Ordinary and partial differential equations for the beginner:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2016]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 239 Seiten |
| ISBN: | 9789814723985 9789814723992 |
Internformat
MARC
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|---|---|---|---|
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| 008 | 161028s2016 |||| 00||| eng d | ||
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| 020 | |a 9789814723992 |c pbk. : alk. paper |9 978-981-4723-99-2 | ||
| 035 | |a (OCoLC)965331638 | ||
| 035 | |a (DE-599)HBZHT019123879 | ||
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| 100 | 1 | |a Székelyhidi, László |d 1977- |e Verfasser |0 (DE-588)129186236 |4 aut | |
| 245 | 1 | 0 | |a Ordinary and partial differential equations for the beginner |c László Székelyhidi, University of Debrecen, Hungary |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xiv, 239 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-029261328 | ||
Datensatz im Suchindex
| _version_ | 1804176724168015872 |
|---|---|
| adam_text | Titel: Ordinary and partial differential equations for the beginner
Autor: Székelyhidi, László
Jahr: 2016
Contents
Preface xiii
1. ORDINARY DIFFERENTIAL EQUATIONS 1
1.1 Basic concepts and terminology 1
1.2 Problems 4
1.3 Auxiliary results from functional analysis 5
1.4 Problems 7
1.5 Approximate solutions. Peano s theorem 8
1.6 Problems 13
1.7 Existence and uniqueness 13
1.8 Problems 18
1.9 Parametric differential equations 19
1.10 Problems 26
1.11 Characteristic function 26
1.12 Problems 28
2. ELEMENTARY SOLUTION METHODS 29
2.1 Separable differential equations 29
2.2 Problems 31
2.3 Differential equations of homogeneous degree 32
2.4 Problems 35
2.5 First order linear differential equations 36
2.6 Problems 38
2.7 Bernoulli equations 39
2.8 Problems * 39
2.9 Riccati equations 40
vii
vjii Ordinary and Partial Differential Equations for the Beginner
2.10 Problems ^
2.11 Exact differential equations 41
2.12 Problems 4^
2.13 Incomplete differential equations 46
2.14 Problems ^
2.15 Implicit differential equations
2.1G Problems ^
2.17 Lagrange and Clairut equations 52
2.18 Problems 54
3. LINEAR DIFFERENTIAL EQUATIONS 55
3.1 Integrals of linear differential equations 55
3.2 Problems 59
3.3 Linear differential equations with constant coefficients . . 59
1 3.4 Problems 51
3.5 Computation of the exponential matrix 63
3.6 Problems • 66
4. FUNCTIONAL DEPENDENCE, INDEPENDENCE 69
4.1 Functional independence 69
4.2 Functional expressibility 72
4.3 First integrals 74
4.4 Problems 76
5. HIGHER ORDER DIFFERENTIAL EQUATIONS 77
5.1 A reduction principle 77
5.2 Problems 79
5.3 Intermediate integrals 79
5.4 Problems 83
5.5 Higher order linear differential equations 83
5.6 Problems 85
5.7 Linear differential equations with constant coefficients . . 86
5.8 Problems 87
5.9 Decreasing the order of linear homogeneous equations . . 88
5.10 Problems 91
5.11 Euler differential equations 91
5.12 Problems 92
5.13 Exponential polynomials 92
Contents ix
5.14 Problems 95
5.15 Boundary value problems 95
5.16 Problems 101
5.17 Power series solutions 101
5.18 Problems 106
5.19 The Laplace transform 106
5.20 Problems 109
5.21 The Fourier transform of exponential polynomials 110
5.22 Problems 118
6. FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 119
6.1 Homogeneous linear partial differential equations 119
6.2 Problems 123
6.3 Quasilinear partial differential equations 124
6.4 Problems 127
7. THEORY OF CHARACTERISTICS 129
7.1 First order partial differential equations 129
7.2 Problems 131
7.3 Cauchy problem for first order equations 132
7.4 Problems 139
7.5 Special Cauchy problem for first order partial
differential equation 139
7.6 Problems 144
7.7 Complete integral 144
7.8 Problems 150
8. HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS 151
8.1 Special Cauchy problems for higher order partial
differential equations 151
8.2 Theorems of Kovalevskaya and Holmgren 153
8.3 Linear partial differential operators 154
8.4 Problems 158
8.5 Exponential polynomial solutions of partial
differential equations 158
8.6 Problems 163
Ordinary and Partial Differential Equations for the Beginner
9. SECOND ORDER QUASILINEAR PARTIAL
DIFFERENTIAL EQUATIONS 16
9.1 Second order partial differential equations with linear
principal part
9.2 Problems ... ^
9.3 Linear transformation, normal form ^
9.4 Problems ^
9.5 Reduced normal form 169
9.6 Problems ^
9.7 Normal form in two variables ^
9.8 Hyperbolic equations ^
9.9 Problems ^
9.10 Parabolic equations ^7
9.11 Problems ^
9.12 Elliptic equations
9.13 Problems 189
10. SPECIAL PROBLEMS IN TWO VARIABLES 185
10.1 Goursat problem for hyperbolic equations 185
10.2 Problems 188
10.3 Cauchy problem for hyperbolic equations 189
10.4 Problems 192
10.5 Mixed problem for the wave equation 192
10.6 Problems 195
10.7 Fourier method 195
10.8 Problems 192
11. TABLE OF LAPLACE TRANSFORMS 199
12. ANSWERS TO SELECTED PROBLEMS 203
1.2 Basic concepts and terminology 203
1.10 Parametric differential equations 203
1.12 Characteristic function 203
2.2 Separable differential equations 204
2.4 Differential equations of homogeneous degree 204
2.6 First order linear differential equations 205
2.8 Bernoulli equations 205
2.10 Riccati equations onfi
Contents xi
2.12 Exact differential equations 206
2.14 Incomplete differential equations 207
2.16 Implicit differential equations 208
2.18 Lagrange and Clairut equations 210
3.2 Integrals of linear differential equations 211
3.4 Linear differential equations with constant coefficients . . . 211
3.6 Computation of the exponential matrix 213
4.4 First integrals 214
5.4 Intermediate integrals 214
5.6 Higher order linear differential equations 215
5.8 Linear differential equations with constant coefficients . . . 215
5.10 Decreasing the order of linear homogeneous equations . . . 216
5.12 Euler differential equations 216
5.14 Exponential polynomials 216
5.16 Boundary value problems 216
5.20 Power series solutions 217
5.22 The Laplace transform 218
5.24 The Fourier transform of exponential polynomials 218
6.2 Homogeneous linear partial differential equations 219
6.4 Quasilinear partial differential equations 219
7.2 First order partial differential equations 220
7.4 Cauchy problem for first order equations 221
7.6 Special Cauchy problem for first order
partial differential equation 221
7.8 Complete integral 221
8.6 Exponential polynomial solutions of partial
differential equations 222
9.2 Second order partial differential equations with linear
principal part 222
9.4 Linear transformation, normal form 223
9.6 Reduced normal form 224
9.9 Hyperbolic equations 225
9.11 Parabolic equations 225
9.13 Elliptic equations 225
10.2 Goursat problem for hyperbolic equations 229
10.4 Cauchy problem for hyperbolic equations 229
10.6 Mixed problem for the wave equation 229
10.8 Fourier method 229
xii Ordinary and Partial Differential Equations for the Beginner
Bibliography 231
Index 233
|
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| author | Székelyhidi, László 1977- |
| author_GND | (DE-588)129186236 |
| author_facet | Székelyhidi, László 1977- |
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| author_variant | l s ls |
| building | Verbundindex |
| bvnumber | BV043851016 |
| classification_rvk | SK 500 |
| classification_tum | MAT 350f |
| ctrlnum | (OCoLC)965331638 (DE-599)HBZHT019123879 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:36:44Z |
| institution | BVB |
| isbn | 9789814723985 9789814723992 |
| language | English |
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| physical | xiv, 239 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
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| publisher | World Scientific |
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| spelling | Székelyhidi, László 1977- Verfasser (DE-588)129186236 aut Ordinary and partial differential equations for the beginner László Székelyhidi, University of Debrecen, Hungary New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2016] © 2016 xiv, 239 Seiten txt rdacontent n rdamedia nc rdacarrier Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029261328&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Székelyhidi, László 1977- Ordinary and partial differential equations for the beginner Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Ordinary and partial differential equations for the beginner |
| title_auth | Ordinary and partial differential equations for the beginner |
| title_exact_search | Ordinary and partial differential equations for the beginner |
| title_full | Ordinary and partial differential equations for the beginner László Székelyhidi, University of Debrecen, Hungary |
| title_fullStr | Ordinary and partial differential equations for the beginner László Székelyhidi, University of Debrecen, Hungary |
| title_full_unstemmed | Ordinary and partial differential equations for the beginner László Székelyhidi, University of Debrecen, Hungary |
| title_short | Ordinary and partial differential equations for the beginner |
| title_sort | ordinary and partial differential equations for the beginner |
| topic | Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029261328&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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