Linear Ordinary Differential Equations
Will be published approx. on 31. December 1997
Book
Paperback/Softback
353 pages
978-0-89871-388-6 (ISBN)
Description
Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering.
Three recurrent themes run through the book:
The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions.
The use of power series, beginning with the matrix exponential function, leads to the special functions solving classical equations.
Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.
Three recurrent themes run through the book:
The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions.
The use of power series, beginning with the matrix exponential function, leads to the special functions solving classical equations.
Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.
More details
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
College/higher education
Product notice
Paperback (trade)
Dimensions
Height: 253 mm
Width: 178 mm
Thickness: 15 mm
Weight
636 gr
ISBN-13
978-0-89871-388-6 (9780898713886)
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
Preface
Chapter 1: Simple Applications. Introduction
Compartment systems
Springs and masses
Electric circuits
Notes
Exercises
Chapter 2: Properties of Linear Systems. Introduction
Basic linear algebra
First-order systems
Higher-order equations
Notes
Exercises
Chapter 3: Constant Coefficients. Introduction
Properties of the exponential of a matrix
Nonhomogeneous systems
Structure of the solution space
The Jordan canonical form of a matrix
The behavior of solutions for large t
Higher-order equations
Exercises
Chapter 4: Periodic Coefficients. Introduction
Floquet's theorem
The logarithm of an invertible matrix
Multipliers
The behavior of solutions for large t
First-order nonhomogeneous systems
Second-order homogeneous equations
Second-order nonhomogeneous equations
Notes
Exercises
Chapter 5: Analytic Coefficients. Introduction
Convergence
Analytic functions
First-order linear analytic systems
Equations of order n
The Legendre equation and its solutions
Notes
Exercises
Chapter 6: Singular Points. Introduction
Systems of equations with singular points
Single equations with singular points
Infinity as a singular point
Notes
Exercises
Chapter 7: Existence and Uniqueness. Introduction
Convergence of successive approximations
Continuity of solutions
More general linear equations
Estimates for second-order equations
Notes
Exercises
Chapter 8: Eigenvalue Problems. Introduction
Inner products
Boundary conditions and operators
Eigenvalues
Nonhomogeneous boundary value problems
Notes
Exercises
Chapter 9: Eigenfunction Expansions. Introduction
Selfadjoint integral operators
Eigenvalues for Green's operator
Convergence of eigenfunction expansions
Extensions of the expansion results
Notes
Exercises
Chapter 10: Control of Linear Systems. Introduction
Convex sets
Control of general linear systems
Constant coefficient equations
Time-optimal control
Notes
Exercises
Bibliography.
Chapter 1: Simple Applications. Introduction
Compartment systems
Springs and masses
Electric circuits
Notes
Exercises
Chapter 2: Properties of Linear Systems. Introduction
Basic linear algebra
First-order systems
Higher-order equations
Notes
Exercises
Chapter 3: Constant Coefficients. Introduction
Properties of the exponential of a matrix
Nonhomogeneous systems
Structure of the solution space
The Jordan canonical form of a matrix
The behavior of solutions for large t
Higher-order equations
Exercises
Chapter 4: Periodic Coefficients. Introduction
Floquet's theorem
The logarithm of an invertible matrix
Multipliers
The behavior of solutions for large t
First-order nonhomogeneous systems
Second-order homogeneous equations
Second-order nonhomogeneous equations
Notes
Exercises
Chapter 5: Analytic Coefficients. Introduction
Convergence
Analytic functions
First-order linear analytic systems
Equations of order n
The Legendre equation and its solutions
Notes
Exercises
Chapter 6: Singular Points. Introduction
Systems of equations with singular points
Single equations with singular points
Infinity as a singular point
Notes
Exercises
Chapter 7: Existence and Uniqueness. Introduction
Convergence of successive approximations
Continuity of solutions
More general linear equations
Estimates for second-order equations
Notes
Exercises
Chapter 8: Eigenvalue Problems. Introduction
Inner products
Boundary conditions and operators
Eigenvalues
Nonhomogeneous boundary value problems
Notes
Exercises
Chapter 9: Eigenfunction Expansions. Introduction
Selfadjoint integral operators
Eigenvalues for Green's operator
Convergence of eigenfunction expansions
Extensions of the expansion results
Notes
Exercises
Chapter 10: Control of Linear Systems. Introduction
Convex sets
Control of general linear systems
Constant coefficient equations
Time-optimal control
Notes
Exercises
Bibliography.