Differential equations: an introduction with Mathematica
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1995
|
| Series: | Textbooks in mathematical sciences
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 491 - 493 |
| Physical Description: | XIII, 503 S. graph. Darst. |
| ISBN: | 3540943013 0387943013 |
Staff View
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| 245 | 1 | 0 | |a Differential equations |b an introduction with Mathematica |c Clay C. Ross |
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Record in the Search Index
| _version_ | 1804124500159102976 |
|---|---|
| adam_text | DIFFERENTIAL EQUATIONS
AN INTRODUCTION WITH
MATHEMATICA
CLAY C. ROSS
THE UNIVERSITY OF THE SOUTH
SPRINGER-VERLAG
NEW YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO HONG KONG BARCELONA BUDAPEST
CONTENTS
PREFACE VI
I
1 ABOU
T DIFFERENTIAL EQUATION
S AND LINEAR ALGEBR
A 1
1.0 INTRODUCTION 1
1.1 SOME LINEAR ALGEBRA 9
1.2 DIFFERENTIAL EQUATIONS FROM SOLUTIONS 14
1.3 NUMERICAL METHODS 19
1.4 UNIQUENESS CONSIDERATIONS 29
1.5 DIFFERENTIAL INCLUSIONS (OPTIONAL) 33
2 FIRST-ORDER DIFFERENTIAL EQUATION
S 37
2.0 INTRODUCTION 37
2.1 FIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS 37
2.2 LINEAR EQUATIONS BY
MATHEMATICA
43
2.3 EXACT EQUATIONS 46
2.4 VARIABLES SEPARABLE 56
2.5 HOMOGENEOUS NONLINEAR DIFFERENTIAL EQUATIONS 62
2.6 BERNOULLI AND RICCATI DIFFERENTIAL EQUATIONS (OPTIONAL) 67
2.7 CLAIRAUT DIFFERENTIAL EQUATIONS (OPTIONAL) 75
3 APPLICATION
S OF FIRST-ORDE
R EQUATION
S 79
3.0 INTRODUCTION 79
3.1 ORTHOGONAL TRAJECTORIES 80
3.2 LINEAR APPLICATIONS 84
3.3 NONLINEAR APPLICATIONS 107
4 HIGHER-ORDER LINEAR DIFFERENTIAL EQUATION
S 119
4.0 INTRODUCTION 119
4.1 THE FUNDAMENTAL THEOREM 120
4.2 MORE LINEAR ALGEBRA 129
XII ! CONTENTS
4.
3 HOMOGENEOU
S SECOND-ORDE
R LINEA
R CONSTAN
T COEFFICIENT
S ...
. 14
3
4.
4 HIGHER-ORDE
R CONSTAN
T COEFFICIENT
S (HOMOGENEOUS
) 15
8
4.
5 TH
E METHO
D OF UNDETERMINE
D COEFFICIENT
S 16
9
4.
6 VARIATIO
N OF PARAMETER
S 18
1
APPLICATION
S OF SECOND-ORDER EQUATIONS 189
5.0 INTRODUCTION 189
5.1 SIMPLE HARMONIC MOTION 190
5.2 DAMPED HARMONIC MOTION 200
5.3 FORCED OSCILLATION 208
5.4 SIMPLE ELECTRONIC CIRCUITS 214
5.5 TWO NONLINEAR EXAMPLES (OPTIONAL) 219
TH
E LAPLACE TRANSFORM 22
3
6.0 INTRODUCTION 223
6.1 THE LAPLACE TRANSFORM 224
6.2 PROPERTIES OF THE LAPLACE TRANSFORM 228
6.3 THE INVERSE LAPLACE TRANSFORM 240
6.4 DISCONTINOUS FUNCTIONS AND THEIR TRANSFORMS 246
HIGHER-ORDE
R DIFFERENTIA
L EQUATION
S WIT
H
VARIABL
E COEFFICIENT
S 25
9
7.0 INTRODUCTIO
N 25
9
7.1 CAUCHY-EULE
R DIFFERENTIA
L EQUATION
S 260
7.2 OBTAININ
G A SECON
D SOLUTIO
N 272
7.3 SUMS
, PRODUCTS
, AN
D RECURSIO
N RELATION
S 27
4
7.4 SERIE
S SOLUTION
S OF DIFFERENTIA
L EQUATION
S 28
4
7.5 SERIE
S SOLUTION
S ABOU
T ORDINAR
Y POINT
S 29
1
7.6 SERIE
S SOLUTIO
N ABOU
T REGULA
R SINGULA
R POINT
S
....
:
300
7.7 IMPORTAN
T CLASSICA
L DIFFERENTIA
L EQUATION
S AN
D FUNCTION
S ...
. 31
8
DIFFERENTIAL SYSTEM
S WIT
H CONSTAN
T COEFFICIENTS 32
3
8.0 INTRODUCTION 323
8.1 REDUCTION TO FIRST-ORDER SYSTEMS 329
8.2 THEORY OF FIRST-ORDER SYSTEMS 336
8.3 FIRST-ORDER CONSTANT COEFFICIENTS SYSTEMS 344
8.4 REPEATED AND COMPLEX ROOTS 364
8.5 NONHOMOGENEOUS EQUATIONS AND BOUNDARY-VALUE PROBLEMS . . . 376
8.6 APPLICATIONS OF SYSTEMS OF DIFFERENTIAL EQUATIONS 390
8.7 PHASE PORTRAITS 405
8.8 TWO NONLINEAR EXAMPLES (OPTIONAL) 426
8.9 DEFECTIVE SYSTEMS OF FIRST-ORDER DIFFERENTIAL
EQUATIONS (OPTIONAL) 432
8.10 SOLUTION OF LINEAR SYSTEMS BY LAPLACE TRANSFORMS (OPTIONAL) . . 438
CONTENTS I XIII
9 DIFFERENTIAL SYSTEM
S WIT
H VARIABLE COEFFICIENTS 445
9.0 INTRODUCTION 445
9.1 CAUCHY-EULER SYSTEMS 446
9.2 SOLUTION ABOUT ORDINARY POINTS 458
9.3 SOLUTION ABOUT REGULAR SINGULAR POINTS 470
A
MATHEMATICAL
GENERAL INTRODUCTIO
N 475
B
MATHEMATICA
STYLE: SOME CONSIDERATIONS 47
7
C
MATHEMATICA
FUNCTIONS FOR DIFFERENTIAL EQUATIONS 48
3
BIBLIOGRAPHY 49
1
INDEX OF
MATHEMATICA
COMMAND
S 495
INDEX 499
|
| any_adam_object | 1 |
| author | Ross, Clay C. |
| author_facet | Ross, Clay C. |
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| dewey-full | 515/.35/078 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35/078 |
| dewey-search | 515/.35/078 |
| dewey-sort | 3515 235 278 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| spelling | Ross, Clay C. Verfasser aut Differential equations an introduction with Mathematica Clay C. Ross New York u.a. Springer 1995 XIII, 503 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Textbooks in mathematical sciences Literaturverz. S. 491 - 493 Mathematica (Computer file) Differentiaalvergelijkingen gtt Mathematica (computerprogramma) gtt Differential equations Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content Differentialgleichung (DE-588)4012249-9 s Mathematica Programm (DE-588)4268208-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006711542&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ross, Clay C. Differential equations an introduction with Mathematica Mathematica (Computer file) Differentiaalvergelijkingen gtt Mathematica (computerprogramma) gtt Differential equations Mathematica Programm (DE-588)4268208-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)4012249-9 (DE-588)4151278-9 (DE-588)4143389-0 |
| title | Differential equations an introduction with Mathematica |
| title_auth | Differential equations an introduction with Mathematica |
| title_exact_search | Differential equations an introduction with Mathematica |
| title_full | Differential equations an introduction with Mathematica Clay C. Ross |
| title_fullStr | Differential equations an introduction with Mathematica Clay C. Ross |
| title_full_unstemmed | Differential equations an introduction with Mathematica Clay C. Ross |
| title_short | Differential equations |
| title_sort | differential equations an introduction with mathematica |
| title_sub | an introduction with Mathematica |
| topic | Mathematica (Computer file) Differentiaalvergelijkingen gtt Mathematica (computerprogramma) gtt Differential equations Mathematica Programm (DE-588)4268208-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematica (Computer file) Differentiaalvergelijkingen Mathematica (computerprogramma) Differential equations Mathematica Programm Differentialgleichung Einführung Aufgabensammlung |
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