Elementary Differential Equations and Boundary Value Problems / Edition 9

Elementary Differential Equations and Boundary Value Problems / Edition 9

by William E. Boyce, Richard C. DiPrima
     
 

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ISBN-10: 0470383348

ISBN-13: 9780470383346

Pub. Date: 10/27/2008

Publisher: Wiley

Details the methods for solving ordinary and partial differential equations. New material on limit cycles, the Lorenz equations and chaos has been added along with nearly 300 new problems. Also features expanded discussions of competing species and predator-prey problems plus extended treatment of phase plane analysis, qualitative methods and stability.

Overview

Details the methods for solving ordinary and partial differential equations. New material on limit cycles, the Lorenz equations and chaos has been added along with nearly 300 new problems. Also features expanded discussions of competing species and predator-prey problems plus extended treatment of phase plane analysis, qualitative methods and stability.

Product Details

ISBN-13:
9780470383346
Publisher:
Wiley
Publication date:
10/27/2008
Edition description:
Older Edition
Pages:
816
Product dimensions:
8.39(w) x 10.14(h) x 1.32(d)

Table of Contents

Prefacevii
Chapter 1Introduction1
1.1Some Basic Mathematical Models; Direction Fields1
1.2Solutions of Some Differential Equations9
1.3Classification of Differential Equations17
1.4Historical Remarks23
Chapter 2First Order Differential Equations29
2.1Linear Equations with Variable Coefficients29
2.2Separable Equations40
2.3Modeling with First Order Equations47
2.4Differences Between Linear and Nonlinear Equations64
2.5Autonomous Equations and Population Dynamics74
2.6Exact Equations and Integrating Factors89
2.7Numerical Approximations: Euler's Method96
2.8The Existence and Uniqueness Theorem105
2.9First Order Difference Equations115
Chapter 3Second Order Linear Equations129
3.1Homogeneous Equations with Constant Coefficients129
3.2Fundamental Solutions of Linear Homogeneous Equations137
3.3Linear Independence and the Wronskian147
3.4Complex Roots of the Characteristic Equation153
3.5Repeated Roots; Reduction of Order160
3.6Nonhomogeneous Equations; Method of Undetermined Coefficients169
3.7Variation of Parameters179
3.8Mechanical and Electrical Vibrations186
3.9Forced Vibrations200
Chapter 4Higher Order Linear Equations209
4.1General Theory of nth Order Linear Equations209
4.2Homogeneous Equations with Constant Coeffients214
4.3The Method of Undetermined Coefficients222
4.4The Method of Variation of Parameters226
Chapter 5Series Solutions of Second Order Linear Equations231
5.1Review of Power Series231
5.2Series Solutions near an Ordinary Point, Part I238
5.3Series Solutions near an Ordinary Point, Part II249
5.4Regular Singular Points255
5.5Euler Equations260
5.6Series Solutions near a Regular Singular Point, Part I267
5.7Series Solutions near a Regular Singular Point, Part II272
5.8Bessel's Equation280
Chapter 6The Laplace Transform293
6.1Definition of the Laplace Transform293
6.2Solution of Initial Value Problems299
6.3Step Functions310
6.4Differential Equations with Discontinuous Forcing Functions317
6.5Impulse Functions324
6.6The Convolution Integral330
Chapter 7Systems of First Order Linear Equations339
7.1Introduction339
7.2Review of Matrices348
7.3Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors357
7.4Basic Theory of Systems of First Order Linear Equations368
7.5Homogeneous Linear Systems with Constant Coefficients373
7.6Complex Eigenvalues384
7.7Fundamental Matrices393
7.8Repeated Eigenvalues401
7.9Nonhomogeneous Linear Systems411
Chapter 8Numerical Methods419
8.1The Euler or Tangent Line Method419
8.2Improvements on the Euler Method430
8.3The Runge-Kutta Method435
8.4Multistep Methods439
8.5More on Errors; Stability445
8.6Systems of First Order Equations455
Chapter 9Nonlinear Differential Equations and Stability459
9.1The Phase Plane; Linear Systems459
9.2Autonomous Systems and Stability471
9.3Almost Linear Systems479
9.4Competing Species491
9.5Predator-Prey Equations503
9.6Liapunov's Second Method511
9.7Periodic Solutions and Limit Cycles521
9.8Chaos and Strange Attractors; the Lorenz Equations532
Chapter 10Partial Differential Equations and Fourier Series541
10.1Two-Point Boundary Valve Problems541
10.2Fourier Series547
10.3The Fourier Convergence Theorem558
10.4Even and Odd Functions564
10.5Separation of Variables; Heat Conduction in a Rod573
10.6Other Heat Conduction Problems581
10.7The Wave Equation; Vibrations of an Elastic String591
10.8Laplace's Equation604
Appendix A.Derivation of the Heat Conduction Equation614
Appendix B.Derivation of the Wave Equation617
Chapter 11Boundary Value Problems and Sturm-Liouville Theory621
11.1The Occurrence of Two Point Boundary Value Problems621
11.2Sturm-Liouville Boundary Value Problems629
11.3Nonhomogeneous Boundary Value Problems641
11.4Singular Sturm-Liouville Problems656
11.5Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion663
11.6Series of Orthogonal Functions: Mean Convergence669
Answers to Problems679
Index737

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