Differential Equations and Boundary Value Problems: Computing and Modeling, 6th edition

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

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Differential Equations and Boundary Value Problems: Computing and Modeling balances concepts, visualization, applications and skills, helping you develop the conceptual understanding and geometric visualization that are essential for science and engineering students. It utilizes computer algebra systems such as Mathematica, Maple, and MATLAB plus online platforms like Wolfram|Alpha and GeoGebra, along with traditional manual methods. The text begins and ends with discussion of mathematical modeling of real-world phenomena, evident in its figures, examples, problems and applications. The 6th Edition adds and updates content throughout, including an expanded Application Module for Section 6.4 that discusses COVID-19.

Published by Pearson (July 7th 2022) - Copyright © 2023

ISBN-13: 9780137540365

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 
References for Further Study
Appendix: Existence and Uniqueness of Solutions
Answers to Selected Problems

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