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Differential equations

Author: C Henry Edwards; David E Penney
Publisher: Upper Saddle River, NJ : Pearson Education, 2003.
Edition/Format:   Print book : English : 3rd edView all editions and formats

Provides the conceptual development and geometric visualization of a modern differential equations course. This text reflects the emphases that permeate the learning of elementary differential  Read more...


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Document Type: Book
All Authors / Contributors: C Henry Edwards; David E Penney
ISBN: 0130673374 9780130673374
OCLC Number: 52092122
Description: 1 volume (various pagings) : illustrations (some color) ; 27 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.
Other Titles: Differential equations and boundary value problems.
Responsibility: C. Henry Edwards, David E. Penney.


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