Advanced Mathematical Methods

This text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics.

Adam Ostaszewski (Author)

9780521289641, Cambridge University Press

Paperback, published 25 January 1991

560 pages
22.5 x 15.1 x 2.9 cm, 0.77 kg

"A wonderful reference book." The American Mathematical Monthly

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. 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, giving concrete and geometric explanations, 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 interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.

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.

Subject Areas: Maths for engineers [TBJ], Maths for scientists [PDE]