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 () & Assignment 1
Lecture 8, August 12, 11:00-11:55 ()
Lecture 9, August 13, 10:00-10:55 ()
Lecture 10, August 17, 09:00-09:55 ()
Lecture 11, August 19, 11:00-11:55 ()
Lecture 12, August 20, 10:00-10:55 ()
Lecture 13, August 24, 09:00-09:55 () & Assignment 2
Lecture 14, August 27, 10:00-10:55 ()
Entire Lecture Notes (will be uploaded after the end of Lecture 14)
Exam, August 29, 17:00-19:00, Venue LHC 5 and LHC 6 & Solution