Limits, continuity and differentiability. Definition and proofs of important theorems via the application of ed concept.

Power series: radius of convergence, interval of convergence, differentiation and integration of power series.



Taylor series: expansion of basic functions (e.g., sin x, cos x, log (1 + x), exp (x)). Taylors formula for the remainder, improper integrals, convergence and divergence tests.

Partial derivatives: total differential, chain rule, implicit function. Maximum and minimum, Lagrange multiplier.

Multiple integral: iterated integral, variable conversion.

Sequences: introduction to limit of a sequence, limit theorems, techniques of finding limits and sequence of functions.



References:

1. Salas, S.L., Hille, E., & Etgen, G. (2003). Calculus: One and Several Variables (9th Edition). John Wiley & Sons.

2. Fitzpatrick, P.M. (2006). Advanced Calculus (2nd Edition). Brooks/ Cole.

3. Wrede, R.C., & Spiegel, M. (2002). Shaums Outline of Advanced Calculus (2nd Edition). McGraw-Hill.