by John Polking, Al Boggess and David Arnold
List price: $213.50
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
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Other Editions for Differential Equations With Boundary Value Problems
John Polking, Al Boggess and David Arnold
ISBN13: 978-0131862364Combining 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
Digital Rights
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.
Download Requirements: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.
User Help:
Click Here to access the VitalSource Bookshelf FAQ
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."
Expires - Books that have no expiration (the date upon which you will no longer be able to access your eBook) will read "No Expiration." Otherwise it will state the number of days from activation (the first time you actually read it).
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.
Other Editions for Differential Equations With Boundary Value Problems