(Ebook) Differential Equations with Boundary Value Problems 2nd Edition by John Polking, Al Boggess, David Arnold ISBN 9780131862364 0131862367

(Ebook) Differential Equations with Boundary Value Problems 2nd Edition by John Polking, Al Boggess, David Arnold ISBN 9780131862364 0131862367

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ISBN 10: 0131862367
ISBN 13: 9780131862364
Author: John Polking, Al Boggess, David Arnold

(Ebook) Differential Equations with Boundary Value Problems 2nd Edition 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

• 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

Chapter 8: An Introduction to Systems

• Systems of Differential Equations

• Phase Plane Portraits

• Autonomous Systems

• Stability of Linear Systems

• Project 8.5: The Predator-Prey Model

Chapter 9: Linear Systems with Constant Coefficients

• Linear Systems with Constant Coefficients

• Complex Eigenvalues

• Real Eigenvalues

• Nonhomogeneous Systems

• Project 9.7: The Forced Spring-Mass System

Chapter 10: Nonlinear Systems

• Nonlinear Systems

• Phase Plane Portraits for Nonlinear Systems

• Stability of Nonlinear Systems

• Project 10.6: The Van der Pol Oscillator

Chapter 11: Series Solutions to Differential Equations

• Power Series Solutions

• The Method of Frobenius

• Regular Singular Points

• Project 11.4: Bessel’s Equation

Chapter 12: Fourier Series

• Fourier Series

• Even and Odd Functions

• Fourier Cosine and Sine Series

• Fourier Series for Periodic Functions

• Project 12.3: Heat Conduction in a Rod

Chapter 13: Partial Differential Equations

• Introduction to Partial Differential Equations

• The Heat Equation

• The Wave Equation

• Laplace’s Equation

• Separation of Variables

• Project 13.4: Vibrations of a Drumhead

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Tags: John Polking, Al Boggess, David Arnold, Differential Equations, Value Problems