# Basic Calculus - 1

By Prof. Arindama Singh   |   IIT Madras
Learners enrolled: 1064
This course is a follow up to the calculus course taught in schools. Some of the notions done earlier will be presented in a more rigorous manner and some new notions will be introduced. The course aims at treating rigorously the notions of continuity, differentiabilty and integrability and their applications.

INTENDED AUDIENCE
B.Sc.
PREREQUISITES : School Mathematics
INDUSTRIES  SUPPORT     : None
Summary
 Course Status : Upcoming Course Type : Core Duration : 12 weeks Start Date : 24 Jan 2022 End Date : 15 Apr 2022 Exam Date : 24 Apr 2022 IST Category : Mathematics Foundations of Mathematics Credit Points : 3 Level : Undergraduate

### Course layout

Week 1:Real numbers, Functions and their graphs.
Week 2:Limits of functions, Left and Right hand limits.
Week 3: Continuity, Intermediate value property.
Week 4:Differentiation, Chain rule, Implicit differentiation.
Week 5:Extreme values, Rolle’s theorem, Mean value theorems.
Week 6:Local extrema.
Week 7: Limits at infinity, Infinite limits, Asymptotes, Differentials.
Week 8:Definite integrals, Area, Mean value theorem.
Week 9:The fundamental theorem, Indefinite integral.
Week 10:Integration by substitution, Area between curves.
Week 11: Volume by slicing, Volume of revolution, Cylindrical shells.
Week 12:Lengths of plane curves, Area of surface of revolution.

### Books and references

Calculus, Thomas & Fenny, 9th Ed. Pearson, 2002. (Chapters 1 – 5).

### Prof. Arindama Singh

I am a professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai (India).I typically teach courses related to Logic, Theory of Computation, Linear Algebra, Numerical analysis, and Differential Equations. My research interests include Knowledge Compilation, Singular Perturbation, Mathematical Learning Theory, Image Processing, and Numerical Linear Algebra. All are related to Computational Mathematics.I enjoy teaching more than doing research; thus for me, research is a means to make myself fit for teaching. Though I do not like to use any particular method, I am attracted towards Moore's method, albeit, in a softer way. I gain much by interacting with students and ofcourse, they gain more than what they might have anticipated. Over the years, I came to believe in the maxim of Lebesgue -- `Think in front of students'. This does not mean 'no preparation on my part'. On the contrary, interaction with students requires much more preparation than one does for usual 'one way' lectures."

### 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: 24 April 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 Madras .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