Introduction to Linear Algebra and Differential Equations

By John W. Dettman

Book Overview

Written for the undergraduate who has completed a year of calculus, this clear, skillfully organized text combines two important topics in modern mathematics in one comprehensive volume.
As Professor Dettman (Oakland University, Rochester, Michigan) points out, "Not only is linear algebra indispensable to the mathematics major, but . . . it is that part of algebra which is most useful in the application of mathematical analysis to other areas, e.g. linear programming, systems analysis, statistics, numerical analysis, combinatorics, and mathematical physics."
The book progresses from familiar ideas to more complex and difficult concepts, with applications introduced along the way, to clarify or illustrate theoretical material.
Among the topics covered are complex numbers, including two-dimensional vectors and functions of a complex variable; matrices and determinants; vector spaces; symmetric and hermitian matrices; first order nonlinear equations; linear differential equations; power-series methods; Laplace transforms; Bessel functions; systems of differential equations; and boundary value problems.
To reinforce and expand each chapter, numerous worked-out examples are included. A unique pedagogical feature is the starred section at the end of each chapter. Although these sections are not essential to the sequence of the book, they are related to the basic material and offer advanced topics to stimulate the more ambitious student. These topics include power series; existence and uniqueness theorems; Hilbert spaces; Jordan forms; Green's functions; Bernstein polynomials; and the Weierstrass approximation theorem.
This carefully structured textbook provides an ideal, step-by-step transition from first-year calculus to multivariable calculus and, at the same time, enables the instructor to offer special challenges to students ready for more advanced material.

• Format: Paperback
• Language: English
• ISBN: 0486651916
• ISBN13: 9780486651910
• Release Date: December 1986
• Publisher: Dover Publications
• Length: 432 Pages
• Weight: 0.99 lbs.
• Dimensions: 0.8" x 5.4" x 8.5"

Customer Reviews

Good for reference or self study

The book is easy to read. Dettman manages to find an excellent balance between formal proof and informal explanation. The first two chapters on Complex Numbers and Linear Algebraic Equations are particularly good, and this has become the first book I usually reach for if I need to look up something about matrices. Matrix notation is used throughout the book for topics such as linear transformations and systems of equations. There are hints and answers to about half the exercises at the end of the book, making it very helpful for self study.

Excellent for Physicists

I am a physicist, and as a sophomore in college I was warned by the juniors: "Learn linear algebra!!!! They hardly teach any of it in the required math classes, and you'll die in quantum without it!!!" So I studied this book. Even without doing many of the problems I got a clear grasp of what a vector space is, why it is more than mere formalism, what a linear transformation is, the significance of bases, diagonalization, and how to work with matrices and really understand them. All of this was indispensable in studying quantum mechanics.Of course, solving the problems will only help your understanding. I HIGHLY recommend this for any physics student who had a bad (or non-existent) linear algebra class.