2K6 301 : ENGINEERING MATHEMATICS II

Module I:
Infinite Series: Convergence and divergence of infinite series – Ratio test – Comparison test – Raabe’s test – Root test – Series of positive and negative terms- absolute convergence – Test for alternating series. Power Series: Interval of convergence – Taylors and Maclaurins series representation of functions – Leibnitz formula for the derivative of the product of two functions – use of Leibnitz formula in the Taylor and Maclaurin expansions
Module II:
Matrices: Concept of rank of a matrix –echelon and normal forms – System of linear equation – consistency – Gauss elimination– Homogeneous liner equations-Fundamental system of solutions- Inverse of a matrix – solution of a system of equations using matrix inversion – eigen values and eigen vectors – Cayley- Hamilton Theorem.
Module III:
Vector Integral Calculus: Evaluation of line integral, surface integral and volume integrals – Line integrals independent of the path, conservative force fields, scalar potential- Green’s theorem- Gauss’ divergence theorem- Stoke’s theorem (proof of these not required).
Module IV:
Vector Spaces: subspaces–linear dependence and independence–bases and dimension-linear
transformations -sums, products and inverse of linear transformations.

References:
1. Kreyszing E. Advanced Engineering Mathematics, Wiley Eastern
2. Sastri. S. S. Engineering Mathematics, Prentice Hall of India.
3. Wylie .C. R. Advanced Engineering Mathematics, Mc Grawhill.
4. B .S. Grewal. Higher Engineering Mathematics, Khanna Publishers.
5. Greenberg. M.D. Advanced Engineering Mathematics, Pearson Education Asia.
6. Narayanan .S. Manickavachagom Pella and Ramaiah. Advanced Mathematics for Engineering Students, S. Viswanathan Publishers