Differential equations with boundary value problems
 Author/Creator
 Polking, John C.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Upper Saddle River, N.J. : Pearson/Prentice Hall, c2006.
 Physical description
 xiv, 703, [48] p. : ill. ; 27 cm.
Access
Available online

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QA371 .D4495 2006
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QA371 .D4495 2006

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QA371 .D4495 2006
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Contributors
 Contributor
 Boggess, Albert.
 Arnold, David, 1945
Contents/Summary
 Contents

 Chapter 1: Introduction to Differential Equations Differential Equation Models. The Derivative. Integration. Chapter 2: FirstOrder 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: SecondOrder Equations Definitions and Examples. SecondOrder 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. RungeKutta 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 LongTerm Behavior of Solutions. Chapter 9: Linear Systems with Constant Coefficients Overview of the Technique. Planar Systems. Phase Plane Portraits. The TraceDeterminant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. HigherOrder 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. LongTerm Behavior of Solutions. Invariant Sets and the Use of Nullclines. LongTerm Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. PredatorPrey 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 PointsEuler'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 BallLegendre Polynomials. Time Dependent PDEs in Higher Dimension. Domains with Circular SymmetryBessel Functions. Appendix: Complex Numbers and Matrices Answers to OddNumbered Problems Index.
 (source: Nielsen Book Data)
 Publisher's 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2006
 Responsibility
 John Polking, Albert Boggess, David Arnold.
 Note
 Includes index.
 ISBN
 0131862367
 9780131862364