Venue & Time: LHC 13, Mon 9:00-9:55, Wed 11:00-11:55, Thu 10:00 - 10:55
Office hours: By appointment scheduled through email (prasunrc@math.iith.ac.in)
Lecture 1, July 27, 09:00-09:55 (Real Number System, Law of Trichotomy, Upper Bound, Lower Bound, Bounded Sets, Maximum, Minimum, Least Upper Bound (Supremum), Greatest Lower Bound (Infimum), Examples of Supremum and Infimum)
Lecture 2, July 29, 11:00-11:55 (Completeness Property, Archimedean Property, Density of Rational and Irrational Numbers)
Lecture 3, July 30, 10:00-10:55 (Sequences, Convergence, Limit of a Sequence, ε-N Definition, Uniqueness of Limit)
Lecture 4, August 03, 09:00-09:55 (Divergent Sequences, Bounded Sequences, Algebra of Limits, Cauchy Sequences, Cauchy Criterion)
Lecture 5, August 05, 11:00-11:55 (Monotone Sequences, Monotone Convergence Theorem, Sandwich Theorem, Important Limits)
Lecture 6, August 06, 10:00-10:55 (Sequences Diverging to ± ∞, Ratio and Root Test, Subsequences, Bolzano–Weierstrass Theorem, Infinite Series, Partial Sums, Convergent and Divergent Series)
Lecture 7, August 10, 09:00-09:55 (Absolute Convergence, Conditional Convergence, Comparison Test, Ratio Test, Root Test, Abel's Test, Alternating Series, Leibniz Test) & Assignment 1
Lecture 8, August 12, 11:00-11:55 (Continuity, Sequential Criterion for Continuity, Continuous Functions, Algebra of Continuous Functions, Composition of Continuous Functions)
Lecture 9, August 13, 10:00-10:55 (ε-δ Continuity, Continuous Functions, Intermediate Value Theorem)
Lecture 10, August 17, 09:00-09:55 (Fixed Point Theorem, Weierstrass Theorem, Extreme Value Theorem, Integral Test, p-Series, Limits, ε-δ Definition, Algebra of Limits)
Lecture 11, August 19, 11:00-11:55 (One-Sided Limits, Continuity and One-Sided Limits, Types of Discontinuity, Sequential Characterization of Limits, Infinite Limits, Limits at Infinity, Differentiability, Differentiability Implies Continuity)
Lecture 12, August 20, 10:00-10:55 (Non-continuous Derivative, Algebra of Differentiation, Linear Approximation, Chain Rule, Local and Global Extrema, Fermat’s Theorem)
Lecture 13, August 24, 09:00-09:55 (Cauchy’s Mean Value Theorem, Rolle’s Theorem, Lagrange’s Mean Value Theorem, Taylor’s Theorem) & Assignment 2
Problem Session, August 27, 10:00-10:55
Handwritten Notes, Entire Lecture Notes
Exam Instructions, Seating Plan
Exam, August 29, 17:00-19:00, Venue LHC 6, LHC 7 and LHC 13 & Solution