Reference Books:

Matrices: Rank and inverse of matrix by elementary transformations, consistency of linear system of equations and their solution, Eigen values and Eigen vectors, Cayley- Hamilton theorem (statement only) & its applications, diagonalization of matrices. Differential Calculus: Curvature, concavity, convexity and points of inflexion, asymptotes, partial differentiation, Euler’s theorem on homogeneous functions, total differentiation, approximate calculation, curve tracing (Cartesian and five polar curves-Folium of Descartes, Limacon, Cardioids, Lemniscates of Bernoulli and Equiangular spiral). Integral Calculus: Improper Integrals, area and length of curves. Surface area and volume of solid of revolution, multiple integrals, change of order of integration. (Cartesian form). Vector Calculus: Differentiation and integration of vector functions of scalar variables, scalar and vector fields, gradient, directional derivative, divergence, curl. Line integral, surface integral and volume integral. Green’s, Gauss’s and Stokes’s theorems (statement only) and their simple applications. Text Books