MA 102 Mathematics-II 3-1-0-8

Prerequisite: Nil

Syllabus:

Systems of linear equations and their solutions; vector space Rⁿ and its subspaces; spanning set and linear independence; matrices, inverse and determinant; range space and rank, null space and nullity, eigenvalues and eigenvectors; diagonalization of matrices; similarity; inner product, Gram-Schmidt process; vector spaces (over the field of real and complex numbers), linear transformations.

First order differential equations – exact differential equations, integrating factors, Bernoulli equations, existence and uniqueness theorem, applications; higher-order linear differential equations – solutions of homogeneous and nonhomogeneous equations, method of variation of parameters, operator method; series solutions of linear differential equations, Legendre equation and Legendre polynomials, Bessel equation and Bessel functions of first and second kinds; systems of first-order equations, phase plane, critical points, stability.

Texts:

1.D. Poole, Linear Algebra: A Modern Introduction, 2^nd Edition, Brooks/Cole, 2005.

2.S. L. Ross, Differential Equations, 3^rd Edition, Wiley India, 1984.

References:

1.G. Strang, Linear Algebra and Its Applications, 4^th Edition, Brooks/Cole India, 2006.

2.K. Hoffman and R. Kunze, Linear Algebra, 2^nd Edition, Prentice Hall India, 2004.

3.E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice Hall India, 1995.

4.E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958