MAT 101

Differential calculus: Functions of real variable and their plots, limit. Continuity and derivatives, physical meaning of derivative of a function. Successive derivatives: Leibniz Theorem; Roll’s theorem, new value theorem, and Taylor’s theorem. Taylor’s and Maclaurin’s series and expansion inunctions. Maximum and minimum values of function: Functions of two or three variables partial and total derivatives. Euler’s theorem. Tangent and normal. Subtangent and subnormal in Cartesian and polar coordinates. Curvature, asymptotes and curve tracing. Integral Calculus: Different techniques of integration. Definite integral as the limit of a sum and as an area. Definition of remain integral, fundamental theorem of integral calculus and its applications to definite integrals, reduction formulae, Walli’s formulae. Improper integrals. Improper integrals: Beta and gamma functions.