NOC:Calculus of One Real Variable


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