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

Published by Pearson (January 1, 2021) © 2019

  • C Henry Edwards University of Georgia, Athens
  • David E. Penney University of Georgia, Athens
  • David Calvis Baldwin Wallace University
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Buy nowOpens in a new tab

In this eTextbook — More ways to learn

  • More flexible. Start learning right away, on any device.
  • More supportive. Get AI explanations and practice questions (select titles).
  • More interactive. Bring learning to life with audio, videos, and diagrams.
  • More memorable. Make concepts stick with highlights, search, notes, and flashcards.
  • More understandable. Translate text into 100+ languages with one tap.
$59.94
monthly payments or
pay undefined one-time
Instant access

In this eTextbook — More ways to learn

  • More flexible. Start learning right away, on any device.
  • More supportive. Get AI explanations and practice questions (select titles).
  • More interactive. Bring learning to life with audio, videos, and diagrams.
  • More memorable. Make concepts stick with highlights, search, notes, and flashcards.
  • More understandable. Translate text into 100+ languages with one tap.
$59.94
monthly payments or
pay undefined one-time
Instant access

In this eTextbook — More ways to learn

  • More flexible. Start learning right away, on any device.
  • More supportive. Get AI explanations and practice questions (select titles).
  • More interactive. Bring learning to life with audio, videos, and diagrams.
  • More memorable. Make concepts stick with highlights, search, notes, and flashcards.
  • More understandable. Translate text into 100+ languages with one tap.

Title overview

For 1-semester sophomore- or junior-level courses in Differential Equations.

The right balance between concepts, visualization, applications and skills

Differential Equations: Computing and Modeling, 5th Edition provides the conceptual development and geometric visualization that are essential to science and engineering students. It balances traditional manual methods with the computer-based methods that illuminate qualitative phenomena. This comprehensive approach makes accessible a wider range of more realistic applications. The authors begin and end the text with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems and applications throughout.

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

Author bios

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