Advanced Mathematical Methods [Hardcover]

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.Accessible to students lacking in depth studies in mathematics, this self-contained second course on algebra and multivariate calculus will have particular appeal to those interested in applications rather than theory.Accessible to students lacking in depth studies in mathematics, this self-contained second course on algebra and multivariate calculus will have particular appeal to those interested in applications rather than theory.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.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 l£¾