unitary and orthogonal transformations Exercises 2.A. The Jordan canonical form 2.B. Schur’s upper triangular representation 2.C. The fundamental theorem of algebra 131 132 135 138 139 140 Chapter 3. Linear systems of differential equations 3.1. The matrix exponential Exercises 3.2. Exponentials and trigonometric functions 143 144 150 153 Exercises 3.3. First order systems derived from higher order equations Exercises 3.4. Nonhomogeneous equations and Duhamel’s formula Exercises 3.5. Simple electrical circuits Exercises 3.6. Second order systems Exercises 155 156 158 158 160 161 165 166 171 3.7. Curves in R3 and the Frenet-Serret equations Exercises 3.8. Variable coefficient systems Exercises 3.9. Variation of parameters and Duhamel’s formula Exercises 3.10. Power series expansions Exercises 3.11. Regular singular points Exercises 3.A. Logarithms of matrices 3.B. The matrix Laplace transform 3.C. Complex analytic functions 172 177 178 182 184 186 186 193 194 204 206 207 210 Chapter 4. Nonlinear systems of differential equations 4.1. Existence and uniqueness of solutions Exercises 4.2. Dependence of solutions on initial data andother parameters 213 215 221 224
viii Contents Exercises 4.3. Vector fields, orbits, and flows Exercises 4.4. Gradient vector fields Exercises 4.5. Newtonian equations 227 228 242 245 251 251 Exercises 4.6. Central force problems and two-body planetary motion Exercises 4.7. Variational problems and the stationary action principle 255 256 262 264 Exercises 4.8. The brachistochrone problem Exercises 4.9. The double pendulum Exercises 4.10. Momentum-quadratic Hamiltonian systems Exercises 4.11. Numerical study-difference schemes Exercises 4.12. Limit sets and periodic orbits Exercises 4.13. Predator-prey equations Exercises 4.14. Competing species equations Exercises 4.15. Chaos in multidimensional systems Exercises 4.A. The derivative in several variables 4.B. Convergence, compactness, and continuity 4.C. Critical points that are saddles 4.D. Blown up phase portrait at a critical point 4.E. Periodic solutions of x" + x = εψ^χ) 4.F. A dram of potential theory 4.G. Brouwer’s fixed-point theorem 269 274 278 278 282 282 286 287 294 295 304 306 316 320 324 326 336 337 340 343 352 358 364 366 4.H. Geodesic equations on surfaces 4.1. Rigid body motion in Rn and geodesics on SO{n) 368 371 Bibliography 381 Index 385 |
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| spelling | Taylor, Michael Eugene 1946- Verfasser (DE-588)123980119 aut Introduction to differential equations Michael E. Taylor Second edition Providence, Rhode Island, USA AMS American Mathematical Society [2022] xiv, 388 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 52 Includes bibliographical references and index "The pdf contains a draft title page, draft copyright page and a draft manuscript"-- Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differential equations Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) Ordinary differential equations -- General theory -- Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions Ordinary differential equations -- General theory -- Linear equations and systems, general Ordinary differential equations -- General theory -- Nonlinear equations and systems, general Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-6772-2 ebook Pure and applied undergraduate texts 52 (DE-604)BV035489189 52 https://zbmath.org/?q=an%3A1236.34001 zbMATH Rezension 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=033031106&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Introduction to differential equations |
| title_auth | Introduction to differential equations |
| title_exact_search | Introduction to differential equations |
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| title_full | Introduction to differential equations Michael E. Taylor |
| title_fullStr | Introduction to differential equations Michael E. Taylor |
| title_full_unstemmed | Introduction to differential equations Michael E. Taylor |
| title_short | Introduction to differential equations |
| title_sort | introduction to differential equations |
| topic | Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Gewöhnliche Differentialgleichung |
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