Advanced Mathematical Methods

by Adam Ostaszewski

Overview

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods in linear algebra and multivariate calculus. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a "cookbook" approach, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interests are in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.

Product Details

ISBN-13:	9780521247887
Publisher:	Cambridge University Press
Publication date:	01/25/1991
Series:	London School of Economics Mathematics
Pages:	560
Product dimensions:	5.98(w) x 9.02(h) x 1.38(d)

Table of Contents

Preface; Part I. Linear Algebra: 1. Vector spaces (revision); 2. Geometry in R; 3. Matrices; 4. Projections; 5. Spectral theory; 6. The upper triangular form; 7. The tri-diagonal form; 8. Inverses; 9. Convexity; 10. The separating hyperplane theorem; 11. Linear inequalities; 12. Linear programming and game theory; 13. The simplex method; 14. Partial derivatives (revision); 15. Convex functions; 16. Non-linear programming; Part II. Advanced Calculus: 1. The integration process; 2. Manipulation of integrals; 3. Multiple integrals; 4. Differential and difference equations (revision); 5. Laplace transforms; 6. Series solutions of differential equations; 7. Calculus of variations; Part III. Solutions to Selected Exercises; Index.

Editorial Reviews

"A wonderful reference book." The American Mathematical Monthly

From the Publisher