Differential Equations with Boundary Value Problems
Pearson New International Edition
2nd Edition
Published on 8. November 2013
Book
Paperback/Softback
708 pages
978-1-292-03915-2 (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
Harlow
United Kingdom
Target group
College/higher education
Dimensions
Height: 226 mm
Width: 155 mm
Thickness: 15 mm
Weight
476 gr
ISBN-13
978-1-292-03915-2 (9781292039152)
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
Content
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. T
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. T