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Calculus - II

By Prof. Arup Chattopadhyay, Prof. M. Guru Prem Prasad   |   IIT Guwahati
Learners enrolled: 85
ABOUT THE COURSE:

Multivariable calculus is one of the fundamental mathematics subjects which is introduced to the undergraduate students of Engineering, Technology and Mathematical Science programmes. Single-Variable Calculus is introduced in some form at Higher Secondary Level, whereas the Multivariable Calculus is not introduced. Much importance is given to single variable calculus and general belief that multivariable calculus is similar, but it is not true. Therefore, the students won’t be able to grasp the important concepts of multivariable calculus, such as differentiation and integration properly even though there exist many books and online resource material. While modelling most of the engineering, industrial or real life problems, it is inevitable to handle functions of several variables or equations involving several variables. To study and analyze them, the multivariable calculus serves as a basic tool.

INTENDED AUDIENCE: Undergraduate Students of BTech/BE and B.Sc.(Mathematics) Students
Summary
Course Status : Upcoming
Course Type : Core
Language for course content : English
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate
Start Date : 21 Jul 2025
End Date : 10 Oct 2025
Enrollment Ends : 28 Jul 2025
Exam Registration Ends : 15 Aug 2025
Exam Date : 26 Oct 2025 IST
NCrF Level   : 4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

Week 1: 
  • Introduction to Vector Algebra
  • Vector Valued Function of a Real Variable and Applications
Week 2: Functions from m-dimensional to n-dimensional Euclidean spaces, Limit, Continuity

Week 3: Partial derivatives, Directional Derivatives, Tangent Plane and Normal Line for a Surface, Total Derivative, Chain rule, Higher order Partial Derivatives

Week 4: Mixed Derivative Theorem, Mean Value Theorem, Hessian, Linear approximation and Increment Estimation, Taylor’s theorem for functions of two variables.

Week 5: Maxima, Minima and Saddle point, The method of Lagrange multiplies, Exact differentials.

Week 6: Double integrals, Fubini’s theorem, Volume and Areas, Change of Variables in a Double Integral, Applications.

Week 7: Triple Integrals, Change of Variables in a triple integral, Applications.

Week 8: Gradient, Divergence, Curl, Laplacian

Week 9: Smooth curves, Contours, Oriented curves, Scalar Line Integrals, Vector Line Integrals and their properties.

Week 10: Smooth surfaces, Oriented surfaces, Scalar Surface Integrals, Vector Surface Integrals and their properties.

Week 11: Green’s Theorem

Week 12: Gauss Theorem and Stokes Theorem

Books and references

  1. S. R. Ghorpade and B. V. Limaye, A Course in Multivariable Calculus and Analysis, Springer, 2010. 
  2. J. E. Marsden, A. J. Tromba and A. Weinstein, Basic Multivariable Calculus, Springer India, 2002. 
  3. T. M. Apostol, Calculus, Volume-II, Wiley India, 2003.

Instructor bio

Prof. Arup Chattopadhyay

IIT Guwahati
Dr. Arup Chattopadhyay: He has obtained his PhD degree from Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore in 2013. His research areas of interests are Functional Analysis and Operatory Theory. He has a teaching experience of 10 years in teaching undergraduate, postgraduate and doctoral level mathematics courses. He has published more than 25 research articles. He is the member secretary of Department of Undergraduate Programme Committee, Department of Mathematics, IIT Guwahati.


Prof. M. Guru Prem Prasad

Prof. M. Guru Prem Prasad: He has obtained his PhD degree from IIT Kanpur in 1998. His research areas of interests are Complex Dynamics, Fractals, Chaos, and Computational Complex Analysis. He has a teaching experience of 25 years in teaching undergraduate, postgraduate and doctoral level mathematics courses.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: October 26, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Guwahati .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team


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