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, 9th Edition,
Pearson Education India, 1996.
References:
1.R. G. Bartle
and D. R. Sherbert, Introduction to Real Analysis, 3rd 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, 2nd Edition, Wiley India, 2003.