Differential Equations: Computing and Modeling, Tech Update, 5th edition

Published by Pearson (January 1, 2021) © 2022

  • C Henry Edwards University of Georgia, Athens
  • David E. Penney University of Georgia, Athens
  • David Calvis Baldwin Wallace University
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Platform features

  • Pearson+ eTextbook with study tools
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  • Interactive course-specific content
  • Real-time analytics and insights
Products list

Platform features

  • Pearson+ eTextbook with study tools
  • Tailored feedback on assignments
  • Interactive course-specific content
  • Real-time analytics and insights
Products list

Platform features

  • Pearson+ eTextbook with study tools
  • Tailored feedback on assignments
  • Interactive course-specific content
  • Real-time analytics and insights
Products list

Platform features

  • Pearson+ eTextbook with study tools
  • Tailored feedback on assignments
  • Interactive course-specific content
  • Real-time analytics and insights

Title overview

Differential Equations: Computing and Modeling, 5th Edition gives you the right balance between concepts, visualization, applications and skills. It provides the conceptual development and geometric visualization that are essential to science and engineering students, balancing traditional manual methods with the computer-based methods that illuminate qualitative phenomena. This comprehensive approach makes a wider range of realistic applications more accessible. The authors start and end the text with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems and applications throughout. This text is ideal for 1-semester sophomore- or junior-level courses in Differential Equations.

Table of contents

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 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
  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

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