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Calculus Of One Real Variable

By Prof. Joydeep Dutta   |   IIT Kanpur
Learners enrolled: 3264
This course intend to develop a thorough understanding of the fundamental aspects of calculus of single variable which is fundamental tool in Sciences, Engineering and Economics.

Intended Audience : First year engineering, science and economics students with mathematics as main course.

Prerequisites Basic mathematics till 12th standard
Summary
Course Status : Completed
Course Type : Core
Duration : 8 weeks
Start Date : 14 Sep 2020
End Date : 06 Nov 2020
Exam Date : 18 Dec 2020 IST
Enrollment Ends : 25 Sep 2020
Category :
  • Mathematics
Credit Points : 2
Level : Undergraduate

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Course layout

Week 1: Lecture 1: Introduction to Numbers
Lecture 2: Countability and Uncountability
Lecture 3: Examples of Irrational numbers
Lecture 4: Functions
Lecture 5: Limits of Functions-I
 
Week 2: Lecture 6: Limit of Functions-II
Lecture 7: Continuous Functions
Lecture 8: Intermediate Value Theorem
Lecture 9: Maximum Value Theorem
Lecture 10: Supremum & Infimum

Week 3: Lecture 11: Derivative of a Function
Lecture 12: Rules of Differentiation
Lecture 13: Derivatives maxima & minima
Lecture 14: Rolle’s Theorem and Lagrange MVT(Mean-Value Theorem)
Lecture 15: Monotonic Functions and Inverse Function

Week 4: Lecture 16: Newton’s Method for solving Equations
Lecture 17: Optimization Problems
Lecture 18: Integration-I : In the style of Newton and Leibnitz
Lecture 19: Integration-II : In the spirit of Newton and Leibnitz
Lecture 20: Integration-III : Newton and Leibnitz Style

Week 5: Lecture 21: Indefinite Integrals
Lecture 22: Integration by Parts
Lecture 23: Integration of Rational Functions
Lecture 24: Trapezoidal Rule for evaluating definite integral
Lecture 25: Simpson’s Rule for evaluating definite integral
 
Week 6: Lecture 26: Applications of Definite Integral-I
Lecture 27: Applications of Definite Integral-II
Lecture 28: Applications of Definite Integral-III
Lecture 29: Applications of Definite Integral-IV
Lecture 30: Transcendental Functions-I

Week 7: Lecture 31: Transcendental Functions-II
Lecture 32: Taylor’s Expansion-I
Lecture 33: Taylor’s Expansion-II
Lecture 34: Infinite Sequence-I
Lecture 35: Infinite Sequence-II

Week 8: Lecture 36: Infinite series and their convergence
Lecture 37: Tests for Convergence of a series
Lecture 38: Absolute and conditional convergence
Lecture 39: Power Series
Lecture 40: Historical Development of the Calculus


Books and references

Calculus by M Spivak
Calculus by Thomos and Finney.

Instructor bio

Prof. Joydeep Dutta

IIT Kanpur
Prof.Joydeep Dutta is currently a Professor of Economics at the Department of Humanities and Social Sciences, IIT Kanpur. He was previously a Professor at the Department of Mathematics and Statistics at IIT Kanpur. His reseach interest primarily lies in optimization though he loves mathematics as a whole.

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: 18 December 2020 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 6 assignments out of the total 8 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 Kanpur .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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