Weeks Weekly Lecture Topics (Module Titles)
1 Day 1 Module 1 : METRIC SPACES AND EXAMPLES
Day 2 Module 2 : METRIC SPACES - MORE EXAMPLES
Day 3 Module 3 : SEQUENCES IN METRIC SPACES
Day 4 Module 4 : CONVERGENCE OF SEQUENCES IN METRIC SPACES
Day 5
2 Day 1 Module 5 : OPEN SETS
Day 2 Module 6 : FUNDAMENTAL PROPERTIES OF OPEN SETS
Day 3 Module 7 : CLOSED SETS
Day 4 Module 8 : CANTOR SET AND CLOSURE OF A SET
Day 5
3 Day 1 Module 9 : BOUNDARY OF A SET AND DENSE SET
Day 2 Module 10 : THEOREMS ON OPEN AND CLOSED SETS
Day 3 Module 11: SUBSPACES IN METRIC SPACES
Day 4 Module 12 : SEPARABLE SPACES
Day 5
4 Day 1 Module 13 : CONTINUITY
Day 2 Module 14: UNIFORM CONTINUITY
Day 3 Module 15: BAIRE'S THEOREM
Day 4 Module 16: THEOREMS ON CONTINUITY AND UNIFORM CONTINUITY
Day 5
5 Day 1 Module 17: HOMEOMORPHISM
Day 2 Module 18 : CONNECTEDNESS
Day 3 Module 19 : ROPERTIES OF COMPLEX NUMBERS
Day 4 Module 20 : FURTHER PROPERTIES OF COMPLEX NUMBERS
Day 5
6 Day 1 Module 21 : POLAR AND EXPONETIAL FORM
Day 2 Module 22 : FUNCTIONS OF A COMPLEX VARIABLE
Day 3 Module 23 : LIMIT OF FUNCTIONS OF A COMPLEX VARIABLE
Day 4 Module 24 : POINT AT INFINITY
Day 5
7 Day 1 Module 25 : CONTINUITY OF FUNCTIONS OF A COMPLEX VARIABLE
Day 2 Module 26 : MAPPINGS
Day 3 Module 27 : DIFFERENTIATION OF FUNCTIONS OF A COMPLEX VARIABLE
Day 4 Module 28 : CAUCHY-RIEMANN EQUATIONS - I
Day 5
8 Day 1 Module 29 : CAUCHY-RIEMANN EQUATIONS - II
Day 2 Module 30 : ANALYTIC FUNCTIONS
Day 3 Module 31 : FURTHER PROPERTIES OF ANALYTIC FUNCTIONS
Day 4
Day 5
9 Day 1 Module 32 : EXPONENTIAL FUNCTIONS
Day 2 Module 33 : TRIGONOMETRIC FUNCTIONS
Day 3 Module 34 : LOGARITHMIC FUNCTIONS
Day 4
Day 5
10 Day 1 Module 35 : HARMONIC FUNCTIONS
Day 2 Module 36 : MAPPINGS BY ELEMENTARY FUNCTIONS
Day 3 Module 37 : THEOREMS ON LIMITS AND DIFFERENTIATION FORMULAE
Day 4
Day 5
11 Day 1 Module 38 : ELEMENTARY FUNCTIONS - I
Day 2 Module 39 : ELEMENTARY FUNCTIONS - II
Day 3 Module 40 : DEFINITE INTEGRALS
Day 4
Day 5
12 Day 1 Module 41 : CONTOURS
Day 2 Module 42 : CONTOUR INTEGRALS
Day 3 Module 43 : CAUCHY-GOURSAT THEOREM
Day 4
Day 5
13 Day 1 Module 44 : CAUCHY'S INTEGRAL FORMULA
Day 2 Module 45 : LIOVILLE'S THEOREM
Day 3 Module 46 : SEQUENCES AND SERIES -I
Day 4
Day 5
15 Day 1 Module 47 : SEQUENCES AND SERIES -II
Day 2 Module 48 : TAYLOR SERIES
Day 3 Module 49 : LAURENT SERIES
Day 4
Day 5
16 Day 1 Module 50 : POWER SERIES
Day 2 Module 51: FURTHER PROBLEMS ON POWER SERIES
Day 3
Day 4
Day 5
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