Description: About this productProduct InformationCombining 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.Product IdentifiersPublisherPrentice Hall PTRISBN-100131437380ISBN-139780131437388eBay Product ID (ePID)43551005Product Key FeaturesAuthorDavid Arnold, Al Boggess, John PolkingPublication NameDifferential EquationsFormatHardcoverLanguageEnglishPublication Year2005TypeTextbookNumber of Pages656 PagesDimensionsItem Length9.7in.Item Height1in.Item Width7.8in.Item Weight48.3 OzAdditional Product FeaturesLc Classification NumberQa371.P565 2006Edition Number2Table of ContentChapter 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 System s 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.Copyright Date2006Target AudienceCollege AudienceTopicDifferential Equations / General, GeneralLccn2005-048914Dewey Decimal515.35Dewey Edition22IllustratedYesGenreMathematics
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Item Length: 9.7in.
Item Height: 1in.
Item Width: 7.8in.
Author: David Arnold, Al Boggess, John Polking
Publication Name: Differential Equations
Format: Hardcover
Language: English
Publisher: Prentice Hall PTR
Publication Year: 2005
Type: Textbook
Item Weight: 48.3 Oz
Number of Pages: 656 Pages
