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Differential equations : computing and modeling

Author: C Henry Edwards; David E Penney; David Calvis
Publisher: Upper Saddle River, NJ : Pearson/Prentice Hall, ©2008.
Edition/Format:   Print book : English : 4th edView all editions and formats

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Additional Physical Format: Online version:
Edwards, C.H. (Charles Henry), 1937-
Differential equations.
Upper Saddle River, NJ : Pearson/Prentice Hall, ©2008
Document Type: Book
All Authors / Contributors: C Henry Edwards; David E Penney; David Calvis
ISBN: 9780136004387 0136004385
OCLC Number: 144228009
Description: xii, 575 pages : illustrations ; 26 cm
Contents: 1. First Order Differential Equations. Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Slope Fields and Solution Curves. Separable Equations and Applications. Linear First Order Equations. Substitution Methods and Exact Equations.2. Mathematical Models and Numerical Methods. Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method, and Improvements. The Runge-Kutta Method.3. Linear Equations of Higher Order. Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and Undetermined Coefficients. Forced Oscillations and Resonance. Electrical Circuits. Endpoint Problems and Eigenvalues.4. Introduction to Systems of Differential Equations. First-Order Systems and Applications. The Method of Elimination. Numerical Methods for Systems.5. Linear Systems of Differential Equations. Linear Systems and Matrices. The Eigenvalue Method for Homogeneous Systems. Second Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogeneous Linear Systems.6. Nonlinear Systems and Phenomena. Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems. Chaos in Dynamical Systems.7. Laplace Transform Methods. Laplace Transforms and Inverse Transforms. Transformation of Initial Value Problems. Translation and Partial Fractions. Derivatives, Integrals, and Products of Transforms. Periodic and Piecewise Continuous Forcing Functions. Impulses and Delta Functions.
Responsibility: C. Henry Edwards, David E. Penney, with the assistance of David Calvis.


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