Partial differential equations: an introduction with Mathematica and MAPLE
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
River Edge, NJ [u.a.]
World Scientific
2007
|
| Edition: | 2. ed., reprint. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 306 S. graph. Darst. |
| ISBN: | 981238815X 9789812388155 |
Staff View
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| 245 | 1 | 0 | |a Partial differential equations |b an introduction with Mathematica and MAPLE |c Ioannis P. Stavroulakis ; Stepan A. Tersian |
| 250 | |a 2. ed., reprint. | ||
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| 300 | |a XII, 306 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1.
First-order Partial Differential Equations
1
1.1.
Introduction
1
1.2.
Linear First-order Equations
4
1.3.
The Cauchy Problem for First-order Quasi-linear Equations
11
1.4.
General Solutions of Quasi-linear Equations
23
1.5.
Fully-nonlinear First-order Equations
28
2.
Second-order Partial Differential Equations
39
2.1.
Linear Equations
39
2.2.
Classification and Canonical Forms of Equations in
Two Independent Variables
46
2.3.
Classification of Almost-linear Equations in R™
59
3.
One Dimensional Wave Equation
67
3.1.
The Wave Equation on the Whole Line. D Alembert Formula
67
3.2.
The Wave Equation on the Half-line. Reflection Method
78
3.3.
Mixed Problem for the Wave Equation
84
3.4.
Inhomogeneous Wave Equation
87
3.5.
Conservation of the Energy
92
4.
One Dimensional Diffusion Equation
97
4.1.
Maximum-minimum Principle for the Diffusion Equation
97
4.2.
The Diffusion Equation on the Whole Line
103
4.3.
Diffusion on the Half-line
115
4.4.
Inhomogeneous Diffusion Equation on the Whole Line
118
5.
Weak Solutions, Shock Waves and Conservation Laws
123
5.1.
Weak Derivatives and Weak Solutions
123
xi
xij Contents
5.2.
Conservation Laws
130
5.3.
Burgers Equation
140
5.4.
Weak Solutions. Riemann Problem
153
5.5.
Discontinuous Solutions of Conservation Laws.
Rankine-Hugoniot Condition
162
6.
The Laplace Equation
169
6.1.
Harmonic Functions. Maximum-minimum Principle
169
6.2.
Green s Identities
173
6.3.
Green s Functions
182
6.4.
Green s Functions for a Half-space and Sphere
185
6.5.
Harnack s Inequalities and Theorems
193
7.
Fourier Series and Fourier Method for PDEs
199
7.1.
Fourier Series
199
7.2.
Orthonormal
Systems. General Fourier Series
217
7.3.
Fourier Method for the Diffusion Equation
229
7.4.
Fourier Method for the Wave Equation
238
7.5.
Fourier Method for the Laplace Equation
243
8.
Diffusion and Wave Equations in Higher Dimensions
255
8.1.
The Diffusion Equation in Three Dimensional Space
255
8.2.
Fourier Method for the Diffusion Equation in Higher Dimensions
262
8.3. Kirchoff s
Formula for the Wave Equation. Huygens Principle
269
8.4.
Fourier Method for the Wave Equation on the Plane.
Nodal Sets
276
References
287
Answers and Hints to Exercises
291
Index
301
|
| adam_txt |
Contents
1.
First-order Partial Differential Equations
1
1.1.
Introduction
1
1.2.
Linear First-order Equations
4
1.3.
The Cauchy Problem for First-order Quasi-linear Equations
11
1.4.
General Solutions of Quasi-linear Equations
23
1.5.
Fully-nonlinear First-order Equations
28
2.
Second-order Partial Differential Equations
39
2.1.
Linear Equations
39
2.2.
Classification and Canonical Forms of Equations in
Two Independent Variables
46
2.3.
Classification of Almost-linear Equations in R™
59
3.
One Dimensional Wave Equation
67
3.1.
The Wave Equation on the Whole Line. D'Alembert Formula
67
3.2.
The Wave Equation on the Half-line. Reflection Method
78
3.3.
Mixed Problem for the Wave Equation
84
3.4.
Inhomogeneous Wave Equation
87
3.5.
Conservation of the Energy
92
4.
One Dimensional Diffusion Equation
97
4.1.
Maximum-minimum Principle for the Diffusion Equation
97
4.2.
The Diffusion Equation on the Whole Line
103
4.3.
Diffusion on the Half-line
115
4.4.
Inhomogeneous Diffusion Equation on the Whole Line
118
5.
Weak Solutions, Shock Waves and Conservation Laws
123
5.1.
Weak Derivatives and Weak Solutions
123
xi
xij Contents
5.2.
Conservation Laws
130
5.3.
Burgers' Equation
140
5.4.
Weak Solutions. Riemann Problem
153
5.5.
Discontinuous Solutions of Conservation Laws.
Rankine-Hugoniot Condition
162
6.
The Laplace Equation
169
6.1.
Harmonic Functions. Maximum-minimum Principle
169
6.2.
Green's Identities
173
6.3.
Green's Functions
182
6.4.
Green's Functions for a Half-space and Sphere
185
6.5.
Harnack's Inequalities and Theorems
193
7.
Fourier Series and Fourier Method for PDEs
199
7.1.
Fourier Series
199
7.2.
Orthonormal
Systems. General Fourier Series
217
7.3.
Fourier Method for the Diffusion Equation
229
7.4.
Fourier Method for the Wave Equation
238
7.5.
Fourier Method for the Laplace Equation
243
8.
Diffusion and Wave Equations in Higher Dimensions
255
8.1.
The Diffusion Equation in Three Dimensional Space
255
8.2.
Fourier Method for the Diffusion Equation in Higher Dimensions
262
8.3. Kirchoff 's
Formula for the Wave Equation. Huygens' Principle
269
8.4.
Fourier Method for the Wave Equation on the Plane.
Nodal Sets
276
References
287
Answers and Hints to Exercises
291
Index
301 |
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| id | DE-604.BV035110396 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:17:14Z |
| indexdate | 2024-07-09T21:22:32Z |
| institution | BVB |
| isbn | 981238815X 9789812388155 |
| language | English |
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| spelling | Stavroulakis, Ioannis P. Verfasser aut Partial differential equations an introduction with Mathematica and MAPLE Ioannis P. Stavroulakis ; Stepan A. Tersian 2. ed., reprint. River Edge, NJ [u.a.] World Scientific 2007 XII, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier aMathematica (Computer file) aMaple (Computer file) aMathematical physics Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Maple Programm (DE-588)4209397-1 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Mathematica Programm (DE-588)4268208-3 s DE-604 Maple Programm (DE-588)4209397-1 s Tersian, Stepan A. Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stavroulakis, Ioannis P. Partial differential equations an introduction with Mathematica and MAPLE aMathematica (Computer file) aMaple (Computer file) aMathematical physics Partielle Differentialgleichung (DE-588)4044779-0 gnd Maple Programm (DE-588)4209397-1 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4209397-1 (DE-588)4268208-3 |
| title | Partial differential equations an introduction with Mathematica and MAPLE |
| title_auth | Partial differential equations an introduction with Mathematica and MAPLE |
| title_exact_search | Partial differential equations an introduction with Mathematica and MAPLE |
| title_exact_search_txtP | Partial differential equations an introduction with Mathematica and MAPLE |
| title_full | Partial differential equations an introduction with Mathematica and MAPLE Ioannis P. Stavroulakis ; Stepan A. Tersian |
| title_fullStr | Partial differential equations an introduction with Mathematica and MAPLE Ioannis P. Stavroulakis ; Stepan A. Tersian |
| title_full_unstemmed | Partial differential equations an introduction with Mathematica and MAPLE Ioannis P. Stavroulakis ; Stepan A. Tersian |
| title_short | Partial differential equations |
| title_sort | partial differential equations an introduction with mathematica and maple |
| title_sub | an introduction with Mathematica and MAPLE |
| topic | aMathematica (Computer file) aMaple (Computer file) aMathematical physics Partielle Differentialgleichung (DE-588)4044779-0 gnd Maple Programm (DE-588)4209397-1 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| topic_facet | aMathematica (Computer file) aMaple (Computer file) aMathematical physics Partielle Differentialgleichung Maple Programm Mathematica Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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