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

  • C Henry Edwards
  • , David E. Penney
  • , David Calvis

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

The right balance between concepts, visualization, applications and skills

Differential Equations and Boundary Value Problems: 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.

Published by Pearson (December 11th 2020) - Copyright © 2019

ISBN-13: 9780137399413

Subject: Advanced Math

Category: Differential Equations

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
  8. Power Series Methods
    • 8.1 Introduction and Review of Power Series
    • 8.2 Series Solutions Near Ordinary Points
    • 8.3 Regular Singular Points
    • 8.4 Method of Frobenius: The Exceptional Cases
    • 8.5 Bessel’s Equation
    • 8.6 Applications of Bessel Functions
  9. Fourier Series Methods and Partial Differential Equations
    • 9.1 Periodic Functions and Trigonometric Series
    • 9.2 General Fourier Series and Convergence
    • 9.3 Fourier Sine and Cosine Series
    • 9.4 Applications of Fourier Series
    • 9.5 Heat Conduction and Separation of Variables
    • 9.6 Vibrating Strings and the One-Dimensional Wave Equation
    • 9.7 Steady-State Temperature and Laplace’s Equation
  10. Eigenvalue Methods and Boundary Value Problems
    • 10.1 Sturm—Liouville Problems and Eigenfunction Expansions
    • 10.2 Applications of Eigenfunction Series
    • 10.3 Steady Periodic Solutions and Natural Frequencies
    • 10.4 Cylindrical Coordinate Problems
    • 10.5 Higher-Dimensional Phenomena