There will be around 19 Lectures. Each lectures will be of 50 minutes. There will be tutorial each week and will be taken by an assigned tutor. Office hours will be provided by tutors. Students can clear their doubts during the office hours or mailing to the respective tutors. Lecture notes are available in the website
https://sites.google.com/site/abhijitwebpage/lecture-notes-mth113m.
Feedback and suggestions are always welcome and can be communicated by mailing to abhipal@iitk.ac.in
Application of definite integral, Area between two curves, Polar coordinates, Graphs of polar coordinates, Area between two curves when their equations are given in polar coordinates, Volumes by slicing, Volumes by Shells and Washers, Length of a curve, Area of surface of revolution, Pappus's theorem, Review of vector algebra, Equations of lines and planes, Continuity and Differentiability of vector functions, Arc length for space curves, Unit tangent vector, Unit normal and curvature to plane and space curves, Binormal, Functions of several variables, Continuity, Partial derivatives, Differentiability, Differentiability implies continuity, Increment theorem, Chain rule, Gradient, Directional derivatives, Tangent plane and Normal line, Mixed derivative theorem, Mean value theorem, Minima and Saddle point, Necessary and sufficient conditions for Maxima, minima and Saddle point, The method of Lagrange multipliers, Double Integral, Fubini's theorem, Volumes and Areas, Change of variable in double integral. Special cases: Polar coordinates, Triple integral, Applications, Change of variable in triple integral. Special cases: Cylindrical and Spherical coordinates, Surface area, Surface integral, Line integrals, Green's theorem, Vector fields Divergence and Curl of a vector field, Stoke's theorem, The divergence theorem.