Differential Calculus: ∈ – δ definition of the limit of a function. Basic properties of limits. Continuous functions and classification of discontinuities. Differentiability, Derivative of nth order, Leibnitz theorem, Asymptotes. Test for concavity and convexity , Points of inflexion, Tracing of Curves with y¢ and y¢¢ (Standard curves in Cartesian form without use of Grapher).
Functions of several variables: Limits, continuity and differentiability of two variables. Partial derivatives and its Linearization, Chain rule, Partial derivative with constrained variables. Homogeneous functions, Euler theorem and its applications, Extreme values and saddle points, Lagrange multipliers, Taylor’s theorem and its linear and quadratic approximation.