Differential equations: an introduction with Mathematica
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2004
|
| Edition: | 2. ed. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 491 - 493 |
| Physical Description: | XIII, 431 S. graph. Darst. |
| ISBN: | 0387212841 9780387212845 |
Staff View
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| 100 | 1 | |a Ross, Clay C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential equations |b an introduction with Mathematica |c Clay C. Ross |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2004 | |
| 300 | |a XIII, 431 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate texts in mathematics | |
| 500 | |a Literaturverz. S. 491 - 493 | ||
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Record in the Search Index
| _version_ | 1804133038734442496 |
|---|---|
| adam_text | Contents
Preface
............................................................
VII
1
About Differential Equations
.................................... 1
1.0
Introduction
............................................... 1
1.1
Numerical Methods
......................................... 8
1.2
Uniqueness Considerations
.................................. 17
1.3
Differential Inclusions (Optional)
............................. 22
2
Linear Algebra
................................................ 26
2.0
Introduction
............................................... 26
2.1
Familiar Linear Spaces
...................................... 31
2.2
Abstract Linear Spaces
...................................... 31
2.3
Differential Equations from Solutions
......................... 44
2.4
Characteristic Value Problems
................................ 48
3
First-Order Differential Equations
............................... 52
3.0
Introduction
............................................... 52
3.1
First-Order Linear Differential Equations
....................... 52
3.2
Linear Equations by
Mathematica
............................ 57
3.3
Exact Equations
............................................ 59
3.4
Variables Separable
......................................... 69
3.5
Homogeneous Nonlinear Differential Equations
................. 75
3.6
Bernoulli and Riccati Differential Equations (Optional)
........... 79
3.7
Clairaut Differential Equations (Optional)
...................... 86
4
Applications of First-Order Equations
............................ 90
4.0
Introduction
............................................... 90
4.1
Orthogonal Trajectories
..................................... 90
4.2
Linear Applications
......................................... 95
4.3
Nonlinear Applications
...................................... 117
XII Contents
5
Higher-Order Linear Differential Equations
...................... 129
5.0
Introduction
............................................... 129
5.1
The Fundamental Theorem
.................................. 130
5.2
Homogeneous Second-Order Linear Constant Coefficients
........ 139
5.3
Higher-Order Constant Coefficients (Homogeneous)
............. 152
5.4
The Method of Undetermined Coefficients
..................... 160
5.5
Variation of Parameters
...................................... 171
6
Applications of Second-Order Equations
.......................... 179
6.0
Introduction
............................................... 179
6.1
Simple Harmonic Motion
.................................... 179
6.2
Damped Harmonic Motion
................................... 190
6.3
Forced Oscillation
.......................................... 197
6.4
Simple Electronic Circuits
................................... 202
6.5
Two Nonlinear Examples (Optional)
........................... 206
7
The Laplace Transform
......................................... 210
7.0
Introduction
............................................... 210
7.1
The Laplace Transform
...................................... 211
7.2
Properties of the Laplace Transform
........................... 214
7.3
The Inverse Laplace Transform
............................... 225
7.4
Discontinous Functions and Their Transforms
................... 230
8
Higher-Order Differential Equations with Variable Coefficients
..... 240
8.0
Introduction
............................................... 240
8.1
Cauchy-Euler Differential Equations
.......................... 241
8.2
Obtaining a Second Solution
................................. 251
8.3
Sums, Products and Recursion Relations
....................... 253
8.4
Series Solutions of Differential Equations
...................... 262
8.5
Series Solutions About Ordinary Points
........................ 269
8.6
Series Solution About Regular Singular Points
.................. 277
8.7
Important Classical Differential Equations and Functions
......... 293
9
Differential Systems: Theory
.................................... 297
9.0
introduction
............................................... 297
9.1
Reduction to First-Order Systems
............................. 302
9.2
Theory of First-Order Systems
............................... 309
9.3
First-Order Constant Coefficients Systems
...................... 317
9.4
Repeated and Complex Roots
................................ 331
9.5
Nonhomogeneous Equations and Boundary-Value Problems
...... 344
9.6
Cauchy-Euler Systems
...................................... 358
Contents XIII
10 Differential Systems: Applications............................... 369
10.0
Introduction
............................................... 369
10.1 Applications
of
Systems
of
Differential
Equations
............... 369
10.2 Phase
Portraits
............................................ 384
10.3
Two Nonlinear Examples (Optional)
........................... 404
10.4
Defective Systems of First-Order Differential
Equations (Optional)
........................................ 410
10.5
Solution of Linear Systems by Laplace Transforms (Optional)
.....416
References
......................................................... 423
Index
............................................................. 426
|
| any_adam_object | 1 |
| author | Ross, Clay C. |
| author_facet | Ross, Clay C. |
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| dewey-full | 515/.35 |
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| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Ross, Clay C. Verfasser aut Differential equations an introduction with Mathematica Clay C. Ross 2. ed. New York, NY [u.a.] Springer 2004 XIII, 431 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Literaturverz. S. 491 - 493 Mathematica (Computer file) Differentiaalvergelijkingen gtt Mathematica (computerprogramma) gtt Differential equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012988131&sequence=000002&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 Differentialgleichung (DE-588)4012249-9 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4268208-3 (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 Differentialgleichung (DE-588)4012249-9 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| topic_facet | Mathematica (Computer file) Differentiaalvergelijkingen Mathematica (computerprogramma) Differential equations Differentialgleichung Mathematica Programm Einführung Aufgabensammlung |
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