MA 102 Mathematics-II 3-1-0-8
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.
1.D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
2.S. L. Ross, Differential Equations, 3rd Edition, Wiley India, 1984.
1.G. Strang, Linear Algebra and Its Applications, 4th Edition, Brooks/Cole India, 2006.
2.K. Hoffman and R. Kunze, Linear Algebra, 2nd 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