Differential Equations With Applications - Brossura

Ritger, Paul D.; Rose, Nicholas J.

Brossura

ISBN 10: 0486411540 ISBN 13: 9780486411545

Casa editrice: Dover Pubns, 2010

Riassunto

Coherent, balanced introductory text focuses on initial- and boundary-value problems, general properties of linear equations, and the differences between linear and nonlinear systems. Includes large number of illustrative examples worked out in detail and extensive sets of problems. Answers or hints to most problems appear at end.

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Contenuti

Preface Chap. 1 Basic Concepts 1-1 Introduction 1-2 Classifications and Examples of Differential Equations 1-3 The Motion of a Particle 1-4 The Solution of a Differential Equation 1-5 Initial- and Boundary-value Problems 1-6 The Differential Equation y' = f(x) 1-7 Integrals as Functions of Parameters 1-8 Elementary and Non-elementary Functions 1-9 The Gamma Function Appendix Chap. 2 Special Methods for First-order Equations 2-1 Introduction 2-2 Separation of Variables 2-3 The First-order Linear Differential Equation 2-4 Exact Differential Equations 2-5 Integrating Factors 2-6 Use of Substitutions 2-7 Second-order Equations Reducible to First-order 2-8 Summary Chap. 3 Applications of First-order Equations 3-1 Introduction 3-2 Falling Bodies with Air Resistance 3-3 Motion on a Given Curve 3-4 Linear Motion with Variable Mass 3-5 Newton's Law of Cooling 3-6 Dilution Problems 3-7 Chemical Reactions 3-8 Population Growth 3-9 A Simple Electrical Circuit 3-10 Families of Curves and Orthogonal Trajectories Chap. 4 Existence and Uniqueness and Methods of Approximation 4-1 Introduction 4-2 The Direction Field 4-3 Existence and Uniqueness of Solutions 4-4 The Picard Method 4-5 The Cauchy-Euler Method 4-6 Taylor Series 4-7 Existence and Uniqueness Theorems for Systems of Equations and Higher-order Equations 4-8 Existence and Uniqueness Theorems for Linear Equations Appendix: Proof of existence and uniqueness for Linear Equations Chap. 5 Linear Differential Equations 5-1 Introduction 5-2 Fundamental Theory of Second-order Linear Equations 5-3 Complex-valued Solutions 5-4 Homogeneous Linear Equations with Constant Coefficients 5-5 Undetermined Coefficients 5-6 Variation of Parameters 5-7 Euler's Equation 5-8 Formulas of Lagrange and Abel 5-9 Linear Equations of the nth Order Chap. 6 Applications of Second-order Linear Differential Equations 6-1 Introduction 6-2 Free Vibrations 6-3 Forced Vibrations 6-4 Electrical Circuits 6-5 The Equations of Planetary Motives Chap. 7 Linear Differential Equations with Variable Coefficients 7-1 Introduction 7-2 Solution by Power Series 7-3 Solution near a Singular Point 7-4 Bessel's Equation 7-5 Hypergeometric Equation 7-6 Legendre's Equation Chap. 8 Systems of Linear Differential Equations 8-1 Introduction 8-2 Some Illustrative Examples 8-3 A Two-degree-of-freedom Vibration 8-4 Vectors and Matrics 8-5 Theory of Systems of Linear Differential Equations 8-6 Homogeneous Linear Systems with Constant Coefficients 8-7 Solution by Matrix Methods Chap. 9 The Laplace Transform 9-1 Introduction 9-2 Improper Integrals 9-3 The Laplace Transform 9-4 Properties of the Laplace Transform 9-5 Solution of Linear Equations with Constant Coefficients 9-6 Product of Transform Functions; Convolutions 9-7 Discontinuous Functions 9-8 Linear Systems Analysis Appendix Chap. 10 Nonlinear Differential Equations 10-1 Introduction 10-2 The Pendulum 10-3 Singularities and the Phase Plane 10-4 Van der Pol's Equation 10-5 Piecewise Linear System 10-6 Liapunov's Second Method Chap. 11 Linear Difference Equations 11-1 Introduction 11-2 First-order Linear Difference Equations 11-3 Second-order Linear Difference Equations 11-4 Homogeneous Linear Difference Equations with Constant Coefficients 11-5 The Nonhomogeneous Equation 11-6 The Vector Space EN 11-7 A Boundary-value Problem 11-8 N Beads on a Tightly Stretched String Chap. 12 Numerical Methods 12-1 Introduction 12-2 The Euler Method 12-3 Error Analysis 12-4 Parasitic Solutions and Stability 12-5 A Second-order Predictor-Corrector Method 12-6 Fourth-order Predictor-Corrector Methods 12-7 Starting Methods and Runge-Kutta Methods 12-8 Higher-order Equations and Systems of Equations Chap. 13 Boundary-value Problems 13-1 Introduction 13-2 Homogenous Boundary-value Problems 13-3 Eigenvalue Problems 13-4 Orthogonal Functions 13-5 Generalized Fourier Series 13-6 Weight Functions 13-7 The Sturm-Liouville Problem 13-8 Theorems on Eigenvalues and Eigenfunctions 13-9 Ordinary Fourier Series 13-10 Fourier-Bessel Series 13-11 Fourier-Legendre Series 13-12 Nonhomogeneous Boundary-value Problems Chap. 14 Partial Differential Equations of Mathematical Physics 14-1 Introduction 14-2 The Vibrating String 14-3 Heat Conduction 14-4 Laplace's Equation 14-5 Theory of Second-order Equations Chap. 15 Further Applications of Partial Differential Equations 15-1 Introduction 15-2 Laplace's Equation in Three Dimensions 15-3 Temperature in an Infinite Cylinder 15-4 Vibrating Membranes Appendix A Infinite Series Appendix B Functions of a Complex Variable References Answers and Hints Index

Product Description

Coherent introductory text focuses on initial- and boundary-value problems, general properties of linear equations, and differences between linear and nonlinear systems. Answers to most problems.

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 0486411540
• ISBN 13: 9780486411545
• Rilegatura: Copertina flessibile
• Numero di pagine: 545
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia