Bhaskar Dasgupta is associate professor in the Department of Mechanical Engineering at Indian Institute of Technology Kanpur. He received his doctorate from the Indian Institute of Science, Bangalore, India in 1997. His ever-expanding research interests include topics in robotics such as serial and parallel manipulators, and motion planning methods; as well as nonlinear optimization, domain mapping, geometric modelling and protein docking. In his spare time, he takes a zealous interest in languages, literature, history and philosophy.

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*