Calculus II | Department of Mathematics

Calculus II

Core course for B.Sc. (Research) programs in Mathematics, Physics. Optional course for B.Sc. (Research) Chemistry.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: MAT 101 (Calculus I)

Overview: The first part is an introduction to multivariable differential calculus. The second part covers sequences and series of numbers and functions. The concepts and techniques covered here are used extensively in the social and natural sciences as well as in engineering.

Detailed Syllabus:

  1. Differential calculus in several variables: Functions of several variables, level curves and surfaces, limits and continuity, partial derivatives, tangent planes, chain rule, directional derivatives, gradient, Lagrange multipliers, extreme values and saddle points, 2nd derivative test
  2. Sequences and Series: Limits of sequences, algebra of limits, series, divergence test, comparison and limit comparison tests, integral test, alternating series test, absolute convergence, root & ratio tests, Abel and Dirichlet tests, power series, Taylor series, Fourier Series.


  • Calculus, Volume II, by Tom M Apostol, Wiley.
  • Essential Calculus – Early Transcendentals by James Stewart, Cengage, India Edition.
  • Calculus and Analytic Geometry by G B Thomas and R L Finney, 9th edition, Pearson.
  • Basic Multivariable Calculus by J E Marsden, A J Tromba and A Weinstein, 1st edition, Springer (India), 2011.
  • Calculus by Ken Binmore and Joan Davies, 1st edition, Cambridge, 2010.

Past Instructors: Amber Habib, Debashish Bose


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