Differential Equations with Boundary Value Problems
2nd Edition
Published on 22. August 2005
Book
Hardback
768 pages
978-0-13-186236-4 (ISBN)
Description
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.
More details
Edition
2nd edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 261 mm
Width: 207 mm
Thickness: 29 mm
Weight
1560 gr
ISBN-13
978-0-13-186236-4 (9780131862364)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
John Polking | Al Boggess | David Arnold
Differential Equations with Boundary Value Problems (Classic Version)
Book
09/2017
2nd Edition
Pearson
€133.69
Article exhausted; check different version
Previous edition
John Polking | Albert Boggess | David Arnold
Differential Equations with Boundary Value Problems
Book
09/2002
Pearson
€90.36
Article exhausted; check for reprint
Content
Chapter 1: Introduction to Differential EquationsDifferential Equation Models. The Derivative. Integration.
Chapter 2: First-Order EquationsDifferential 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 ApplicationsModeling 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 EquationsDefinitions 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 TransformThe 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 MethodsEuler's Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale.
Project 6.6 Numerical Error Comparison.
Chapter 7: Matrix AlgebraVectors 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
Index
Chapter 2: First-Order EquationsDifferential 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 ApplicationsModeling 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 EquationsDefinitions 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 TransformThe 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 MethodsEuler's Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale.
Project 6.6 Numerical Error Comparison.
Chapter 7: Matrix AlgebraVectors 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
Index