Basic Calculus - 1

This course is a follow up to the calculus course taught in schools. Some of the notions done earlier will be presented in a more rigorous manner and some new notions will be introduced. The course aims at treating rigorously the notions of continuity, differentiabilty and integrability and their applications. INTENDED AUDIENCE :B.Sc. PREREQUISITES : School MathematicsINDUSTRIES SUPPORT :None

Week 1:Real numbers, Functions and their graphs. Week 2:Limits of functions, Left and Right hand limits. Week 3:Continuity, Intermediate value property. Week 4:Differentiation, Chain rule, Implicit differentiation.
Week 5:Extreme values, Rolle’s theorem, Mean value theorems. Week 6:Local extrema. Week 7:Limits at infinity, Infinite limits, Asymptotes, Differentials. Week 8:Definite integrals, Area, Mean value theorem.
Week 9:The fundamental theorem, Indefinite integral. Week 10:Integration by substitution, Area between curves. Week 11:Volume by slicing, Volume of revolution, Cylindrical shells. Week 12:Lengths of plane curves, Area of surface of revolution.