Elementary differential equations and boundary value problems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken [u.a.]
Wiley
2010
|
| Edition: | 9. ed., internat. student version |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 796 S. Ill., graph. Darst. |
| ISBN: | 9780470398739 |
Staff View
MARC
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| 245 | 1 | 0 | |a Elementary differential equations and boundary value problems |c William E. Boyce ; Richard C. DiPrima |
| 250 | |a 9. ed., internat. student version | ||
| 264 | 1 | |a Hoboken [u.a.] |b Wiley |c 2010 | |
| 300 | |a XIX, 796 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804138081936211968 |
|---|---|
| adam_text | CONTENTS
Chapter
1
Introduction
1
1.1
Some Basic Mathematical Models; Direction Fields
1
1.2
Solutions of Some Differential Equations
10
1.3
Classification of Differential Equations
19
1.4
Historical Remarks
26
Chapter
2
First Order Differential Equations
31
2.1
Linear Equations; Method of Integrating Factors
31
2.2
Separable Equations
42
2.3
Modeling with First Order Equations
50
2.4
Differences Between Linear and Nonlinear Equations
68
2.5
Autonomous Equations and Population Dynamics
78
2.6
Exact Equations and Integrating Factors
94
2.7
Numerical Approximations: Euler s Method
101
2.8
The Existence and Uniqueness Theorem 111
2.9
First Order Difference Equations
121
Chapter
3
Second Order Linear Equations
137
3.1
Homogeneous Equations with Constant Coefficients
137
3.2
Solutions of Linear Homogeneous Equations; the Wronskian
145
3.3
Complex Roots of the Characteristic Equation
157
3.4
Repeated Roots; Reduction of Order
166
3.5
Nonhomogeneous Equations; Method of Undetermined Coefficients
174
3.6
Variation of Parameters
185
3.7
Mechanical and Electrical Vibrations
191
3.8
Forced Vibrations
206
Chapter
4
Higher Order Linear Equations
219
4.1
General Theory of nth Order Linear Equations
219
4.2
Homogeneous Equations with Constant Coefficients
226
4.3
The Method of Undetermined Coefficients
234
4.4
The Method of Variation of Parameters
239
Chapter
5
Series Solutions of Second Order Linear Equations
243
5.1
Review of Power Series
243
5.2
Series Solutions Near an Ordinary Point, Part I
250
5.3
Series Solutions Near an Ordinary Point, Part II
261
5.4
Euler
Equations; Regular Singular Points
268
5.5
Series Solutions Near a Regular Singular Point, Part I
278
5.6
Series Solutions Near a Regular Singular Point, Part II
284
5.7
Bessel s Equation
292
Chapter
6
The Laplace Transform
305
6.1
Definition of the Laplace Transform
305
6.2
Solution of Initial Value Problems
312
6.3
Step Functions
323
6.4
Differential Equations with Discontinuous Forcing Functions
331
6.5
Impulse Functions
339
6.6
The Convolution Integral
345
Chapter
7
Systems of First Order Linear Equations
355
7.1
Introduction
355
7.2
Review of Matrices
364
7.3
Linear Algebraic Equations; Linear Independence, Eigenvalues,
Eigenvectors
373
7.4
Basic Theory of Systems of First Order Linear Equations
385
7.5
Homogeneous Linear Systems with Constant Coefficients
390
7.6
Complex Eigenvalues
401
7.7
Fundamental Matrices
413
7.8
Repeated Eigenvalues
422
7.9
Nonhomogeneous Linear Systems
432
Chapter
8
Numerical Methods
443
8.1
The
Euler
or Tangent Line Method
443
8.2
Improvements on the
Euler
Method
454
8.3
The Runge-Kutta Method
459
8.4
Multistep Methods
464
8.5
More on Errors; Stability
470
8.6
Systems of First Order Equations
480
Chapter
9
Nonlinear Differential Equations and Stability
485
9.1
The Phase Plane: Linear Systems
485
9.2
Autonomous Systems and Stability
497
9.3
Locally Linear Systems
508
9.4
Competing Species
520
9.5
Predator-Prey Equations
533
9.6
Liapunov s Second Method
543
9.7
Periodic Solutions and Limit Cycles
554
9.8
Chaos and Strange Attractors: The
Lorenz
Equations
566
Chapter
^0
Partial Differential Equations and Fourier Series
577
10.1
Two-Point Boundary Value Problems
577
10.2
Fourier Series
584
10.3
The Fourier Convergence Theorem
595
10.4
Even and Odd Functions
602
10.5
Separation of Variables; Heat Conduction in a Rod
611
10.6
Other Heat Conduction Problems
620
10.7
The Wave Equation: Vibrations of an Elastic String
631
10.8
Laplace s Equation
646
Appendix A Derivation of the Heat Conduction Equation
657
Appendix
В
Derivation of the Wave Equation
661
Chapter
11
Boundary Value Problems and Sturm-Liouville Theory
665
11.1
The Occurrence of Two-Point Boundary Value Problems
665
11.2
Sturm-Liouville Boundary Value Problems
673
11.3
Nonhomogeneous Boundary Value Problems
687
11.4
Singular Sturm-Liouville Problems
702
11.5
Further Remarks on the Method of Separation of Variables: A Bessel
Series Expansion
709
11.6
Series of Orthogonal Functions: Mean Convergence
716
Answers to Problems
727
Index
786
|
| adam_txt |
CONTENTS
Chapter
1
Introduction
1
1.1
Some Basic Mathematical Models; Direction Fields
1
1.2
Solutions of Some Differential Equations
10
1.3
Classification of Differential Equations
19
1.4
Historical Remarks
26
Chapter
2
First Order Differential Equations
31
2.1
Linear Equations; Method of Integrating Factors
31
2.2
Separable Equations
42
2.3
Modeling with First Order Equations
50
2.4
Differences Between Linear and Nonlinear Equations
68
2.5
Autonomous Equations and Population Dynamics
78
2.6
Exact Equations and Integrating Factors
94
2.7
Numerical Approximations: Euler's Method
101
2.8
The Existence and Uniqueness Theorem 111
2.9
First Order Difference Equations
121
Chapter
3
Second Order Linear Equations
137
3.1
Homogeneous Equations with Constant Coefficients
137
3.2
Solutions of Linear Homogeneous Equations; the Wronskian
145
3.3
Complex Roots of the Characteristic Equation
157
3.4
Repeated Roots; Reduction of Order
166
3.5
Nonhomogeneous Equations; Method of Undetermined Coefficients
174
3.6
Variation of Parameters
185
3.7
Mechanical and Electrical Vibrations
191
3.8
Forced Vibrations
206
Chapter
4
Higher Order Linear Equations
219
4.1
General Theory of nth Order Linear Equations
219
4.2
Homogeneous Equations with Constant Coefficients
226
4.3
The Method of Undetermined Coefficients
234
4.4
The Method of Variation of Parameters
239
Chapter
5
Series Solutions of Second Order Linear Equations
243
5.1
Review of Power Series
243
5.2
Series Solutions Near an Ordinary Point, Part I
250
5.3
Series Solutions Near an Ordinary Point, Part II
261
5.4
Euler
Equations; Regular Singular Points
268
5.5
Series Solutions Near a Regular Singular Point, Part I
278
5.6
Series Solutions Near a Regular Singular Point, Part II
284
5.7
Bessel's Equation
292
Chapter
6
The Laplace Transform
305
6.1
Definition of the Laplace Transform
305
6.2
Solution of Initial Value Problems
312
6.3
Step Functions
323
6.4
Differential Equations with Discontinuous Forcing Functions
331
6.5
Impulse Functions
339
6.6
The Convolution Integral
345
Chapter
7
Systems of First Order Linear Equations
355
7.1
Introduction
355
7.2
Review of Matrices
364
7.3
Linear Algebraic Equations; Linear Independence, Eigenvalues,
Eigenvectors
373
7.4
Basic Theory of Systems of First Order Linear Equations
385
7.5
Homogeneous Linear Systems with Constant Coefficients
390
7.6
Complex Eigenvalues
401
7.7
Fundamental Matrices
413
7.8
Repeated Eigenvalues
422
7.9
Nonhomogeneous Linear Systems
432
Chapter
8
Numerical Methods
443
8.1
The
Euler
or Tangent Line Method
443
8.2
Improvements on the
Euler
Method
454
8.3
The Runge-Kutta Method
459
8.4
Multistep Methods
464
8.5
More on Errors; Stability
470
8.6
Systems of First Order Equations
480
Chapter
9
Nonlinear Differential Equations and Stability
485
9.1
The Phase Plane: Linear Systems
485
9.2
Autonomous Systems and Stability
497
9.3
Locally Linear Systems
508
9.4
Competing Species
520
9.5
Predator-Prey Equations
533
9.6
Liapunov's Second Method
543
9.7
Periodic Solutions and Limit Cycles
554
9.8
Chaos and Strange Attractors: The
Lorenz
Equations
566
Chapter
^0
Partial Differential Equations and Fourier Series
577
10.1
Two-Point Boundary Value Problems
577
10.2
Fourier Series
584
10.3
The Fourier Convergence Theorem
595
10.4
Even and Odd Functions
602
10.5
Separation of Variables; Heat Conduction in a Rod
611
10.6
Other Heat Conduction Problems
620
10.7
The Wave Equation: Vibrations of an Elastic String
631
10.8
Laplace's Equation
646
Appendix A Derivation of the Heat Conduction Equation
657
Appendix
В
Derivation of the Wave Equation
661
Chapter
11
Boundary Value Problems and Sturm-Liouville Theory
665
11.1
The Occurrence of Two-Point Boundary Value Problems
665
11.2
Sturm-Liouville Boundary Value Problems
673
11.3
Nonhomogeneous Boundary Value Problems
687
11.4
Singular Sturm-Liouville Problems
702
11.5
Further Remarks on the Method of Separation of Variables: A Bessel
Series Expansion
709
11.6
Series of Orthogonal Functions: Mean Convergence
716
Answers to Problems
727
Index
786 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Boyce, William E. 1930- DiPrima, Richard C. 1927-1984 |
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| 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 |
| discipline_str_mv | Mathematik |
| edition | 9. ed., internat. student version |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035109822 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:17:04Z |
| indexdate | 2024-07-09T21:22:31Z |
| institution | BVB |
| isbn | 9780470398739 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016777665 |
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| physical | XIX, 796 S. Ill., graph. Darst. |
| publishDate | 2010 |
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| spelling | Boyce, William E. 1930- Verfasser (DE-588)11468409X aut Elementary differential equations and boundary value problems William E. Boyce ; Richard C. DiPrima 9. ed., internat. student version Hoboken [u.a.] Wiley 2010 XIX, 796 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Boundary value problems Differential equations Randwertproblem (DE-588)4048395-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialgleichung (DE-588)4012249-9 s Randwertproblem (DE-588)4048395-2 s 1\p DE-604 Gewöhnliche Differentialgleichung (DE-588)4020929-5 s 2\p DE-604 DiPrima, Richard C. 1927-1984 Verfasser (DE-588)114684103 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016777665&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 | Boyce, William E. 1930- DiPrima, Richard C. 1927-1984 Elementary differential equations and boundary value problems Boundary value problems Differential equations Randwertproblem (DE-588)4048395-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4020929-5 (DE-588)4012249-9 (DE-588)4123623-3 |
| title | Elementary differential equations and boundary value problems |
| title_auth | Elementary differential equations and boundary value problems |
| title_exact_search | Elementary differential equations and boundary value problems |
| title_exact_search_txtP | Elementary differential equations and boundary value problems |
| title_full | Elementary differential equations and boundary value problems William E. Boyce ; Richard C. DiPrima |
| title_fullStr | Elementary differential equations and boundary value problems William E. Boyce ; Richard C. DiPrima |
| title_full_unstemmed | Elementary differential equations and boundary value problems William E. Boyce ; Richard C. DiPrima |
| title_short | Elementary differential equations and boundary value problems |
| title_sort | elementary differential equations and boundary value problems |
| topic | Boundary value problems Differential equations Randwertproblem (DE-588)4048395-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Boundary value problems Differential equations Randwertproblem Gewöhnliche Differentialgleichung Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016777665&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boycewilliame elementarydifferentialequationsandboundaryvalueproblems AT diprimarichardc elementarydifferentialequationsandboundaryvalueproblems |