**Prerequisite: **Nil

**Syllabus:**

Convergence of sequences and series of real numbers; continuity of
functions; differentiability, Rolle's theorem, mean value theorem, Taylor's
theorem; power series; Riemann integration, fundamental theorem of calculus,
improper integrals; application to length, area, volume and surface area of
revolution.

Vector functions of one variable – continuity and differentiability;
functions of several variables – continuity, partial derivatives, directional
derivatives, gradient, differentiability, chain rule; tangent planes and
normals, maxima and minima, Lagrange multiplier method; repeated and multiple
integrals with applications 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:**

1.G. B. Thomas,
Jr. and R. L. Finney, Calculus and Analytic Geometry, 9^{th} Edition,
Pearson Education India, 1996.

**References:**

1.R. G. Bartle
and D. R. Sherbert, Introduction to Real Analysis, 3^{rd} Edition,
Wiley India, 2005.

2.S. R.
Ghorpade and B. V. Limaye, An Introduction to Calculus and Real Analysis,
Springer India, 2006.

3.T. M.
Apostol, Calculus, Volume-2, 2^{nd} Edition, Wiley India, 2003.