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Courses » Calculus of One Real Variable

Calculus of One Real Variable

About the course
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.

Industries that will recognize this course
Not Applicable

2104 students have enrolled already!!

Course instructor



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 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


Suggested Reading

  • Calculus by M Spivak
  • Calculus by Thomos and Finney.
More details about the course

Course url: https://onlinecourses.nptel.ac.in/noc17_hs25
Course duration: 08 weeks
Start date and end date of course: 21 August 2017-13 October 2017
Date of exam: 22 October, 2017
Time of exam: Shift 1: 9 am-12 noon; Shift 2: 2 pm-5 pm
Any one shift can be chosen to write the exam for a course

Final List of exam cities will be available in exam registration form.
Registration url - Announcements will be made when the registration form is open for registrations.
Exam Fee: The online registration form has to be filled and the certification exam fee of approximately Rs 1000 needs to be paid. 


Certificate

E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score.

Final score = 25% assignment score + 75% exam score
25% assignment score is calculated as 25% of average of scores of Best 6 out of 8 assignments 

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.