MA15010H (CSE): Multi Variable Calculus, during Sep-Nov 2025

 Preamble: This course covers essential topics in multivariable calculus and vector analysis. It develops continuity and differentiability of vector and scalar functions, partial and directional derivatives, gradients, and optimization with constraints. Integral calculus is extended to multiple integrals with applications, change of variables, and vector fields. The course culminates with Green’s, Gauss’s, and Stokes’s theorems, highlighting fundamental links between differential and integral calculus.

 Syllabus: Vector functions of one variable - continuity and differentiability; Scalar valued functions of several variables, continuity, partial derivatives, directional derivatives, gradient, differentiability, chain rule; Tangent planes and normals, maxima and minima, Lagrange multiplier method; Repeated and multiple integrals with applications to volume, surface area; Change of variables; Vector fields, line and surface integrals; Green’s, Gauss and Stokes theorems and their applications.

Texts/References:
1. G. B. Thomas, Jr. and R. L. Finney, Calculus and Analytic Geometry, Pearson India, 9th Edition, 2006
2. S. R. Ghorpade and B. V. Limaye, A Course in Multivariable Calculus and Analysis, Springer India, 2010.
3. T. M. Apostol, Calculus, Volume 2, Wiley India, 2003
4. J. E. Marsden, A. J. Tromba and A. Weinstein, Basic Multivariable Calculus, Springer India, 2002.

 Course policy (click here)

Classroom and slot: 5305, Slot-B (Mon 09:00 - 09:55, Tue 10:00 -10:55, Wed 11:00 -11:55), Exam slot- B1

Tutorial Slot-B, Fri 08:00 - 08:55

 Tutorial Group

 T1

 T2

 T3

 Tutorial Room

 5002

 5004

 5102

 Tutor Name

 Mr. Aayushman Raina

Dr. Sudipta Sarkar

 Mr. Koushik Bhakta


Lecture Notes: Lectuenotes 1, Lecturenotes 2

Assignments: Assignment 1, Assignment 2

Assignments solution: Assignment 1

Practice problem set: Practice 1, Practice 2

Practice problem set soultion:

Exams:

Class Discipline:

Students must ensure that mobile phones are switched off or set to silent mode and kept securely inside their bags, which must remain under the desk throughout the class. Only a notebook and a pen are permitted on the desk - no other items are allowed. Any student found with a mobile phone or any electronic device on the desk, regardless of intent, will be required to leave the classroom immediately and the incident will be reported to the Academic Section without exception.