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

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

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Overview

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
Index

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

ISBN-13: 9780137540365

Subject: Advanced Math

Category: Differential Equations

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