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Differential Equations with Boundary Value Problems (Classic Version), 2nd edition

  • John Polking
  • Al Boggess
  • David Arnold

Published by Pearson (February 8th 2017) - Copyright © 2018

2nd edition

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Differential Equations with Boundary Value Problems (All Inclusive)

ISBN-13: 9780134310534

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Overview

Table of contents

Chapter 1: Introduction to Differential Equations

Differential Equation Models. The Derivative. Integration.

 

Chapter 2:  First-Order Equations

Differential Equations and Solutions. Solutions to Separable Equations. Models of Motion. Linear Equations.

Mixing Problems. Exact Differential Equations. Existence and Uniqueness of Solutions. Dependence of Solutions on Initial Conditions. Autonomous Equations and Stability.

Project 2.10 The Daredevil Skydiver.

 

Chapter 3: Modeling and Applications

Modeling Population Growth. Models and the Real World. Personal Finance. Electrical Circuits. Project 3.5 The Spruce Budworm. Project 3.6 Social Security, Now or Later.

 

Chapter 4: Second-Order Equations

Definitions and Examples. Second-Order Equations and Systems. Linear, Homogeneous Equations with Constant Coefficients. Harmonic Motion. Inhomogeneous Equations; the Method of Undetermined Coefficients. Variation of Parameters. Forced Harmonic Motion. Project 4.8 Nonlinear Oscillators.

 

Chapter 5: The Laplace Transform

The Definition of the Laplace Transform. Basic Properties of the Laplace Transform 241. The Inverse Laplace Transform

Using the Laplace Transform to Solve Differential Equations. Discontinuous Forcing Terms. The Delta Function. Convolutions. Summary. Project 5.9 Forced Harmonic Oscillators.

 

Chapter 6: Numerical Methods

Euler’s Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale.

Project 6.6 Numerical Error Comparison.

 

Chapter 7: Matrix Algebra

Vectors and Matrices. Systems of Linear Equations with Two or Three Variables. Solving Systems of Equations. Homogeneous and Inhomogeneous Systems. Bases of a subspace. Square Matrices. Determinants.

 

Chapter 8:  An Introduction to Systems

Definitions and Examples. Geometric Interpretation of Solutions. Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8.6 Long-Term Behavior of Solutions.

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