Differential equations with boundary value problems: an introduction to modern methods and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIV, 952 S. Ill., graph. Darst. |
| ISBN: | 9780470418505 |
Internformat
MARC
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| 245 | 1 | 0 | |a Differential equations with boundary value problems |b an introduction to modern methods and applications |c James R. Brannan ; William E. Boyce |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2010 | |
| 300 | |a XXIV, 952 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Engineering mathematics / Data processing | |
| 650 | 4 | |a Boundary value problems / Data processing | |
| 650 | 4 | |a Differential equations / Numerical solutions / Data processing | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Boundary value problems |x Data processing | |
| 650 | 4 | |a Differential equations |x Numerical solutions |x Data processing | |
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Datensatz im Suchindex
| _version_ | 1822663816930918400 |
|---|---|
| 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 Model
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
xxii
I Contents
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
8
Contents I
xxiii
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
Series Solutions of Second Order Linear Equations
537
8.1
Review of Power Series
539
8.2
Series Solutions Near an Ordinary Point, Part I
547
8.3
Series Solutions Near an Ordinary Point, Part II
558
8.4
Regular Singular Points
564
8.5
Series Solutions Near a Regular Singular Point, Part I
571
8.6
Series Solutions Near a Regular Singular Point, Part II
576
8.7
Bessel's Equation
584
Projects
598
8.P.1 Diffraction Through a Circular Aperture
598
8.P.2 Hermite Polynomials and the Quantum Mechanical Harmonic Oscillator
603
8.P.3 Perturbation Methods
605
Partial Differential Equations and Fourier Series
біз
9.1
Two-Point Boundary Value Problems
613
9.2
Fourier Series
619
9.3
The Fourier Convergence Theorem
629
9.4
Even and Odd Functions
635
9.5
Separation of Variables; Heat Conduction in a Rod
642
9.6
Other Heat Conduction Problems
650
9.7
The Wave Equation: Vibrations of an Elastic String
661
9.8
Laplace's Equation
674
Projects
693
9.P.1 Estimating the Diffusion Coefficient in the Heat Equation
693
9.P.2 The Transmission Line Problem
695
9.P.3 Solving Poisson's Equation by Finite Differences
700
Boundary Value Problems and Sturm-Liouville Theory
706
10.1
The Occurrence of Two-Point Boundary Value Problems
706
10.2
Sturm-Liouville Boundary Value Problems
713
10.3
Nonhomogeneous Boundary Value Problems
726
10.4
Singular Sturm-Liouville Problems
739
10.5
Further Remarks on the Method of Separation of Variables: A Bessel Series
Expansion
745
10.6
Series of Orthogonal Functions: Mean Convergence
751
Projects
763
10.P.1 Dynamic Behavior of a Hanging Cable
763
1
0.P.2 Advection Dispersion: A Model for Solute Transport in Saturated
Porous Media
766
1
0.P.3 Fisher's Equation for Population Growth and Dispersion
772
xxiv
j
Contents
Matrices and Linear Algebra
777
A.1 Matrices
777
A.2 Systems of Linear Algebraic Equations, Linear Independence,
and Rank
786
A.3 Determinants and Inverses
803
A.4 The Eigenvalue Problem
812
В
Complex Variables
823
ANSWERS TO SELECTED PROBLEMS
827
REFERENCES
933
PHOTO CREDITS
936
INDEX
937 |
| any_adam_object | 1 |
| author | Brannan, James R. Boyce, William E. 1930- |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
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| indexdate | 2025-01-30T09:01:09Z |
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| isbn | 9780470418505 |
| language | English |
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| spelling | Brannan, James R. Verfasser aut Differential equations with boundary value problems an introduction to modern methods and applications James R. Brannan ; William E. Boyce Hoboken, NJ Wiley 2010 XXIV, 952 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering mathematics / Data processing Boundary value problems / Data processing Differential equations / Numerical solutions / Data processing Datenverarbeitung Boundary value problems Data processing Differential equations Numerical solutions Data processing Engineering mathematics Data processing Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Randelemente-Methode (DE-588)4076508-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Randelemente-Methode (DE-588)4076508-8 s Boyce, William E. 1930- Verfasser (DE-588)11468409X aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017638536&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brannan, James R. Boyce, William E. 1930- Differential equations with boundary value problems an introduction to modern methods and applications Engineering mathematics / Data processing Boundary value problems / Data processing Differential equations / Numerical solutions / Data processing Datenverarbeitung Boundary value problems Data processing Differential equations Numerical solutions Data processing Engineering mathematics Data processing Differentialgleichung (DE-588)4012249-9 gnd Randelemente-Methode (DE-588)4076508-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4076508-8 (DE-588)4128130-5 |
| title | Differential equations with boundary value problems an introduction to modern methods and applications |
| title_auth | Differential equations with boundary value problems an introduction to modern methods and applications |
| title_exact_search | Differential equations with boundary value problems an introduction to modern methods and applications |
| title_full | Differential equations with boundary value problems an introduction to modern methods and applications James R. Brannan ; William E. Boyce |
| title_fullStr | Differential equations with boundary value problems an introduction to modern methods and applications James R. Brannan ; William E. Boyce |
| title_full_unstemmed | Differential equations with boundary value problems an introduction to modern methods and applications James R. Brannan ; William E. Boyce |
| title_short | Differential equations with boundary value problems |
| title_sort | differential equations with boundary value problems an introduction to modern methods and applications |
| title_sub | an introduction to modern methods and applications |
| topic | Engineering mathematics / Data processing Boundary value problems / Data processing Differential equations / Numerical solutions / Data processing Datenverarbeitung Boundary value problems Data processing Differential equations Numerical solutions Data processing Engineering mathematics Data processing Differentialgleichung (DE-588)4012249-9 gnd Randelemente-Methode (DE-588)4076508-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Engineering mathematics / Data processing Boundary value problems / Data processing Differential equations / Numerical solutions / Data processing Datenverarbeitung Boundary value problems Data processing Differential equations Numerical solutions Data processing Engineering mathematics Data processing Differentialgleichung Randelemente-Methode Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017638536&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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