ABOUT THE COURSE This course is a basic course offered to UG and PG students of Engineering/Science background. It contains various topics related to the calculus of the functions of two or more variables. In particular, this course includes topics like differentiation and integration of the functions of two or more variables together with their various applications. This course also includes the calculus of vector functions with different applications.
INTENDED AUDIENCE UG students of technical universities/colleges It is a core course for UG.
PRE-REQUISITES None
INDUSTRY SUPPORT – LIST OF COMPANIES/INDUSTRY THAT WILL RECOGNIZE/VALUE THIS ONLINE COURSE None
3354 students have enrolled already!!
COURSE INSTRUCTORS
Dr. S. K. Gupta is an Associate Professor in the Department of Mathematics, IIT Roorkee. His area of expertise includes nonlinear, non-convex and Fuzzy optimization. He has guided three PhD thesis and have published more than 40 papers in various international journals of repute.
Dr. Sanjeev Kumar is working as an associate professor with Department of Mathematics, IIT Roorkee. Earlier, he worked as a postdoctoral fellow with Department of Mathematics and Computer Science, University of Udine, Italy and assistant professor with IIT Roorkee. He is actively involved in teaching and research in the area of computational algorithms, inverse problems and image processing. He has published more than 55 papers in various international journals conferences of repute. He has completed a couple of sponsored research projects and written several chapters in reputed books published with Springer and CRC press.
COURSE LAYOUT
Week 1: Limits, continuity and partial derivatives of multivariable functions
Week 2: Differentiability and chain rule
Week 3: Change of variables, Euler’s theorem, tangent planes, normal lines and extreme values
Week 5: Change of order and change of variables in multiple integral
Week 6: Beta and gamma functions
Week 7: Normal vector and potential field Week 8: vector identities and line integral
SUGGESTED READING
1. E. Kreyszig, Advanced Engineering Mathematics, 9th edition, John Wiley and Sons, Inc., U.K. (2011) 2. R.K. Jain and S.R.K. Iyenger, Advanced Engineering Mathematics, 2nd Edition, Narosa Publishing House (2005) 3. M.D. Weir, J. Hass, F.R. Giordano, Thomas’ Calculus, 11th Edition, Pearson Education (2008)
CERTIFICATION EXAM
• The exam is optional for a fee. • Date and Time of Exams: April 28 (Saturday) and April 29 (Sunday) : Afternoon session: 2pm to 5pm • Exam for this course will be available in one session on both 28 and 29 April. • 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.
CERTIFICATE
• Final score will be calculated as : 25% assignment score + 75% final exam score. • 25% assignment score is calculated as 25% of average of Best 6 out of 8 assignments. • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and Roorkee. It will be e-verifiable at nptel.ac.in/noc
