MA102 Mathematics II (3-1-0-8)
Linear Algebra: Systems of linear equations, matrices, Gaussian elimination, echelon form, column space, null space, rank of a matrix, inverse and determinant; Vector spaces (over the field of real and complex numbers), subspaces, spanning set, linear independence, basis and dimension; Linear transformations, rank-nullity theorem, matrix of a linear trans-formation, change of basis and similarity; Eigenvalues and eigenvectors, algebraic and geometric multiplicity, diagonalization by similarity; Inner product spaces, Gram-Schmidt process, orthonormal basis; Orthogonal, Hermitian and symmetric matrices, spectral theorem for real symmetric matrices.
Ordinary Differential Equations: 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.
 D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
 S. L. Ross, Differential Equations, 3rd Edition, Wiley India, 1984.
 G. Strang, Linear Algebra and Its Applications, 4th Edition, Brooks/Cole India, 2006.
 K. Hoffman and R. Kunze, Linear Algebra, 2nd Edition, Prentice Hall India, 2004.
 E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice Hall India, 1995.
 E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958.