Analysis and differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2015
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | IX, 244 S. graph. Darst. |
| ISBN: | 9789814635950 |
Internformat
MARC
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| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2015 | |
| 300 | |a IX, 244 S. |b graph. Darst. | ||
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| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Differential equations |v Textbooks | |
| 650 | 4 | |a Calculus |v Textbooks | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027839116 | ||
Datensatz im Suchindex
| _version_ | 1804153060049551360 |
|---|---|
| adam_text | Contents
Preface
1. Introduction
1.1 Differential equations..................
1.2 Second order differential equations . . .
1.3 Differential equations for functions on Rp
1.4 Multidimensional differential equations .
1.5 Overview ...............................
1.6 Exercises ..............................
v
1
1
3
9
15
19
20
2. Expansions with orthogonal polynomials
2.1 Introduction....................
2.2 Laguerre’s polynomials..........
2.3 Hcrmite’s polynomials...........
2.4 Legendre s polynomials .........
2.5 Generalizations.................
2.6 Bilinear functions..............
2.7 Hermite’s polynomials in K2 . · ·
2.8 Legendre s polynomials in 1R2 . ·
2.9 Exercises ......................
23
23
25
30
38
42
44
47
50
55
3- Differential and integral calculus
3.1 Differentiability of functions.......
3.2 Maximum and minimum of functions
3.3 Euler֊Lagrange conditions............
3.4 Integral calculus....................
VII
viii Analysis and differential equations
3.5 Partial derivatives of elliptic functions.................... 71
3.6 Applications.................................................... 80
3.7 Exercises ...................................................... 87
4. Linear differential equations 89
4.1 First order differential equations in .......................... 89
4.2 Second order linear differential equations in K+................ 95
4.3 Sturm-Liouville second order differential equations .... 108
4.4 Applications................................................... 112
4.5 Nonlinear differential equations............................... 113
4.6 Differential equations of higher orders...................... 119
4.7 Exercises ..................................................... 122
5. Linear differential equations in 125
5.1 Introduction................................................. 125
5.2 Laplace’s differential equation.............................. 130
5.3 Potential equations.......................................... 132
5.4 Heat conduction equations...................................... 137
5.5 Wave differential equations ................................... 146
5.6 Elasticity equations........................................... 154
5.7 Exercises...................................................... 156
6. Partial differential equations 157
6.1 Partial differential equations in R2........................... 157
6.2 First order linear partial differential equations.............. 159
6.3 Second order linear partial differential equations............. 170
6.4 Multidimensional differential equations........................ 171
6.5 Lotka-Volterra equations....................................... 177
6.6 Birth-and-death differential equations......................... 181
6.7 Poincare-Lorenz differential system............................ 181
6.8 Exercises ..................................................... 187
7. Special functions 189
7.1 Eulerian functions............................................. 189
7.2 Airy function.................................................. 196
7.3 Bessel’s function.............................................. 198
7.4 Boyd’s function................................................ 199
7.5 Her mite s function......................................... . 199
Contents ix
7.6 Laguerre s functions........................................ 201
7.7 Hydrogen atom equation and others........................... 202
7.8 Exercises .................................................. 203
8. Solutions 205
8.1 Integral and differential calculus ......................... 205
8.2 Orthogonal polynomials...................................... 211
8.3 Calculus and optimization................................... 214
8.4 Linear differential equations............................... 220
8.5 Linear differential equations in ........................... 226
8.6 Partial differential equations.............................. 228
8.7 Special functions........................................... 231
8.8 Programs.................................................... 235
Bibliography 241
Index 243
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:20:36Z |
| institution | BVB |
| isbn | 9789814635950 |
| language | English |
| lccn | 014042633 |
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| physical | IX, 244 S. graph. Darst. |
| publishDate | 2015 |
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| publisher | World Scientific |
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| spelling | Pons, Odile 1953- Verfasser (DE-588)1158864035 aut Analysis and differential equations Odile Pons Singapore [u.a.] World Scientific 2015 IX, 244 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Differential equations Textbooks Calculus Textbooks Differentialgleichung (DE-588)4012249-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialgleichung (DE-588)4012249-9 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027839116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pons, Odile 1953- Analysis and differential equations Differential equations Textbooks Calculus Textbooks Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4123623-3 |
| title | Analysis and differential equations |
| title_auth | Analysis and differential equations |
| title_exact_search | Analysis and differential equations |
| title_full | Analysis and differential equations Odile Pons |
| title_fullStr | Analysis and differential equations Odile Pons |
| title_full_unstemmed | Analysis and differential equations Odile Pons |
| title_short | Analysis and differential equations |
| title_sort | analysis and differential equations |
| topic | Differential equations Textbooks Calculus Textbooks Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differential equations Textbooks Calculus Textbooks Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027839116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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