Basic Calculus 1 and 2

Topics of continuity, differentablity, integrability of a real valued function will be discussed with their applications. Also series representations of some functions will be discussed.
INTENDED AUDIENCE :1st year B.Tech, Mathematics HonoursPREREQUISITES : Grade XIIINDUSTRIES SUPPORT :None

COURSE LAYOUT

Week 1:Algebra of Real Numbers, set of Axioms,Completeness,Density, decimal representation of real numbersWeek 2:Convergence of sequences, properties of limit, Sandwich Theorem, Monotonic sequences, Cantor's completeness Principle, Bolzano-Weierstrass Theorem, Cauchy's completenessWeek 3:Convergence of series, comparison test, Root test, Ratio test ,Power series, Leibniz's conditionWeek 4:Continuity, Intermediate Value theorem, Properties of continuous functions
Week 5:Differentiation, Rolle's Theorem, Mean Value theoremHigher derivatives Taylor theoremWeek 6:Curve tracing, Applications of derivativesWeek 7:Integrations, Week 8:Applications of Integration