Differential equations: a first course on ODE and a brief introduction to PDE
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2019]
|
| Schriftenreihe: | De Gruyter textbook
|
| Schlagwörter: | |
| Links: | https://d-nb.info/1188479288/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031650604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 293 Seiten Illustrationen, Diagramme (überwiegend farbig) |
| ISBN: | 9783110650037 3110650037 |
Internformat
MARC
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| 020 | |a 9783110650037 |c hardcover |9 978-3-11-065003-7 | ||
| 020 | |a 3110650037 |c hardcover |9 3-11-065003-7 | ||
| 024 | 3 | |a 9783110650037 | |
| 035 | |a (OCoLC)1126013194 | ||
| 035 | |a (DE-599)DNB1188479288 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
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| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Ahmad, Shair |d 1934- |e Verfasser |0 (DE-588)1144305713 |4 aut | |
| 245 | 1 | 0 | |a Differential equations |b a first course on ODE and a brief introduction to PDE |c Shair Ahmad, Antonio Ambrosetti |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XV, 293 Seiten |b Illustrationen, Diagramme (überwiegend farbig) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter textbook | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ambrosetti, Antonio |d 1944-2020 |e Verfasser |0 (DE-588)111667070 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-065286-4 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-065008-2 |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1188479288/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031650604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-031650604 | |
Datensatz im Suchindex
| _version_ | 1819360767960416256 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
ACKNOWLEDGMENT
*
IX
1
1.1
1.2
1.3
1.4
1.5
A
BRIEF
SURVEY
OF
SOME
TOPICS
IN
CALCULUS
*
1
FIRST
PARTIAL
DERIVATIVES
*
1
SECOND
PARTIAL
DERIVATIVES
-----
2
LINE
INTEGRALS
-----
3
THE
DIVERGENCE
THEOREM
-----
4
FOURIER
SERIES
-----
5
2
2.1
2.2
2.2.1
2.3
2.4
2.5
FIRST
ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
7
INTRODUCTION
-----
7
LINEAR
HOMOGENEOUS
EQUATIONS
-----
7
CAUCHY
PROBLEM
-----
9
LINEAR
NONHOMOGENEOUS
EQUATIONS
*
11
APPLICATIONS
TO
RC
ELECTRIC
CIRCUITS
-----
15
EXERCISES-----
19
3
3.1
3.1.1
3.2
3.2.1
3.2.2
3.3
3.4
3.5
ANALYTICAL
STUDY
OF
FIRST
ORDER
DIFFERENTIAL
EQUATIONS
*
21
GENERAL
FIRST
ORDER
DIFFERENTIAL
EQUATIONS
*
21
INITIAL
VALUE
PROBLEM
-----
23
EXISTENCE
AND
UNIQUENESS
RESULTS
-----
23
ON
UNIQUENESS
-----
27
LOCAL
VS.
GLOBAL
EXISTENCE
-----
29
QUALITATIVE
PROPERTIES
OF
SOLUTIONS
-----
30
APPENDIX
-----
34
EXERCISES
-----
41
4
4.1
4.2
4.3
4.4
4.5
4.6
4.6.1
4.6.2
4.6.3
4.6.4
SOLVING
AND
ANALYZING
SOME
NONLINEAR
FIRST
ORDER
EQUATIONS
*
43
SEPARABLE
EQUATIONS
-----
43
AN
APPLICATION:
THE
LOGISTIC
EQUATION
IN
POPULATION
DYNAMICS
-----
45
HOMOGENEOUS
EQUATIONS
-----
49
BERNOULLI
*
S
EQUATION
*
52
CLAIRAUT
*
S
EQUATION
-----
54
EXERCISES-----
57
EXERCISES
ON
SEPARABLE
EQUATIONS
*
57
EXERCISES
ON
HOMOGENEOUS
EQUATIONS
-----
57
EXERCISES
ON
BERNOULLI
EQUATIONS
-----
58
EXERCISES
ON
CLAIRAUT
EQUATIONS
-----
58
XII
CONTENTS
5
5.1
5.2
5.2.1
5.3
5.4
5.5
5.6
EXACT
DIFFERENTIAL
EQUATIONS
*
59
EXACT
EQUATIONS
-----
59
SOLVING
EXACT
EQUATIONS
-----
60
THE
INITIAL
VALUE
PROBLEM
FOR
EXACT
EQUATIONS
*
61
GENERAL
SOLUTION
OF
EXACT
EQUATIONS
*
63
INTEGRATING
FACTOR
-----
68
APPENDIX
-----
70
EXERCISES
-----
71
6
6.1
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.3
6.3.1
6.3.2
6.3.3
6.4
6.5
6.5.1
6.5.2
6.5.3
SECOND
ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
73
PRELIMINARIES
-----
73
GENERAL
SOLUTION
OF
[X]
=
H
-----
74
LINEAR
DEPENDENCE
AND
INDEPENDENCE
*
75
GENERAL
SOLUTION
OF
HOMOGENEOUS
EQUATION
-----
78
GENERAL
SOLUTION
OF
THE
NON-HOMOGENEOUS
EQUATION
-----
79
APPENDIX:
REDUCTION
OF
ORDER
METHOD
*
80
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
82
THE
HOMOGENEOUS
CASE
-----
82
APPLICATIONS
-----
84
THE
NON-HOMOGENEOUS
CASE
-----87
EULER
*
S
EQUATION
-----
91
EXERCISES
-----93
EXERCISES
ON
LINEAR
DEPENDENCE
AND
INDEPENDENCE
*
93
EXERCISES
ON
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
93
EXERCISES
ON
EULER
EQUATIONS
-----
94
7
7.1
7.2
7.2.1
7.3
HIGHER
ORDER
LINEAR
EQUATIONS
*
95
GENERAL
RESULTS
-----
95
HIGHER
ORDER
LINEAR
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
96
EULER
EQUATIONS
-----
102
EXERCISES
*
103
8
8.1
8.2
8.3
8.4
8.5
SYSTEMS
OF
FIRST
ORDER
EQUATIONS
*
105
GENERAL
PRELIMINARIES
-----
105
LINEAR
SYSTEMS
*
106
LINEAR
SYSTEMS
WITH
CONSTANT
COEFFICIENTS
*
110
APPENDIX:
THE
EXPONENTIAL
MATRIX
-----
121
EXERCISES
*
123
9
9.1
9.2
PHASE
PLANE
ANALYSIS
*
125
PRELIMINARIES
*
125
PHASE
PLANE
ANALYSIS:
SOME
EXAMPLES
*
126
CONTENTS
*
XIII
9.3 PERIODIC
SOLUTIONS
-----
129
9.3.1
REMARKABLE
EXAMPLES
-----
132
9.4
VAN
DER
POL
*
S
EQUATION
-----
134
9.5
HOMOCLINIC
AND
HETEROCLINIC
SOLUTIONS
-----
137
9.6
ON
PLANAR
AUTONOMOUS
SYSTEMS
*
141
9.6.1
THE
LOTKA-VOLTERRA
PREY-PREDATOR
SYSTEM
-----
141
9.6.2
LIMIT
CYCLES
-----
145
9.7
EXERCISES-----
147
10
INTRODUCTION
TO
STABILITY
-----
149
10.1
DEFINITION
OF
STABILITY
-----
149
10.2
STABILITY
OF
LINEAR
SYSTEMS
-----
150
10.2.1
STABILITY
OF
2
X
2
LINEAR
SYSTEMS
-----
151
10.2.2
STABILITY
FOR
LINEAR
HOMOGENEOUS
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
-----
156
10.3
STABILITY
OF
CONSERVATIVE
SYSTEMS
-----
158
10.4
THE
LYAPUNOV
DIRECT
METHOD
-----
160
10.5
STABILITY
BY
LINEARIZATION
-----
162
10.6
FURTHER
REMARKS
-----
165
10.6.1
STABLE
AND
UNSTABLE
LIMIT
CYCLES
-----
165
10.6.2
HYPERBOLIC
EQUILIBRIA:
STABLE
AND
UNSTABLE
MANIFOLDS
-----
166
10.6.3
CHANGE
OF
STABILITY:
BIFURCATION
OF
EQUILIBRIA
-----
167
10.7
EXERCISES-----
169
11
SERIES
SOLUTIONS
FOR
LINEAR
DIFFERENTIAL
EQUATIONS
*
173
11.1
A
BRIEF
OVERVIEW
OF
POWER
SERIES
*
173
11.2
ORDINARY
POINTS
-----
174
11.3
BESSEL
FUNCTIONS
-----
177
11.3.1
BESSEL
FUNCTIONS
OF
FIRST
KIND
-----
178
11.3.2
GENERAL
SOLUTION
OF
(S
M
)
AND
BESSEL
FUNCTIONS
OF
SECOND
KIND
-----
181
11.4
SINGULAR
POINTS:
THE
FROBENIUS
METHOD
-----
182
11.5 EXERCISES-----
186
12
LAPLACE
TRANSFORM
*
187
12.1
DEFINITION
-----
187
12.2
PROPERTIES
OF
-----
188
12.3
INVERSE
LAPLACE
TRANSFORM
-----
191
12.4
SOLVING
DIFFERENTIAL
EQUATIONS
BY
LAPLACE
TRANSFORM
*
192
12.5 EXERCISES-----
199
13
A
PRIMER
ON
EQUATIONS
OF
STURM-LIOUVILLE
TYPE
*
201
13.1
PRELIMINARIES
-----
201
XIV
*
CONTENTS
13.2
13.2.1
13.2.2
13.3
13.4
14
14.1
14.1.1
14.2
14.3
15
15.1
15.1.1
15.1.2
15.1.3
15.1.4
15.2
15.2.1
15.3
15.3.1
15.3.2
15.3.3
15.3.4
15.4
15.4.1
15.4.2
15.4.3
16
16.1
16.2
16.3
16.3.1
16.3.2
16.4
16.5
OSCILLATION
FOR
SELF-ADJOINT
EQUATIONS
*
203
STURM
SEPARATION
AND
COMPARISON
THEOREMS
*
203
CHECKING
THE
OSCILLATORY
STATUS
OF
EQUATIONS
*
208
STURM-LIOUVILLE
EIGENVALUE
PROBLEMS
*
212
EXERCISES
*
217
A
PRIMER
ON
LINEAR
PDE
IN
2D.
I:
FIRST
ORDER
EQUATIONS
*
221
FIRST
ORDER
LINEAR
EQUATIONS
IN
2D
*
221
LINEAR
TRANSPORT
EQUATIONS
*
221
APPENDIX:
AN
INTRODUCTION
TO
INVISCID
BURGERS
*
EQUATION
*
231
EXERCISES
*
234
A
PRIMER
ON
LINEAR
PDE
IN
2D.
II:
SECOND
ORDER
EQUATIONS
*
237
THE
LAPLACE
EQUATION
*
237
DIRICHLET
PROBLEM
ON
A
BALL
AND
THE
METHOD
OF
SEPARATION
OF
VARIABLES
*
238
THE
MAXIMUM
PRINCIPLE
*
245
UNIQUENESS
OF
THE
DIRICHLET
PROBLEM
*
246
APPENDIX:
DIRICHLET
*
S
INTEGRAL
*
246
THE
HEAT
EQUATION
*
248
APPENDIX:
FURTHER
PROPERTIES
OF
THE
HEAT
EQUATION
-----
250
THE
VIBRATING
STRING
EQUATION
*
253
AN
INITIAL
VALUE
PROBLEM
FOR
THE
VIBRATING
STRING:
D
*
ALEMBERT
*
S
FORMULA
*
254
APPENDIX:
CONTINUOUS
DEPENDENCE
ON
THE
INITIAL
CONDITIONS
*
256
THE
METHOD
OF
THE
CHARACTERISTICS
*
257
A
BOUNDARY
VALUE
PROBLEM
FOR
THE
VIBRATING
STRING:
THE
METHOD
OF
SEPARATION
OF
VARIABLES
*
260
EXERCISES
*
264
EXERCISES
ON
THE
LAPLACE
EQUATION
*
264
EXERCISES
ON
THE
HEAT
EQUATION
*
265
EXERCISES
ON
D
*
ALEMBERT
*
S
EQUATION
*
266
THE
EULER-LAGRANGE
EQUATIONS
IN
THE
CALCULUS
OF
VARIATIONS;
AN
INTRODUCTION
*
267
FUNCTIONALS
-----
267
THE
EULER-LAGRANGE
EQUATION
*
268
LEAST
TIME
PRINCIPLES
*
273
THE
BRACHISTOCHRONE
-----
273
FERMAT
*
S
PRINCIPLE
IN
GEOMETRICAL
OPTICS
*
278
STATIONARY
SOLUTIONS
VS.
MINIMA
*
281
ON
THE
ISOPERIMETRIC
PROBLEM
*
282
CONTENTS
-----
XV
16.6
THE
STURM-LIOUVILLE
EIGENVALUE
PROBLEM
REVISITED
*
284
16.7
EXERCISES-----
288
BIBLIOGRAPHY
-----
289
INDEX
*
291
|
| any_adam_object | 1 |
| author | Ahmad, Shair 1934- Ambrosetti, Antonio 1944-2020 |
| author_GND | (DE-588)1144305713 (DE-588)111667070 |
| author_facet | Ahmad, Shair 1934- Ambrosetti, Antonio 1944-2020 |
| author_role | aut aut |
| author_sort | Ahmad, Shair 1934- |
| author_variant | s a sa a a aa |
| building | Verbundindex |
| bvnumber | BV046272830 |
| classification_rvk | SK 500 |
| ctrlnum | (OCoLC)1126013194 (DE-599)DNB1188479288 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV046272830 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:47:54Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110650037 3110650037 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031650604 |
| oclc_num | 1126013194 |
| open_access_boolean | |
| owner | DE-634 DE-19 DE-BY-UBM DE-83 DE-703 DE-11 DE-20 |
| owner_facet | DE-634 DE-19 DE-BY-UBM DE-83 DE-703 DE-11 DE-20 |
| physical | XV, 293 Seiten Illustrationen, Diagramme (überwiegend farbig) |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter textbook |
| spellingShingle | Ahmad, Shair 1934- Ambrosetti, Antonio 1944-2020 Differential equations a first course on ODE and a brief introduction to PDE Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4123623-3 |
| title | Differential equations a first course on ODE and a brief introduction to PDE |
| title_auth | Differential equations a first course on ODE and a brief introduction to PDE |
| title_exact_search | Differential equations a first course on ODE and a brief introduction to PDE |
| title_full | Differential equations a first course on ODE and a brief introduction to PDE Shair Ahmad, Antonio Ambrosetti |
| title_fullStr | Differential equations a first course on ODE and a brief introduction to PDE Shair Ahmad, Antonio Ambrosetti |
| title_full_unstemmed | Differential equations a first course on ODE and a brief introduction to PDE Shair Ahmad, Antonio Ambrosetti |
| title_short | Differential equations |
| title_sort | differential equations a first course on ode and a brief introduction to pde |
| title_sub | a first course on ODE and a brief introduction to PDE |
| topic | Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differentialgleichung Lehrbuch |
| url | https://d-nb.info/1188479288/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031650604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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