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Differential Equations Computing and Modeling

ISBN-10: 0130673374
ISBN-13: 9780130673374
Edition: 3rd 2004
List price: $138.20
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Description: For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new  More...

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Book details

List price: $138.20
Edition: 3rd
Copyright year: 2004
Publisher: Prentice Hall PTR
Publication date: 6/19/2003
Binding: Hardcover
Pages: 574
Size: 8.50" wide x 10.25" long x 1.00" tall
Weight: 2.794
Language: English

For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new emphases that permeate the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; its focus has shifted from the traditional manual methods to new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

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
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
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
Introduction to Systems of Differential Equations
First-Order Systems and Applications
The Method of Elimination
Numerical Methods for Systems
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
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
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

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