UNIT  I : DIFFERENTIAL CALCULUS – I
Leibnitz’s Theorem, Partial Derivatives, Euler’s theorem for homogeneous functions, Total derivatives,Change of Variables, Curve Tracing, Cartesian and Polar Coordinates.
UNIT  II : DIFFERENTIAL CALCULUS – II
Taylor’s and Maclaurin’s Theorems, Expansion of function of several variables, Jacobian, Approximation of Errors, Extrema of Functions of Several Variables, Lagrange’s Method of Multipliers (Simple Applications)
UNIT  III : LINEAR ALGEBRA
Inverse of a matrix by elementary transformations, Rank of a matrix (Echelon & Normal form), Linear Dependence, Consistency of Linear System of Equations and their Solution , Characteristic Equation, Eigen values and eigen vectors, CayleyHamilton Theorem, Application of matrices to engineering problems, A brief introduction to Vector Spaces, Subspaces, Rank & Nullity, Linear Transformations.
UNIT  IV : MULTIPLE INTEGRALS
Double and triple integrals, Change of order of integration, Change of variables, Application of integration to lengths, Volumes and Surface areas, Cartesian and Polar Coordinates, Beta and Gamma function,s Dirichlet’s integral and applications.
UNIT  V : VECTOR CALCULUS
Point function, Gradient, Divergence and curl and their physical interpretations, Vector identities, Directional derivatives, Line, Surface and volume Integrals, Applications of Green’s, Stoke’s and Gauss divergence theorems (without proofs).
