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by John Polking, Al Boggess and David Arnold

Cover type: HardbackEdition: 2ND 06

Copyright: 2006

Publisher: Prentice Hall, Inc.

Published: 2006

International: No

List price: $213.50

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Combining traditional differential equation material with a modern qualitative and systems approach, this new edition continues to deliver flexibility of use and extensive problem sets. The second edition's refreshed presentation includes extensive new visuals, as well as updated exercises throughout.

**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.

**Chapter 9. Linear Systems with Constant Coefficients**

Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules.

**Chapter 10. Nonlinear Systems**

The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator--Prey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species.

**Chapter 11. Series Solutions to Differential Equations**

Review of Power Series. Series Solutions Near Ordinary Points. Legendre's Equation. Types of Singular Points-Euler's Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points -- the General Case. Bessel's Equation and Bessel Functions

**Chapter 12. Fourier Series**

Computation of Fourier Series. Convergence of Fourier Series. Fourier Cosine and Sine Series. The Complex Form of a Fourier Series. The Discrete Fourier Transform and the FFT.

**Chapter 13. Partial Differential Equations**

Derivation of the Heat Equation. Separation of Variables for the Heat Equation. The Wave Equation. Laplace's Equation. Laplace's Equation on a Disk. Sturm Liouville Problems. Orthogonality and Generalized Fourier Series. Temperature in a Ball-Legendre Polynomials. Time Dependent PDEs in Higher Dimension. Domains with Circular Symmetry--Bessel Functions.

Appendix. Complex Numbers and Matrices

Answers to Odd-Numbered Problems

Index

- Windows 7/8, or Mac OS X 10.6 or above

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Summary

Combining traditional differential equation material with a modern qualitative and systems approach, this new edition continues to deliver flexibility of use and extensive problem sets. The second edition's refreshed presentation includes extensive new visuals, as well as updated exercises throughout.

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.

**Chapter 9. Linear Systems with Constant Coefficients**

Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules.

**Chapter 10. Nonlinear Systems**

The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator--Prey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species.

**Chapter 11. Series Solutions to Differential Equations**

Review of Power Series. Series Solutions Near Ordinary Points. Legendre's Equation. Types of Singular Points-Euler's Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points -- the General Case. Bessel's Equation and Bessel Functions

**Chapter 12. Fourier Series**

Computation of Fourier Series. Convergence of Fourier Series. Fourier Cosine and Sine Series. The Complex Form of a Fourier Series. The Discrete Fourier Transform and the FFT.

**Chapter 13. Partial Differential Equations**

Derivation of the Heat Equation. Separation of Variables for the Heat Equation. The Wave Equation. Laplace's Equation. Laplace's Equation on a Disk. Sturm Liouville Problems. Orthogonality and Generalized Fourier Series. Temperature in a Ball-Legendre Polynomials. Time Dependent PDEs in Higher Dimension. Domains with Circular Symmetry--Bessel Functions.

Appendix. Complex Numbers and Matrices

Answers to Odd-Numbered Problems

Index

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**Copying:** Allowed, 2 selections may be copied every 180 days

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**Expires:** Yes, may be used for 180 days after activation

**Reading Aloud:** Allowed

**Sharing:** Not Allowed

**Min. Software Version:** Online: No additional software required

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**Suitable Devices:** PCs, Tablet PCs, Macs, Laptops

**Copying** - Books that cannot be copied will show "Not Allowed." Otherwise, this will detail the number of times it can be copied, or "Allowed with no limits."

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**Printing** - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."

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**Reading Aloud** - Books enabled with the "text-to-speech" feature so that they can be read aloud will show "Allowed."

**Sharing** - Books that cannot be shared with other computers will show "Not Allowed."

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Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2006

International: No

Published: 2006

International: No

**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.

**Chapter 9. Linear Systems with Constant Coefficients**

Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules.

**Chapter 10. Nonlinear Systems**

The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator--Prey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species.

**Chapter 11. Series Solutions to Differential Equations**

Review of Power Series. Series Solutions Near Ordinary Points. Legendre's Equation. Types of Singular Points-Euler's Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points -- the General Case. Bessel's Equation and Bessel Functions

**Chapter 12. Fourier Series**

Computation of Fourier Series. Convergence of Fourier Series. Fourier Cosine and Sine Series. The Complex Form of a Fourier Series. The Discrete Fourier Transform and the FFT.

**Chapter 13. Partial Differential Equations**

Derivation of the Heat Equation. Separation of Variables for the Heat Equation. The Wave Equation. Laplace's Equation. Laplace's Equation on a Disk. Sturm Liouville Problems. Orthogonality and Generalized Fourier Series. Temperature in a Ball-Legendre Polynomials. Time Dependent PDEs in Higher Dimension. Domains with Circular Symmetry--Bessel Functions.

Appendix. Complex Numbers and Matrices

Answers to Odd-Numbered Problems

Index

- Windows 7/8, or Mac OS X 10.6 or above

eTextbooks and eChapters can be viewed by using the free reader listed below.

Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.

Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.

Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

Click Here to access the VitalSource Bookshelf FAQ

VitalSource

**Copying:** Allowed, 2 selections may be copied every 180 days

**Printing:** Allowed, 2 prints for 180 days

**Expires:** Yes, may be used for 180 days after activation

**Reading Aloud:** Allowed

**Sharing:** Not Allowed

**Min. Software Version:** Online: No additional software required

Offline: VitalSource Bookshelf

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**Copying** - Books that cannot be copied will show "Not Allowed." Otherwise, this will detail the number of times it can be copied, or "Allowed with no limits."

Offline: VitalSource Bookshelf

**Digital Rights Management (DRM) Key**

**Printing** - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."

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**Reading Aloud** - Books enabled with the "text-to-speech" feature so that they can be read aloud will show "Allowed."

**Sharing** - Books that cannot be shared with other computers will show "Not Allowed."

**Min. Software Version** - This is the minimum software version needed to read this book.

**Suitable Devices** - Hardware known to be compatible with this book. Note: Reader software still needs to be installed.