Advanced Mathematical Methods Book

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.