Coordinate Geometry: Coordinates, polar coordinates, straight lines, Changes of axes, Pair of straight lines, Circle, Parabola, Ellipse, Hyperbola, rectangular coordinate, plane. Vector Analysis: Vector components, vector components in spherical and cylindrical system, vector operators, scalar and dot product, application of vector geometry, Derivative of vector, del, gradient, divergence and curl, physical significance, integration of vector. Line, surface and volume integration, Theorems (Green's, Gauss's, Liouville's, Stoke's) and their applications. Linear Algebra: Systems of Linear Equations (SLE): introduction to SLE, solution of a SLE, solution of a system of homogeneous LE, Gaussian and Gauss-Jordan elimination, Determinants: factorization, determinant, fundamental properties of determinants, minors and cofactors, Cramer's rules for solving a SLE, Algebra of Matrices: Matrix, some special types of matrices, transpose, adjoint and inverse of a matrix, algebraic operation on matrices, quadratic forms solution of a LE by applying matrices, Vector Space: space and subspace, Euclidean n-space, basis and dimension, rank and nullity, Linear Transformations (LT) and its Matrix Representations: LT from to , properties of LT, matrix representation of a LT, diagonalization of LT, Eigen Values and Eigen Vectors: polynomials of matrices and linear operators, eigen values and vectors, diagonalizability, Cayley-Hamilton theorem, characteristic and minimum polynomial Inner Product Spaces: inner product spaces, Cauchy-Schwarz inequality, orthogonality, Gram-Schmidt orthogonalization process, linear functional and adjoint operators, Some Applications of LA.
