Venue & Time: LHC 06, Monday 12:00-12:55, Tuesday 9:00-9:55, Friday 11:00 - 11:55
Office hours: By appointment scheduled through email (prasunrc@math.iith.ac.in)
TA: Dipika Robi Das (ma23resch11002@iith.ac.in)
Grading: Students are required to obtain a minimum of 40% of the total marks in order to successfully complete the course.
Lecture Notes (updated on October 30, 2026)
Lecture 1, October 06, 09:00-09:55 (Vectors and vector algebra, dot and cross products, lines and planes in R^3, and basic surfaces in R^3)
Lecture 2, October 09, 11:00-11:55 (Curvilinear coordinates, including polar, cylindrical, and spherical coordinates; vector-valued functions, limits, continuity, differentiation, tangent vectors, and arc length of curves)
Lecture 3, October 12, 12:00-12:55 (Functions of two and three variables, domains and ranges, limits and continuity, partial derivatives, and tangent planes to surfaces)
Lecture 4, October 13, 09:00-09:55 (Directional derivatives, gradient and direction of maximum increase/decrease, tangent planes to implicitly defined surfaces, and local maxima, minima, and saddle points)
Lecture 5, October 16, 11:00-11:55 (Double integrals over rectangles and general regions, iterated integrals)
Lecture 6 & Quiz, Solution, October 26, 12:00-12:55 (Double integrals over general regions, changing the order of integration, applications to areas and volumes, improper double integrals, and triple integrals over solids with iterated integration)
Lecture 7, October 27, 09:00-09:55 (Change of variables in multiple integrals, Jacobians, integration in polar, cylindrical, and spherical coordinates, applications of multiple integrals: center of mass) & Assignment 1
Lecture 8, October 30, 11:00-11:55 (Introduction to line integrals, scalar and vector line integrals, applications to work, parametrization of curves, and properties of line integrals under reversal of orientation)
Lecture 9, November 02, 12:00-12:55 (Properties of line integrals, orientation and parametrization of curves, closed and simple closed curves, path independence, conservative vector fields, potential functions, and the Fundamental Theorem for Line Integrals)
Lecture 10, November 03, 09:00-09:55 ()
Lecture 11, November 06, 11:00-11:55 ()
Lecture 12, November 09, 12:00-12:55 ()
Lecture 13, November 10, 09:00-09:55 () & Assignment 2
Problem Session, November 13, 11:00-11:55
Exam, Solution, November 15, 10:00-12:00, Venue LHC 03
Copy Showing, November 18, 16:00-19:00, Venue MA414