Differential equations: an introduction to modern methods and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erg. bildet: Levandosky, Julie: Student solutions manual to accompany Differential equations ... |
| Physical Description: | XXI, 682 S. Ill., graph. Darst. 1 Beil. |
| ISBN: | 0471651419 9780471651413 |
Staff View
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| 245 | 1 | 0 | |a Differential equations |b an introduction to modern methods and applications |c James R. Brannan ; William E. Boyce |
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Record in the Search Index
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| adam_text | CONTENTS
1
Introduction
1
1.1 Some Basic
Mathematical
Models;
Direction Fields
1
1.2 Solutions
of Some
Differential
Equations
11
1.3
Numerical Approximations: Euler s Method
22
1.4
Classification of Differential Equations
33
First Order Differential Equations
40
2.1
Linear Equations; Method of Integrating Factors
41
2.2
Separable Equations
49
2.3
Modeling with First Order Equations
56
2.4
Differences Between Linear and Nonlinear Equations
71
2.5
Autonomous Equations and Population Dynamics
81
2.6
Exact Equations and Integrating Factors
95
2.7
Accuracy of Numerical Methods
103
2.8
Improved
Euler
and Runge-Kutta Methods
111
Projects
119
2.P.1 Harvesting a Renewable Resource
119
2.P.2 Designing a Drip Dispenser for a Hydrology Experiment
120
2.P.3 A Mathematical Model of a Groundwater Contaminant Source
122
2.P.4 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin
124
Systems of Two First Order Equations
127
3.1
Systems of Two Linear Algebraic Equations
128
3.2
Systems of Two First Order Linear Differential Equations
139
3.3
Homogeneous Linear Systems with Constant Coefficients
148
3.4
Complex Eigenvalues
164
3.5
Repeated Eigenvalues
175
3.6
A Brief Introduction to Nonlinear Systems
187
3.7
Numerical Methods for Systems of First Order Equations
194
Projects
199
3.P.1 Eigenvalue-Placement Design of a Satellite Attitude Control System
199
3.P.2 Estimating Rate Constants for an Open Two-Compartment Model
202
3.P.3 The Ray Theory of Wave Propagation
204
3.P.4 A Blood-Brain Pharmacokinetic Mode!
208
Second Order Linear Equations
210
4.1
Definitions and Examples
210
4.2
Theory of Second Order Linear Homogeneous Equations
223
4.3
Linear Homogeneous Equations with Constant Coefficients
232
4.4
Characteristic Equations with Complex Roots
243
4.5
Mechanical and Electrical Vibrations
252
xix
xx
j
Contents
6
4.6
Nonhomogeneous Equations; Method of Undetermined Coefficients
263
4.7
Forced Vibrations, Frequency Response, and Resonance
272
4.8
Variation of Parameters
283
Projects
293
4.P.1 A Vibration Insulation Problem
293
4.P.2 Linearization of a Nonlinear Mechanical System
294
4.P.3 A Spring-Mass Event Problem
296
4.P.4 Uniformly Distributing Points on a Sphere
297
4.P.5 Euler-Lagrange Equations
301
The Laplace Transform
зоб
5.1
Definition of the Laplace Transform
307
5.2
Properties of the Laplace Transform
316
5.3
The Inverse Laplace Transform
323
5.4
Solving Differential Equations with Laplace Transforms
332
5.5
Discontinuous Functions and Periodic Functions
340
5.6
Differential Equations with Discontinuous Forcing Functions
349
5.7
Impulse Functions
356
5.8
Convolution Integrals and Their Applications
363
5.9
Linear Systems and Feedback Control
372
Projects
382
5.P.1 An Electric Circuit Problem
382
5.P.2 Effects of Pole Locations on Step Responses of Second Order Systems
382
5.P.3 The Watt Governor, Feedback Control, and Stability
385
Systems of First Order Linear Equations
390
6.1
Definitions and Examples
391
6.2
Basic Theory of First Order Linear Systems
402
6.3
Homogeneous Linear Systems with Constant Coefficients
412
6.4
Complex Eigenvalues
423
6.5
Fundamental Matrices and the Exponential of a Matrix
433
6.6
Nonhomogeneous Linear Systems
444
6.7
Defective Matrices
451
Projects
459
6.P.1 A Compartment Model of Heat Flow in a Rod
459
6.P.2 Earthquakes and Tall Buildings
462
6.P.3 Controlling a Spring-Mass System to Equilibrium
464
Nonlinear Differential Equations and Stability
472
7.1
Autonomous Systems and Stability
472
7.2
Almost Linear Systems
482
7.3
Competing Species
493
7.4
Predator-Prey Equations
504
7.5
Periodic Solutions and Limit Cycles
513
7.6
Chaos and Strange Attractors: The
Lorenz
Equations
524
Contents xxi
Projects
532
7.P.1
Modeling of Epidemics
532
7.P.2 Harvesting in a Competitive Environment
534
7.P.3 The
Rössler
System
536
Д
Matrices and Linear Algebra
537
A.1 Matrices
537
A.2 Systems of Linear Algebraic Equations, Linear Independence,
and Rank
546
A.3 Determinants and Inverses
563
A.4 The Eigenvalue Problem
571
ry Complex Variables
583
D
ANSWERS TO SELECTED PROBLEMS
587
REFERENCES
673
INDEX
675
|
| adam_txt |
CONTENTS
1
Introduction
1
1.1 Some Basic
Mathematical
Models;
Direction Fields
1
1.2 Solutions
of Some
Differential
Equations
11
1.3
Numerical Approximations: Euler's Method
22
1.4
Classification of Differential Equations
33
First Order Differential Equations
40
2.1
Linear Equations; Method of Integrating Factors
41
2.2
Separable Equations
49
2.3
Modeling with First Order Equations
56
2.4
Differences Between Linear and Nonlinear Equations
71
2.5
Autonomous Equations and Population Dynamics
81
2.6
Exact Equations and Integrating Factors
95
2.7
Accuracy of Numerical Methods
103
2.8
Improved
Euler
and Runge-Kutta Methods
111
Projects
119
2.P.1 Harvesting a Renewable Resource
119
2.P.2 Designing a Drip Dispenser for a Hydrology Experiment
120
2.P.3 A Mathematical Model of a Groundwater Contaminant Source
122
2.P.4 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin
124
Systems of Two First Order Equations
127
3.1
Systems of Two Linear Algebraic Equations
128
3.2
Systems of Two First Order Linear Differential Equations
139
3.3
Homogeneous Linear Systems with Constant Coefficients
148
3.4
Complex Eigenvalues
164
3.5
Repeated Eigenvalues
175
3.6
A Brief Introduction to Nonlinear Systems
187
3.7
Numerical Methods for Systems of First Order Equations
194
Projects
199
3.P.1 Eigenvalue-Placement Design of a Satellite Attitude Control System
199
3.P.2 Estimating Rate Constants for an Open Two-Compartment Model
202
3.P.3 The Ray Theory of Wave Propagation
204
3.P.4 A Blood-Brain Pharmacokinetic Mode!
208
Second Order Linear Equations
210
4.1
Definitions and Examples
210
4.2
Theory of Second Order Linear Homogeneous Equations
223
4.3
Linear Homogeneous Equations with Constant Coefficients
232
4.4
Characteristic Equations with Complex Roots
243
4.5
Mechanical and Electrical Vibrations
252
xix
xx
j
Contents
6
4.6
Nonhomogeneous Equations; Method of Undetermined Coefficients
263
4.7
Forced Vibrations, Frequency Response, and Resonance
272
4.8
Variation of Parameters
283
Projects
293
4.P.1 A Vibration Insulation Problem
293
4.P.2 Linearization of a Nonlinear Mechanical System
294
4.P.3 A Spring-Mass Event Problem
296
4.P.4 Uniformly Distributing Points on a Sphere
297
4.P.5 Euler-Lagrange Equations
301
The Laplace Transform
зоб
5.1
Definition of the Laplace Transform
307
5.2
Properties of the Laplace Transform
316
5.3
The Inverse Laplace Transform
323
5.4
Solving Differential Equations with Laplace Transforms
332
5.5
Discontinuous Functions and Periodic Functions
340
5.6
Differential Equations with Discontinuous Forcing Functions
349
5.7
Impulse Functions
356
5.8
Convolution Integrals and Their Applications
363
5.9
Linear Systems and Feedback Control
372
Projects
382
5.P.1 An Electric Circuit Problem
382
5.P.2 Effects of Pole Locations on Step Responses of Second Order Systems
382
5.P.3 The Watt Governor, Feedback Control, and Stability
385
Systems of First Order Linear Equations
390
6.1
Definitions and Examples
391
6.2
Basic Theory of First Order Linear Systems
402
6.3
Homogeneous Linear Systems with Constant Coefficients
412
6.4
Complex Eigenvalues
423
6.5
Fundamental Matrices and the Exponential of a Matrix
433
6.6
Nonhomogeneous Linear Systems
444
6.7
Defective Matrices
451
Projects
459
6.P.1 A Compartment Model of Heat Flow in a Rod
459
6.P.2 Earthquakes and Tall Buildings
462
6.P.3 Controlling a Spring-Mass System to Equilibrium
464
Nonlinear Differential Equations and Stability
472
7.1
Autonomous Systems and Stability
472
7.2
Almost Linear Systems
482
7.3
Competing Species
493
7.4
Predator-Prey Equations
504
7.5
Periodic Solutions and Limit Cycles
513
7.6
Chaos and Strange Attractors: The
Lorenz
Equations
524
Contents xxi
Projects
532
7.P.1
Modeling of Epidemics
532
7.P.2 Harvesting in a Competitive Environment
534
7.P.3 The
Rössler
System
536
Д
Matrices and Linear Algebra
537
"
A.1 Matrices
537
A.2 Systems of Linear Algebraic Equations, Linear Independence,
and Rank
546
A.3 Determinants and Inverses
563
A.4 The Eigenvalue Problem
571
ry Complex Variables
583
D
ANSWERS TO SELECTED PROBLEMS
587
REFERENCES
673
INDEX
675 |
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| id | DE-604.BV021840229 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:00:12Z |
| indexdate | 2024-07-09T20:45:51Z |
| institution | BVB |
| isbn | 0471651419 9780471651413 |
| language | English |
| lccn | 2006048264 |
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| spelling | Brannan, James R. Verfasser (DE-588)173981380 aut Differential equations an introduction to modern methods and applications James R. Brannan ; William E. Boyce Hoboken, NJ Wiley 2007 XXI, 682 S. Ill., graph. Darst. 1 Beil. txt rdacontent n rdamedia nc rdacarrier Erg. bildet: Levandosky, Julie: Student solutions manual to accompany Differential equations ... Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Boyce, William E. 1930- Verfasser (DE-588)11468409X aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brannan, James R. Boyce, William E. 1930- Differential equations an introduction to modern methods and applications Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4151278-9 |
| title | Differential equations an introduction to modern methods and applications |
| title_auth | Differential equations an introduction to modern methods and applications |
| title_exact_search | Differential equations an introduction to modern methods and applications |
| title_exact_search_txtP | Differential equations an introduction to modern methods and applications |
| title_full | Differential equations an introduction to modern methods and applications James R. Brannan ; William E. Boyce |
| title_fullStr | Differential equations an introduction to modern methods and applications James R. Brannan ; William E. Boyce |
| title_full_unstemmed | Differential equations an introduction to modern methods and applications James R. Brannan ; William E. Boyce |
| title_short | Differential equations |
| title_sort | differential equations an introduction to modern methods and applications |
| title_sub | an introduction to modern methods and applications |
| topic | Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Équations différentielles Differential equations Gewöhnliche Differentialgleichung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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