Ordinary and partial differential equations: with special functions, Fourier series, and boundary value problems
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
[2009]
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 410 Seiten Illustrationen, Diagramme |
| ISBN: | 9780387791456 |
Internformat
MARC
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| 100 | 1 | |a Agarwal, Ravi P. |d 1947- |0 (DE-588)112040187 |4 aut | |
| 245 | 1 | 0 | |a Ordinary and partial differential equations |b with special functions, Fourier series, and boundary value problems |c Ravi P. Agarwal ; Donal O'Regan |
| 264 | 1 | |a New York, NY |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a xiv, 410 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Fourier analysis | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
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| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a O'Regan, Donal |d 1959- |0 (DE-588)138809879 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-79146-3 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016604880&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805082899381223424 |
|---|---|
| adam_text |
Contents
Preface
vii
1.
Solvable Differential Equations
1
2.
Second-Order Differential Equations
8
3.
Preliminaries to Series Solutions
15
4.
Solution at an Ordinary Point
23
5.
Solution at a Singular Point
31
6.
Solution at a Singular Point (Cont'd.)
37
7.
Legendre Polynomials and Functions
47
8.
Chebyshev, Hermite and Laguerre Polynomials
57
9.
Bessel Functions
64
10.
Hyper geometric Functions
75
11.
Piecewise Continuous and Periodic Functions
83
12.
Orthogonal Functions and Polynomials
90
13.
Orthogonal Functions and Polynomials (Cont'd.)
95
14.
Boundary Value Problems
104
15.
Boundary Value Problems (Cont'd.)
109
16.
Green's Functions
119
17.
Regular Perturbations
129
18.
Singular Perturbations
138
19.
Sturm-Liouville Problems
145
20.
Eigenfunction Expansions
157
21.
Eigenfunction Expansions (Cont'd.)
163
22.
Convergence of the Fourier Series
171
23.
Convergence of the Fourier Series (Cont'd.)
176
24.
Fourier Series Solutions of Ordinary Differential Equations
187
xjv Contents
25.
Partial Differential Equations
194
26.
First-Order Partial Differential Equations
202
27.
Solvable Partial Differential Equations
210
28.
The Canonical Forms
219
29.
The Method of Separation of Variables
227
30.
The One-Dimensional Heat Equation
234
31.
The One-Dimensional Heat Equation (Cont'd.)
241
32.
The One-Dimensional Wave Equation
249
33.
The One-Dimensional Wave Equation (Cont'd.)
256
34.
Laplace Equation in Two Dimensions
266
35.
Laplace Equation in Polar Coordinates
275
36.
Two-Dimensional Heat Equation
284
3T. Two-Dimensional Wave Equation
292
38.
Laplace Equation in Three Dimensions
300
39.
Laplace Equation in Three Dimensions (Cont'd.)
306
40.
Nonhomogeneous Equations
316
41.
Fourier Integral and Transforms
323
42.
Fourier Integral and Transforms (Cont'd.)
330
43.
Fourier Transform Method for Partial DEs
338
44.
Fourier Transform Method for Partial DEs (Cont'd.)
344
45.
Laplace Transforms
354
46.
Laplace Transforms (Cont'd.)
361
47.
Laplace Transform Method for Ordinary DEs
374
48.
Laplace Transform Method for Partial DEs
384
49.
Well-Posed Problems
394
50.
Verification of Solutions
399
References for Further Reading
405
Index 4Q7 |
| adam_txt |
Contents
Preface
vii
1.
Solvable Differential Equations
1
2.
Second-Order Differential Equations
8
3.
Preliminaries to Series Solutions
15
4.
Solution at an Ordinary Point
23
5.
Solution at a Singular Point
31
6.
Solution at a Singular Point (Cont'd.)
37
7.
Legendre Polynomials and Functions
47
8.
Chebyshev, Hermite and Laguerre Polynomials
57
9.
Bessel Functions
64
10.
Hyper geometric Functions
75
11.
Piecewise Continuous and Periodic Functions
83
12.
Orthogonal Functions and Polynomials
90
13.
Orthogonal Functions and Polynomials (Cont'd.)
95
14.
Boundary Value Problems
104
15.
Boundary Value Problems (Cont'd.)
109
16.
Green's Functions
119
17.
Regular Perturbations
129
18.
Singular Perturbations
138
19.
Sturm-Liouville Problems
145
20.
Eigenfunction Expansions
157
21.
Eigenfunction Expansions (Cont'd.)
163
22.
Convergence of the Fourier Series
171
23.
Convergence of the Fourier Series (Cont'd.)
176
24.
Fourier Series Solutions of Ordinary Differential Equations
187
xjv Contents
25.
Partial Differential Equations
194
26.
First-Order Partial Differential Equations
202
27.
Solvable Partial Differential Equations
210
28.
The Canonical Forms
219
29.
The Method of Separation of Variables
227
30.
The One-Dimensional Heat Equation
234
31.
The One-Dimensional Heat Equation (Cont'd.)
241
32.
The One-Dimensional Wave Equation
249
33.
The One-Dimensional Wave Equation (Cont'd.)
256
34.
Laplace Equation in Two Dimensions
266
35.
Laplace Equation in Polar Coordinates
275
36.
Two-Dimensional Heat Equation
284
3T. Two-Dimensional Wave Equation
292
38.
Laplace Equation in Three Dimensions
300
39.
Laplace Equation in Three Dimensions (Cont'd.)
306
40.
Nonhomogeneous Equations
316
41.
Fourier Integral and Transforms
323
42.
Fourier Integral and Transforms (Cont'd.)
330
43.
Fourier Transform Method for Partial DEs
338
44.
Fourier Transform Method for Partial DEs (Cont'd.)
344
45.
Laplace Transforms
354
46.
Laplace Transforms (Cont'd.)
361
47.
Laplace Transform Method for Ordinary DEs
374
48.
Laplace Transform Method for Partial DEs
384
49.
Well-Posed Problems
394
50.
Verification of Solutions
399
References for Further Reading
405
Index 4Q7 |
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| author | Agarwal, Ravi P. 1947- O'Regan, Donal 1959- |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:31:29Z |
| indexdate | 2024-07-20T07:39:59Z |
| institution | BVB |
| isbn | 9780387791456 |
| language | English |
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| spelling | Agarwal, Ravi P. 1947- (DE-588)112040187 aut Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems Ravi P. Agarwal ; Donal O'Regan New York, NY Springer [2009] © 2009 xiv, 410 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Universitext Boundary value problems Differential equations Differential equations, Partial Fourier analysis Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s O'Regan, Donal 1959- (DE-588)138809879 aut Erscheint auch als Online-Ausgabe 978-0-387-79146-3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016604880&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Agarwal, Ravi P. 1947- O'Regan, Donal 1959- Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems Boundary value problems Differential equations Differential equations, Partial Fourier analysis Partielle Differentialgleichung (DE-588)4044779-0 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4020929-5 |
| title | Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems |
| title_auth | Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems |
| title_exact_search | Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems |
| title_exact_search_txtP | Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems |
| title_full | Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems Ravi P. Agarwal ; Donal O'Regan |
| title_fullStr | Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems Ravi P. Agarwal ; Donal O'Regan |
| title_full_unstemmed | Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems Ravi P. Agarwal ; Donal O'Regan |
| title_short | Ordinary and partial differential equations |
| title_sort | ordinary and partial differential equations with special functions fourier series and boundary value problems |
| title_sub | with special functions, Fourier series, and boundary value problems |
| topic | Boundary value problems Differential equations Differential equations, Partial Fourier analysis Partielle Differentialgleichung (DE-588)4044779-0 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Boundary value problems Differential equations Differential equations, Partial Fourier analysis Partielle Differentialgleichung Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016604880&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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