Geometry: Double integration: Evaluation of surface areas and volumes by integration. Area under a plane curve in Cartesian and polar coordinates. Area of the region enclosed by two curves in Cartesian and polar coordinates, Trapezoidal rule, Simpson’s rule, Arc lengths of curves, in Cartesian and polar coordinates, parametric and pedal equations, Intrinsic equation. Volumes of solids of revolution. Volumes of hollow solids of revolutions by shell method. Area of surface of revolution. Linear Algebra: Introduction to systems of linear equations. Gaussian elimination. Definition of matrices. Algebra of matrices. Transpose of a matrix and inverse of matrix. Factorization. Determinants. Quadratic forms. Matrix polynomials. Euclidean n-space. Linear transformation from IRn to IRm. Properties of linear transformation from IRn to IRm. Real vector spaces and subspaces. Basis and dimension. Rank and nullity. Inner product spaces. Gram-Schmidt process and QR-decomposition. Eigenvalues and eigenvectors. Diagonalization. Linear transformations. Kernel and Range. Application of linear algebra to electric networks.
