Syllabus

Sequences and Series:

Limit of a sequence, monotone and Cauchy sequences and properties of convergent sequences, examples. Infinite series, positive series, tests for convergence and divergence, integral test, alternating series, Leibnitz test.

Differential Calculus:

Continuity and differentiability of a function of a single variable, statement of Rolle’s Theorem, Lagrange’s mean value theorem and applications.

Integral Calculus:

Definite Integrals as a limit of sums, Applications of integration to area, volume, surface area, Improper integrals.

Functions of several variables:

Continuity and differentiability, Mixed partial derivatives, Local maxima and minima for function of two variables, Lagrange multipliers.