MTL100 : Introduction to Calculus

Sivananthan Sampath

Review of limit, continuity and differentiability, uniform continuity. Mean value theorems and applications, Taylor’s theorem, maxima and minima. Sequences and series, limsup, liminf, convergence of sequences and series of real numbers, absolute and conditional convergence. Riemann integral, fundamental theorem of integral calculus, applications of definite integrals, improper integrals, beta and gamma functions. Functions of several variables, limit and continuity, partial derivatives and differentiability, gradient, directional derivatives, chain rule, Taylor’s theorem, maxima and minima and the method of Lagrange multipliers. Double and triple integration, Jacobian and change of variables formula.