Table of Content

1. Preliminary Background
2. Matrices and Linear Transformations
3. Operational Fundamentals of Linear Algebra
4. Systems of Linear Equations
5. Gauss Elimination Family of Methods
6. Special Systems and Special Methods
7. Numerical Aspects in Linear Systems
8. Eigenvalues and Eigenvectors
9. Diagonalization and Similarity Transformations
10. Jacobi and Givens Rotation Methods
11. Householder Transformation and Tridiagonal Matrices
12. QR Decomposition Method
13. Eigenvalue Problem of General Matrices
14. Singular Value Decomposition
15. Vector Spaces: Fundamental Concepts*
16. Topics in Multivariate Calculus
17. Vector Analysis: Curves and Surfaces
18. Scalar and Vector Fields
19. Polynomial Equations
20. Solution of Nonlinear Equations and Systems
21. Optimization: Introduction
22. Multivariate Optimization
23. Methods of Nonlinear Optimization*
24. Constrained Optimization
25. Linear and Quadratic Programming Problems*
26. Interpolation and Approximation
27. Basic Methods of Numerical Integration
28. Advanced Topics in Numerical Integration*
29. Numerical Solution of Ordinary Differential Equations
30. ODE Solutions: Advanced Issues
31. Existence and Uniqueness Theory
32. First Order Ordinary Differential Equations
33. Second Order Linear Homogeneous ODE's
34. Second Order Linear Non-Homogeneous ODE's
35. Higher Order Linear ODE's
36. Laplace Transforms
37. ODE Systems
38. Stability of Dynamic Systems
39. Series Solutions and Special Functions
40. Sturm-Liouville Theory
41. Fourier Series and Integrals
42. Fourier Transforms
43. Minimax Approximation*
44. Partial Di_erential Equations
45. Analytic Functions
46. Integrals in the Complex Plane
47. Singularities of Complex Functions
48. Variational Calculus*

Salient Features