NPTEL : NOC:Calculus of One Real Variable (Humanities and Social Sciences)

Co-ordinators : Dr. Joydeep Dutta


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

Lecture 6 - Limits of Functions - II

Lecture 7 - Continuous Functions

Lecture 8 - Intermediate Value Theorem

Lecture 9 - Maximum Value Theorem

Lecture 10 - Supremum and Infimum

Lecture 11 - Derivative of a Function

Lecture 12 - Rules of Differentiation

Lecture 13 - Maxima and Minima

Lecture 14 - Rolles Theorem and Lagrange Mean Value Theorem (MVT)

Lecture 15 - Monotonic Functions and Inverse Functions

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

Lecture 21 - Integration theory of Riemann - I

Lecture 22 - Integration theory of Riemann - II

Lecture 23 - Integration Rule

Lecture 24 - Fundamental Theorem of Calculus (in Riemann style)

Lecture 25 - The Kurzweil-Henstock Integral (K-H Integral)

Lecture 26 - Calculating Indefinite Integrals

Lecture 27 - Improper Integral - I

Lecture 28 - Improper Integral - II

Lecture 29 - Application of Definite Integral - I

Lecture 30 - Application of definite Integral - II

Lecture 31 - Application of definite Integral - III

Lecture 32 - Application of definite Integral - III (Continued......)

Lecture 33 - Numerical Integration - I

Lecture 34 - Numerical Integration - II

Lecture 35 - Sequences

Lecture 36 - Sequences (Continued...)

Lecture 37 - Infinite Series

Lecture 38 - infinite series (Continued...)

Lecture 39 - Taylors Theorem, other issues and end of the course - I

Lecture 40 - Taylors Theorem, other issues and end of the course - II