Differential Equations: Computing And Modeling

Hardcover | September 4, 2014

byC. Henry Edwards, David E. Penney, David Calvis

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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.

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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, includi...

C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief...

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Format:HardcoverDimensions:576 pages, 10.1 × 7.9 × 1 inPublished:September 4, 2014Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0321816250

ISBN - 13:9780321816252

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Table of Contents

 

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

 

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

 

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 Coef cients

3.4 Mechanical Vibrations

3.5 Nonhomogeneous Equations and Undetermined Coef cients

3.6 Forced Oscillations and Resonance

3.7 Electrical Circuits

3.8 Endpoint Problems and Eigenvalues

 

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

 

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

 

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

 

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