Unit-I
Limit and continuity of functions of two and three variables. Partial differentiation. Change of variables. Partial derivation and differentiability of real-valued functions of two and three variables. Schwarz and Young’s theorem. Statements of Inverse and implicit function theorems and applications. Vector differentiation, Gradient, Divergence and Curl with their properties and applications. 
 
Unit-II
Euler’s theorem on homogeneous functions. Taylor’s theorem for functions of two and three variables. Jacobians. Envelopes. Evolutes. Maxima, minima and saddle points of functions of two and three variables. Lagrange’s multiplier method.