Limit and Continuity of functions of two variables. Partial differentiation. Change of variables. Partial derivation and differentiability of real-valued functions of two variables. Schwartz’s and Young’s Theorem. Statements of Inverse and implicit function theorems and applications. Euler’s theorem on homogeneous functions. Taylor’s theorem for functions of two variables. Jacobins. Envelopes. Evolutes. Maxima, Minima and saddle points of functions of two variables. Lagrange’s undetermined multiplier method.
Double and Triple Integrals, Change of variables. Applications to evaluation of areas, Volumes, Surfaces of solid of revolution, Change of order of integration in double integrals.