Advanced Calculus For Engineers

By Prof. Jitendra Kumar, Prof. Somesh Kumar | IIT Kharagpur, IIT Kharagpur

Learners enrolled: 2747

About The Course:
This course is about basic mathematics, which is a fundamental and essential component of all undergraduate studies in sciences and engineering. This course consists of topics in differential, integral, and vector calculus with applications to various engineering problems. This course will cover calculus of two or more variables in detail. Knowledge of ordinary differential equations are part of this course. Students will learn how to perform double and triple integrals. Topic in vector calculus includesline and surface integrals, Green, Gauss and Stokes theorem.

PRE-REQUISITES : Higher Secondary

INTENDED AUDIENCE: All branches of science and engineering

Summary

Course Status :	Completed
Course Type :	Core
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Undergraduate
Start Date :	25 Jul 2022
End Date :	14 Oct 2022
Enrollment Ends :	08 Aug 2022
Exam Date :	30 Oct 2022 IST

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

Page Visits

Course layout

Week 1: Differential calculus of one variable

Week 2: Limit, continuity, partial derivatives of functions of two or more variables

Week 3: Differentiability of functions of two or more variables

Week 4: Differentiation of Homogeneous and Implicit Functions, Taylors theorem of functions of two variables

Week 5: Maxima and Minima

Week 6: First order ODEs

Week 7: Higher order ODEs

Week 8: Improper integrals

Week 9: Double integrals

Week 10: Triple Integrals

Week 11: Vector and scalar field, gradient, divergence and curl

Week 12: Line and surface integrals. Green, Stokes and Gauss divergence theorems

Books and references

1. Piskunov, N., Differential and Integral Calculus, Vol 1 & 2, 2nd edition. Mir Publishers, 1974.

2. Kreyszig, E., Advanced Engineering Mathematics, 10th edition. John Wiley & Sons, 2010.

3. Thomas, G.B. and Finney, R.L., Calculus and Analytic Geometry, 9th Edition, Pearson, Reprint, 2002.

Instructor bio

Prof. Jitendra Kumar

IIT Kharagpur

Jitendra Kumar is an Associate Professor at the Department of Mathematics, IIT Kharagpur. He completed his M.Sc. in Industrial Mathematics from IIT Roorkee and Technical University of Kaiserslautern, Germany in 2001 and 2003, respectively. He received his PhD degree in 2006 from Otto-von-Guericke University Magdeburg, Germany. He was Research Associate at the Institute for Analysis and Numerical Mathematics, Otto-von-Guericke University Magdeburg, Germany from 2006 to 2009. Dr. Kumar is the recipient of several recognized awards and fellowships, including Alexander von Humboldt fellowship, DAAD & DGF scholarships. His research interests include Numerical solutions of integro-differential equations, numerical analysis and modelling and simulations of problem in particulate systems.

Prof. Somesh Kumar

IIT Kharagpur

Prof. Somesh Kumar is a professor in the Department of Mathematics, IIT Kharagpur. He has over 32 years of experience of teaching courses on Probability Statistics, Statistical Inference, Sampling Theory, Stochastic Processes, Multivariate Analysis, Regression Analysis, Time Series, Experimental Designs, Decision Theory to undergraduate, postgraduate and doctorate students. His NPTEL courses (under MHRD) on Probability and Statistics, Statistical Inference and Statistical Methods for Scientists and Engineers (each of 40 hours) are available online and very popular. He has also taught Mathematics-I in QEEE program of MHRD to 130 engineering college students in online mode during Autumn 2014-2015. He offered the course “Probability and Statistics” for certification program in Jan-April 2016, Jan-April 2017, Jan-April 2019. He also offered the course “Statistical Inference” for certification program during Jan-April 2019. His lectures on “Probability” and “Permutation and combinations” for class XII students under IIT-PAL scheme of MHRD are also available through DTH channels of national television.

His research interests are Statistical Decision Theory, Estimation Theory, Testing of Hypothesis, Classification Problems, Directional Distributions, Limit Theorems. He has published more than 100 research papers in refereed reputed international journals and book chapters. He has supervised eleven Ph.D. students and more than two hundred fifty Masters (M.Tech./ M.Sc./B.Tech.) dissertations.

He has been guest professor in University of Ulm, Germany in July 2017 and June-July 2018 and in University of Dortmund in May-June 2019. He is Principal Investigator for a major research project “Drone for Vaccine Delivery” funded by the Indian Council for Medical Research. He has delivered invited lectures in various universities in India and abroad.

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: 30 October 2022 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

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 Kharagpur. 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