|Number of Pages
Educational: Mathematics & numeracy
Linear Ordinary Differential Equationspresents 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 oflinear algebraare 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 classicalpower seriestechniques, matrix-valued series are used for the development of the experimental function. Methods ofreal analysisare 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.
Table of 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