Elementary Differential Equations and Boundary Value Problems

ISBN-10: 0471433381
ISBN-13: 9780471433385
Edition: 88th 2005 (Revised)
List price: $163.95
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Description: This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predecessors, this revision is written from the viewpoint of the  More...

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Book details

List price: $163.95
Edition: 88th
Copyright year: 2005
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/20/2004
Binding: Hardcover
Pages: 800
Size: 8.00" wide x 10.00" long x 1.25" tall
Weight: 3.894
Language: English

This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predecessors, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. Sound and Accurate Exposition of Theory--special attention is made to methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace development of the discipline and identify outstanding individual contributions.

Prefacep. vii
Introductionp. 1
Some Basic Mathematical Models; Direction Fieldsp. 1
Solutions of Some Differential Equationsp. 9
Classification of Differential Equationsp. 17
Historical Remarksp. 23
First Order Differential Equationsp. 29
Linear Equations with Variable Coefficientsp. 29
Separable Equationsp. 40
Modeling with First Order Equationsp. 47
Differences Between Linear and Nonlinear Equationsp. 64
Autonomous Equations and Population Dynamicsp. 74
Exact Equations and Integrating Factorsp. 89
Numerical Approximations: Euler's Methodp. 96
The Existence and Uniqueness Theoremp. 105
First Order Difference Equationsp. 115
Second Order Linear Equationsp. 129
Homogeneous Equations with Constant Coefficientsp. 129
Fundamental Solutions of Linear Homogeneous Equationsp. 137
Linear Independence and the Wronskianp. 147
Complex Roots of the Characteristic Equationp. 153
Repeated Roots; Reduction of Orderp. 160
Nonhomogeneous Equations; Method of Undetermined Coefficientsp. 169
Variation of Parametersp. 179
Mechanical and Electrical Vibrationsp. 186
Forced Vibrationsp. 200
Higher Order Linear Equationsp. 209
General Theory of nth Order Linear Equationsp. 209
Homogeneous Equations with Constant Coeffientsp. 214
The Method of Undetermined Coefficientsp. 222
The Method of Variation of Parametersp. 226
Series Solutions of Second Order Linear Equationsp. 231
Review of Power Seriesp. 231
Series Solutions near an Ordinary Point, Part Ip. 238
Series Solutions near an Ordinary Point, Part IIp. 249
Regular Singular Pointsp. 255
Euler Equationsp. 260
Series Solutions near a Regular Singular Point, Part Ip. 267
Series Solutions near a Regular Singular Point, Part IIp. 272
Bessel's Equationp. 280
The Laplace Transformp. 293
Definition of the Laplace Transformp. 293
Solution of Initial Value Problemsp. 299
Step Functionsp. 310
Differential Equations with Discontinuous Forcing Functionsp. 317
Impulse Functionsp. 324
The Convolution Integralp. 330
Systems of First Order Linear Equationsp. 339
Introductionp. 339
Review of Matricesp. 348
Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectorsp. 357
Basic Theory of Systems of First Order Linear Equationsp. 368
Homogeneous Linear Systems with Constant Coefficientsp. 373
Complex Eigenvaluesp. 384
Fundamental Matricesp. 393
Repeated Eigenvaluesp. 401
Nonhomogeneous Linear Systemsp. 411
Numerical Methodsp. 419
The Euler or Tangent Line Methodp. 419
Improvements on the Euler Methodp. 430
The Runge-Kutta Methodp. 435
Multistep Methodsp. 439
More on Errors; Stabilityp. 445
Systems of First Order Equationsp. 455
Nonlinear Differential Equations and Stabilityp. 459
The Phase Plane; Linear Systemsp. 459
Autonomous Systems and Stabilityp. 471
Almost Linear Systemsp. 479
Competing Speciesp. 491
Predator-Prey Equationsp. 503
Liapunov's Second Methodp. 511
Periodic Solutions and Limit Cyclesp. 521
Chaos and Strange Attractors; the Lorenz Equationsp. 532
Partial Differential Equations and Fourier Seriesp. 541
Two-Point Boundary Valve Problemsp. 541
Fourier Seriesp. 547
The Fourier Convergence Theoremp. 558
Even and Odd Functionsp. 564
Separation of Variables; Heat Conduction in a Rodp. 573
Other Heat Conduction Problemsp. 581
The Wave Equation; Vibrations of an Elastic Stringp. 591
Laplace's Equationp. 604
Derivation of the Heat Conduction Equationp. 614
Derivation of the Wave Equationp. 617
Boundary Value Problems and Sturm-Liouville Theoryp. 621
The Occurrence of Two Point Boundary Value Problemsp. 621
Sturm-Liouville Boundary Value Problemsp. 629
Nonhomogeneous Boundary Value Problemsp. 641
Singular Sturm-Liouville Problemsp. 656
Further Remarks on the Method of Separation of Variables: A Bessel Series Expansionp. 663
Series of Orthogonal Functions: Mean Convergencep. 669
Answers to Problemsp. 679
Indexp. 737
Table of Contents provided by Syndetics. All Rights Reserved.

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