Week |
Topics |
1 |
Finite, countable & uncountable sets -3 lectures. Metric Space, Open set, Closed set, Limit point, Closure of a set -3 lectures |
2 |
Ordered set, least upper bound, greatest lower bound -2 lectures Open cover, compact set & some properties of compact set 2 lectures, Heine-Borel theorem 1 lecture. Weierstrass Theorem, connected Set- 1 lecture |
3 |
Limit of sequences of real number 2 lectures. Some important limits, Ratio test, Cauchy limit theorem -4 lectures |
4 |
Some theorems on limit & Bolzano Weierstrass theorem - 2 lectures Theorems on convergent & divergent sequences- 2 lectures. Cauchy sequence & its properties- 2 lectures |
5 |
Infinite series of real numbers 2 lectures, Comparison test for series, Absolutely convergent and conditional convergent series 2 lectures. Some test for convergence of series-2 lectures |
6 |
Raabe Test & its application 1 lecture. Limit of functions, cluster point 3 lectures |
7 |
Limit theorems for functions 4 lectures |
8 |
Continuity of functions 2 lectures. Properties of continuous functions & composition of continuous functions 2 lectures |
9 |
Boundedness theorem, Bolzano theorem 2 lectures. Uniform & absolute continuity-2lectures. Type of discontinuities 2 lectures |
10 |
Differentiability of functions of real variables 2 lectures. Mean value theorems 2 lectures. Application of derivatives , mean value theorems & Darboux theorem 2 lectures |
11 |
LHospital rule, indeterminate forms, Taylor theorem 4 lectures. Riemann, Riemann-Stieltjes integral 2 lectures |
12 |
Existance of Riemann, Riemann-Stieltjes integral 2 lectures Prperties of Riemann-Stieltjes integral - 2 lectures. Classes of Riemann integrable functions, monotonic functions, step functions 2 lectures |