Properties of real numbers. Sequences of real numbers, montone sequences, Cauchy sequences, divergent sequences. Series of real numbers, Cauchy’s criterion, tests for convergence. Limits of functions, continuous functions, uniform continuity, montone and inverse functions. Differentiable functions, Rolle's theorem, mean value theorems and Taylor's theorem, power series. Riemann integration, fundamental theorem of integral calculus, improper integrals. Application to length, area, volume, surface area of revolution.

Vector functions of one variable and their derivatives. Functions of several variables, partial derivatives, chain rule, gradient and directional derivative. Tangent planes and normals. Maxima, minima, saddle points, Lagrange multipliers, exact differentials.

Repeated and multiple integrals with application to volume, surface area, moments of inertia. Change of variables. Vector fields, line and surface integrals. Green’s, Gauss’ and Stokes’ theorems and their applications.

Texts:

• T. M. Apostol, Calculus, Volume I, 2nd Edition, Wiley, 1967.
• T. M. Apostol, Calculus, Volume II, 2nd Edition, Wiley, 1969.
• G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 6th/9th Edition, Narosa/Addison Wesley, 1985/1996.

References:

• R.G. Bartle and D.R. Sherbert, Introduction to Real Analysis, 3rd Edition, Wiley, 1999.
• J. Stewart, Calculus : Early Transcendentals, 5th Edition, Thomson Learning (Brooks/Cole), Indian Reprint, 2003.