LINEAR ORDINARY DIFFERENTIAL EQUATIONS-------PHI
Description:
Linear Ordinary Differential Equations
presents a thorough discussion of the development of the main topics in
linear differential equations. A rich collection of applications,
examples, and exercises illustrates each topic. The text reinforces
students’ understanding of ideas from calculus, linear algebra, and
analysis while introducing the many applications of differential
equations in science and engineering.
Three main mathematical subdisciplines run throughout the book. The methods of linear algebra are
directly applied to the analysis of systems with constant or periodic
coefficients and also serve as a guide in the study of eigenvalues and
eigenfunction expansions. In addition to the thorough treatment of
classical power series techniques, matrix-valued series are used for the development of the experimental function. Methods of real analysis are
used to understand convergence of series solutions to equations,
existence theorems for initial value problems, the asymptotic behavior
of solutions, and the convergence of eigenfunction expansions.
The book is designed for needs of advanced undergraduate students in
mathematics and postgraduate students in pure mathematics as well as
applied mathematics, engineering, and science. It can also serve as a
useful text for both students and professionals in science and
engineering because ordinary differential equations arise in numerous
scientific and engineering models.
Contents:
Chapter 1: Simple Applications
Chapter 2: Properties of Linear Systems
Chapter 3: Constant Coefficients
Chapter 4: Periodic Coefficients
Chapter 5: Analytic Coefficients
Chapter 6: Singular Points
Chapter 7: Existence and Uniqueness
Chapter 8: Eigenvalue Problems
Chapter 9: Eigenfunction Expansions
Chapter 10: Control of Linear Systems
Bibliography
