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Differential equations and boundary value problems : computing and modeling / C. Henry Edwards, David E. Penney, the University of Georgia ; with the assistance of David Calvis, Baldwin-Wallace College

Author
Edwards, C. Henry (Charles Henry), 1937-
Published
Upper Saddle River, New Jersey : Pearson Education, Inc., [2015]
Edition
Fifth edition.
Physical Description
xi, 780 pages : color illustrations ; 26 cm
Additional Creators
Penney, David E. and Calvis, David

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Contents
Machine generated contents note: ch. 1 First-Order Differential Equations -- 1.1.Differential Equations and Mathematical Models -- 1.2.Integrals as General and Particular Solutions -- 1.3.Slope Fields and Solution Curves -- 1.4.Separable Equations and Applications -- 1.5.Linear First-Order Equations -- 1.6.Substitution Methods and Exact Equations -- ch. 2 Mathematical Models and Numerical Methods -- 2.1.Population Models -- 2.2.Equilibrium Solutions and Stability -- 2.3.Acceleration--Velocity Models -- 2.4.Numerical Approximation: Euler's Method -- 2.5.A Closer Look at the Euler Method -- 2.6.The Runge--Kutta Method -- ch. 3 Linear Equations of Higher Order -- 3.1.Introduction: Second-Order Linear Equations -- 3.2.General Solutions of Linear Equations -- 3.3.Homogeneous Equations with Constant Coefficients -- 3.4.Mechanical Vibrations -- 3.5.Nonhomogeneous Equations and Undetermined Coefficients -- 3.6.Forced Oscillations and Resonance -- 3.7.Electrical Circuits -- 3.8.Endpoint Problems and Eigenvalues -- ch. 4 Introduction to Systems of Differential Equations -- 4.1.First-Order Systems and Applications -- 4.2.The Method of Elimination -- 4.3.Numerical Methods for Systems -- ch. 5 Linear Systems of Differential Equations -- 5.1.Matrices and Linear Systems -- 5.2.The Eigenvalue Method for Homogeneous Systems -- 5.3.A Gallery of Solution Curves of Linear Systems -- 5.4.Second-Order Systems and Mechanical Applications -- 5.5.Multiple Eigenvalue Solutions -- 5.6.Matrix Exponentials and Linear Systems -- 5.7.Nonhomogeneous Linear Systems -- ch. 6 Nonlinear Systems and Phenomena -- 6.1.Stability and the Phase Plane -- 6.2.Linear and Almost Linear Systems -- 6.3.Ecological Models: Predators and Competitors -- 6.4.Nonlinear Mechanical Systems -- 6.5.Chaos in Dynamical Systems -- ch. 7 Laplace Transform Methods -- 7.1.Laplace Transforms and Inverse Transforms -- 7.2.Transformation of Initial Value Problems -- 7.3.Translation and Partial Fractions -- 7.4.Derivatives, Integrals, and Products of Transforms -- 7.5.Periodic and Piecewise Continuous Input Functions -- 7.6.Impulses and Delta Functions -- ch. 8 Power Series Methods -- 8.1.Introduction and Review of Power Series -- 8.2.Series Solutions Near Ordinary Points -- 8.3.Regular Singular Points -- 8.4.Method of Frobenius: The Exceptional Cases -- 8.5.Bessel's Equation -- 8.6.Applications of Bessel Functions -- ch. 9 Fourier Series Methods and Partial Differential Equations -- 9.1.Periodic Functions and Trigonometric Series -- 9.2.General Fourier Series and Convergence -- 9.3.Fourier Sine and Cosine Series -- 9.4.Applications of Fourier Series -- 9.5.Heat Conduction and Separation of Variables -- 9.6.Vibrating Strings and the One-Dimensional Wave Equation -- 9.7.Steady-State Temperature and Laplace's Equation -- ch. 10 Eigenvalue Methods and Boundary Value Problems -- 10.1.Sturm--Liouville Problems and Eigenfunction Expansions -- 10.2.Applications of Eigenfunction Series -- 10.3.Steady Periodic Solutions and Natural Frequencies -- 10.4.Cylindrical Coordinate Problems -- 10.5.Higher-Dimensional Phenomena.
Subject(s)
ISBN
9780321796981 (hardcover)
0321796985 (hardcover)
Bibliography Note
Includes bibliographical references (pages 698-700) and index.
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