Differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester u.a.
Wiley
1974
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 712 S. graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
PART ONE
FUNDAMENTAL METHODS AND APPLICATIONS
1
Differential Equations and
Their Solutions 1
1.1 Classification of Differential Equations; Their Origin and Application 1
1.2 Solutions 5
1.3 Initial Value Problems, Boundary Value Problems, and Existence of Solutions 13
2
First Order Equations for Which
Exact Solutions are Obtainable 23
2.1 Exact Differential Equations and Integrating Factors 23
2.2 Separable Equations and Equations Reducible to This Form 36
2.3 Linear Equations and Bernoulli Equations 45
2.4 Special Integrating Factors and Transformations 57
3
Applications of
First Order Equations 66
3.1 Orthogonal and Oblique Trajectories 66
3.2 Problems in Mechanics 73
3.3 Rate Problems 84
vii
4
Explicit Methods of Solving
Higher Order Linear Differential Equations 92
4.1 Basic Theory of Linear Differential Equations 92
4.2 The Homogeneous Linear Equation with Constant Coefficients 110
4.3 The Method of Undetermined Coefficients 121
4.4 Variation of Parameters 132
4.5 The Cauchy Euler Equation 141
5
Applications of
Second Order Linear Differential Equations
with Constant Coefficients 147
5.1 The Differential Equation of the Vibrations of a Mass on a Spring 147
5.2 Free, Undamped Motion 150
5.3 Free, Damped Motion 157
5.4 Forced Motion 168
5.5 Resonance Phenomena 175
5.6 Electric Circuit Problems 180
6
Series Solutions of
Linear Differential Equations 191
6.1 Power Series Solutions About an Ordinary Point 191
6.2 Solutions About Singular Points; the Method of Frobenius 203
6.3 Bessel s Equation and Bessel Functions 223
7
Systems of
Linear Differential Equations 235
7.1 Differential Operators and an Operator Method 235
7.2 Applications 249
7.3 Basic Theory of Linear Systems in Normal Form: Two Equations in Two
Unknown Functions 258
7.4 Homogeneous Linear Systems with Constant Coefficients: Two Equations in
Two Unknown Functions 267
7.5 Matrices and Vectors 278
7.6 Basic Theory of Linear Systems in Normal Form: n Equations in n Unknown
Functions 298
7.7 Homogeneous Linear Systems with Constant Coefficients: n Equations in n
Unknown Functions 317
8
Approximate Methods of
Solving First Order Equations 330
8.1 Graphical Methods 330
8.2 Power Series Methods 337
8.3 The Method of Successive Approximations 343
8.4 Numerical Methods 347
9
The Laplace Transform 365
9.1 Definition, Existence, and Basic Properties of the Laplace Transform 365
9.2 The Inverse Transform and the Convolution 378
9.3 Laplace Transform Solution of Linear Differential Equations with Constant
Coefficients 385
9.4 Laplace Transform Solution of Linear Systems 397
PART TWO
FUNDAMENTAL THEORY AND FURTHER METHODS
10
The Theory of
First Order Equations 405
10.1 Some Concepts From Real Function Theory 405
10.2 Existence and Uniqueness of Solutions 416
10.3 Dependence of Solutions on Initial Conditions and on the Function/ 432
11
The Theory of
Linear Differential Equations 440
11.1 The Basic Existence Theorem 440
11.2 Basic Theory of the Homogeneous Linear Equation; Linear Independence
and Fundamental Sets 450
11.3 Further Properties of the Homogeneous Linear Equation; Reduction of
Order 464
11.4 The Nonhomogeneous Equation 471
11.5 The Adjoint Equation 475
11.6 The Sturm Theory 487
12
Sturm Liouville Boundary Value
Problems and Fourier Series 497
12.1 Sturm Liouville Problems 497
12.2 Orthogonality of Characteristic Functions 506
12.3 The Expansion of a Function in a Series of Orthonormal Functions 510
12.4 Trigonometric Fourier Series 517
13
Nonlinear Differential Equations 541
13.1 Phase Plane, Paths, and Critical Points 541
13.2 Critical Points and Paths of Linear Systems 553
13.3 Critical Points and Paths of Nonlinear Systems 568
13.4 Limit Cycles and Periodic Solutions 602
13.5 The Method of Kryloff and Bogoliuboff 617
14
Partial Differential Equations 626
14.1 Some Basic Concepts and Examples 626
14.2 The Method of Separation of Variables 633
14.3 Canonical Forms of Second Order Linear Equations with Constant
Coefficients 655
14.4 An Initial Value Problem; Characteristics 669
Appendix 683
Answers 685
Index 707
|
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515.35 |
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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV002656918 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:48:00Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001703531 |
| oclc_num | 2233209 |
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| owner | DE-91G DE-BY-TUM DE-29T |
| owner_facet | DE-91G DE-BY-TUM DE-29T |
| physical | XI, 712 S. graph. Darst. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Wiley |
| record_format | marc |
| spelling | Ross, Shepley L. Verfasser aut Differential equations 2. ed. Chichester u.a. Wiley 1974 XI, 712 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differentialgleichung swd Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703531&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 |
| spellingShingle | Ross, Shepley L. Differential equations Differentialgleichung swd Differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4020929-5 |
| title | Differential equations |
| title_auth | Differential equations |
| title_exact_search | Differential equations |
| title_full | Differential equations |
| title_fullStr | Differential equations |
| title_full_unstemmed | Differential equations |
| title_short | Differential equations |
| title_sort | differential equations |
| topic | Differentialgleichung swd Differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differentialgleichung Differential equations Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703531&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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