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, Properties of Integral, Mean Value Theorem for the Riemann–Stieltjes integral)
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 (Cauchy M-Test, Weierstrass M-Test, Uniform Convergence and Continuity, Interchanging Limits, Dini’s Theorem on Monotone Convergence on Compact Sets)
Lecture-21, November 4, 14:00-16:00 (Uniform Convergence and Integration, Term-by-Term Integration, Uniform Convergence and Differentiation, Differentiation under the Limit Theorem)
Assignment-8, November 6, 12:30-13:00 & Quiz-2, November 6, 12:00-12:30
Lecture-22, November 10, 09:30-11:30 (Equicontinuous Families of Functions, Arzelà–Ascoli Theorem, Stone–Weierstrass Theorem, Functions of Several Variables, Limits and Continuity in Several Variables)
Lecture-23, November 11, 14:00-16:00 (Continuity of Functions in Several Variables, Differentiability in Rn→Rm, Uniqueness of Derivative, Differentiability Implies Continuity)
Lecture-24, November 17, 09:30-11:30 (Chain Rule, Partial Derivatives and Gradient, Jacobian Matrix, Total Derivative, Directional Derivatives)
Lecture-25, November 18, 14:00-16:00 (The Contraction Principle, The Inverse Function Theorem, The Implicit Function Theorem, The Rank Theorem)
Assignment-10, November 20, 12:30-13:00 & Assignment-6 & 10 Test, November 20, 12:00-12:30