Differential equations and group methods for scientists and engineers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
1992
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 201 Seiten |
| ISBN: | 0849344425 |
Staff View
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| 245 | 1 | 0 | |a Differential equations and group methods for scientists and engineers |c James M. Hill, Department of Mathematics, The University of Wollongong, Wollongong, N.S.W., Australia |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 1992 | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Preface vii
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Ordinary differential equations 1
1.3 Partial differential equations 5
1.4 Abel equations of the second kind 7
Problems 13
Chapter 2 One parameter groups and Lie series 17
2.1 Introduction 17
2.2 One parameter transformation groups 17
2.3 Lie series and the Commutation theorem 22
Problems 26
Chapter 3 Invariance of standard linear ordinary differential equations 31
3.1 Introduction 31
3.2 First order equation y + p(x)y = q(x) 31
3.3 Second order homogeneous equation y + p(x)y = 0 34
3.4 Third order homogeneous equation y + p(x)y + q(x)y = 0 37
3.5 Fourth order self adjoint equation y + p{x)y ] + q(x)y =0 40
Problems 43
x Table of contents
Chapter 4 First order ordinary differential equations 51
4.1 Introduction 51
4.2 Infinitesimal versions of y and y = F(x,y) and the 52
fundamental problem
4.3 Integrating factors and canonical coordinates for y = F(x, y) 53
4.4 The alternative problem 57
4.5 The fundamental problem and singular solutions of t/ = F(x,y) 60
4.6 Invariance of the associated first order partial differential 62
equation
4.7 Lie s problem and area preserving groups 64
Problems 68
Chapter 5 Second and higher order ordinary differential equations 79
5.1 Introduction 79
5.2 Infinitesimal versions of y and y = F(x,y,y ) 79
5.3 Examples of the determination of £{x,y) and n(x,y) 81
5.4 Determination of the most general differential equation 84
invariant under a given one parameter group
5.5 Applications 88
Problems 93
Chapter 6 Linear partial differential equations 99
6.1 Introduction 99
6.2 Formulae for partial derivatives 100
6.3 Classical groups for the diffusion equation 102
6.4 Simple examples for the diffusion equation 103
6.5 Moving boundary problems 106
6.6 Fokker Planck equation 109
6.7 Examples for the Fokker Planck equation 114
6.8 Non classical groups for the diffusion equation 118
Problems 120
Table of contents xi
Chapter 7 Non linear partial differential equations 133
7.1 Introduction 133
7.2 Formulae for partial derivatives 135
7.3 Classical groups for non linear diffusion 137
7.4 Non classical groups for non linear diffusion 142
7.5 Transformations of the non linear diffusion equation 144
7.6 Similarity solutions of the non linear diffusion equation 145
7.7 High order non linear diffusion 151
Problems 156
Bibliography 167
Answers and hints 169
Summary of research areas 201
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:49:15Z |
| institution | BVB |
| isbn | 0849344425 |
| language | English |
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| physical | XI, 201 Seiten |
| publishDate | 1992 |
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| publisher | CRC Press |
| record_format | marc |
| spelling | Hill, James M. Verfasser aut Differential equations and group methods for scientists and engineers James M. Hill, Department of Mathematics, The University of Wollongong, Wollongong, N.S.W., Australia Boca Raton, Fla. [u.a.] CRC Press 1992 XI, 201 Seiten txt rdacontent n rdamedia nc rdacarrier Differential equations Numerical solutions Transformation groups Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Transformationsgruppe (DE-588)4127386-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004225423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hill, James M. Differential equations and group methods for scientists and engineers Differential equations Numerical solutions Transformation groups Differentialgleichung (DE-588)4012249-9 gnd Transformationsgruppe (DE-588)4127386-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4127386-2 (DE-588)4128130-5 |
| title | Differential equations and group methods for scientists and engineers |
| title_auth | Differential equations and group methods for scientists and engineers |
| title_exact_search | Differential equations and group methods for scientists and engineers |
| title_full | Differential equations and group methods for scientists and engineers James M. Hill, Department of Mathematics, The University of Wollongong, Wollongong, N.S.W., Australia |
| title_fullStr | Differential equations and group methods for scientists and engineers James M. Hill, Department of Mathematics, The University of Wollongong, Wollongong, N.S.W., Australia |
| title_full_unstemmed | Differential equations and group methods for scientists and engineers James M. Hill, Department of Mathematics, The University of Wollongong, Wollongong, N.S.W., Australia |
| title_short | Differential equations and group methods for scientists and engineers |
| title_sort | differential equations and group methods for scientists and engineers |
| topic | Differential equations Numerical solutions Transformation groups Differentialgleichung (DE-588)4012249-9 gnd Transformationsgruppe (DE-588)4127386-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Differential equations Numerical solutions Transformation groups Differentialgleichung Transformationsgruppe Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004225423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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