Lecture 1 - Rational Numbers and Rational Cuts

Lecture 2 - Irrational numbers, Dedekind's Theorem

Lecture 3 - Continuum and Exercises

Lecture 4 - Continuum and Exercises (Continued.)

Lecture 5 - Cantor's Theory of Irrational Numbers

Lecture 6 - Cantor's Theory of Irrational Numbers (Continued.)

Lecture 7 - Equivalence of Dedekind and Cantor's Theory

Lecture 8 - Finite, Infinite, Countable and Uncountable Sets of Real Numbers

Lecture 9 - Types of Sets with Examples, Metric Space

Lecture 10 - Various properties of open set, closure of a set

Lecture 11 - Ordered set, Least upper bound, greatest lower bound of a set

Lecture 12 - Compact Sets and its properties

Lecture 13 - Weiersstrass Theorem, Heine Borel Theorem, Connected set

Lecture 14 - Tutorial - II

Lecture 15 - Concept of limit of a sequence

Lecture 16 - Some Important limits, Ratio tests for sequences of Real Numbers

Lecture 17 - Cauchy theorems on limit of sequences with examples

Lecture 18 - Fundamental theorems on limits, Bolzano-Weiersstrass Theorem

Lecture 19 - Theorems on Convergent and divergent sequences

Lecture 20 - Cauchy sequence and its properties

Lecture 21 - Infinite series of real numbers

Lecture 22 - Comparison tests for series, Absolutely convergent and Conditional convergent series

Lecture 23 - Tests for absolutely convergent series

Lecture 24 - Raabe's test, limit of functions, Cluster point

Lecture 25 - Some results on limit of functions

Lecture 26 - Limit Theorems for functions

Lecture 27 - Extension of limit concept (one sided limits)

Lecture 28 - Continuity of Functions

Lecture 29 - Properties of Continuous Functions

Lecture 30 - Boundedness Theorem, Max-Min Theorem and Bolzano's theorem

Lecture 31 - Uniform Continuity and Absolute Continuity

Lecture 32 - Types of Discontinuities, Continuity and Compactness

Lecture 33 - Continuity and Compactness (Continued.), Connectedness

Lecture 34 - Differentiability of real valued function, Mean Value Theorem

Lecture 35 - Mean Value Theorem (Continued.)

Lecture 36 - Application of MVT , Darboux Theorem, L Hospital Rule

Lecture 37 - L'Hospital Rule and Taylor's Theorem

Lecture 38 - Tutorial - III

Lecture 39 - Riemann/Riemann Stieltjes Integral

Lecture 40 - Existence of Reimann Stieltjes Integral

Lecture 41 - Properties of Reimann Stieltjes Integral

Lecture 42 - Properties of Reimann Stieltjes Integral (Continued.)

Lecture 43 - Definite and Indefinite Integral

Lecture 44 - Fundamental Theorems of Integral Calculus

Lecture 45 - Improper Integrals

Lecture 46 - Convergence Test for Improper Integrals