Lecture-1, August 11, 09:30-11:30 (Introduction to Metric Spaces, Sequences in Metric Spaces)
Lecture-2, August 12, 14:00-16:00 (Basic Topology on Metric Spaces, Equivalence of Metrics)
Lecture-3, August 18, 09:30-11:30 (Compact Sets in Metric Spaces, Open Cover, Finite Intersection Property, Equivalent Definitions of Compactness)
Lecture-4, August 19, 14:00-16:00 (Completeness and Boundedness, Relative Compact Set, Separated Set, Connected Set, Definition of Limit of Functions)
Assignment-2, August 21, 12:30-13:00 & Assignment-2 Test, August 21, 12:00-12:30
Lecture-5, August 25, 09:30-11:30 (Left and Right Limit, Continuous Functions, Continuity and Compactness)
Lecture-6, August 26, 14:15-16:00 (Extreme Value Theorem in Metric Spaces, Uniform Continuity, Continuity and Connectedness) & Assignment-3 Test-1, August 26, 14:00-14:15
Ayyankali Jayanti, August 28, No Class
Lecture-7, September 1, 09:30-11:30 (Discontinuities, Continuous Extensions, Derivative of a Real Function, Chain Rule)
Lecture-8, September 2, 14:30-16:00 (Monotonic Functions and Number of Discontinuities) & Assignment-3 Test-2, September 2, 14:00-14:30
First Onam, September 4, No Class
Assignment-3, September 8, 10:45-11:30 & Quiz-1, September 8, 09:30-10:45
Lecture-9, September 9, 14:00-16:00 (Infinite Limits and Limits at Infinity, Mean Value Theorems, Fermat's Theorem, Cauchy’s Mean Value Theorem, Continuity of Derivatives & Darboux’s Theorem)
Lecture-10, September 11, 12:00-13:00 (L’Hôpital’s Rule)
Lecture-11, September 15, 09:30-11:30 (Derivatives of Higher Order, Taylor’s Theorem, Differentiation of Vector-Valued Functions, Recap of Sequences and Infinite Series from Basic Real Analysis)
Lecture-12, September 16, 14:00-16:00 (Continuing Recap of Sequences and Infinite Series, and Different Tests of Convergence)
Assignment-4, September 18, 12:30-13:00 & Assignment-4 Test, September 18, 12:00-12:30
Lecture-13, September 22, 09:30-11:30 (Definition and Existence of the Integral, Partition, Refinement, Riemann-Stieltjes Integration, Riemann Integration, Riemann Darboux Criterion)
Lecture-14, September 23, 14:00-16:00 (Integrability of Discontinuous Functions, Integrability of Composition of Integrable Functions, Integrability of Thomae’s Function)
Assignment-5, September 25, 12:30-13:00 & Assignment-5 Test, September 25, 12:00-12:30
Lecture-15, September 29, 09:30-11:30 (Functions of Bounded Variation, Jordan Decomposition, Integration with Respect to BV Functions)
Navratri, September 30, No Class
Gandhi Jyanti, October 2, No Class
Problem Sessions, October 13, 09:30-11:30
Lecture-16, October 14, 14:00-16:00 (Power Series, Some Special Functions)
Deepavali, October 20, No Class
Lecture-17, October 21, 14:00-16:00 (Integration with Respect to Step Functions, Series Representation and integration by Substitution of Riemann–Stieltjes Integral)
October 23, No Class
Lecture-18, October 27, 09:30-11:30 (Change of Variable Theorem, Fundamental Theorem of Calculus, Integration by Parts, Differentiation under the Integral Sign, Integration of Vector-Valued Functions)
Lecture-19, October 28, 14:00-16:00 (Sequences and Series of Functions, Pointwise Convergence, Failure of Continuity/Integrability/Differentiability under Pointwise Limits, Uniform Convergence, Cauchy Criterion for Uniform Convergence)
Lecture-20, November 3, 09:30-11:30
Lecture-21, November 4, 14:00-16:00
Quiz-2, November 6, 12:00-12:30 (weightage 5 points) & Assignment-8, November 6, 12:30-13:00
Lecture-22, November 10, 09:30-11:30
Lecture-23, November 11, 14:00-16:00
Lecture-24, November 17, 09:30-11:30
Lecture-25, November 18, 14:00-16:00
Assignment-6 & 10 Test, November 20, 12:00-12:30 (weightage 2 points) & Assignment-10, November 20, 12:30-13:00
Endsem, During the exam week of December 1-5, 09:30-12:30 (weightage 50 points)