Mathematics Videos

Lecture 1,2,3 : Definition of metric space and examples, Examples 1,2,3,4

Lecture 4,5 : Example 5,6,7

Lecture 6,7 Exercises 1.1 (Kreyszig) Q.1 to Q.9

Lecture 8,9 : Exercise 1.1 Q.11 to 15

Lecture 10,11 Further Examples of Metric Space, Example 1 (Sequence space s) Example 2 (The Space B(A) of bounded Functions)

Lecture 12 : The Space Lp

lecture 13,14,15 Exercise 1.2 Q.1 to Q.7

Lecture 1,2 : Open Ball, closed ball, interior, limit point of a set, Seperable spaces (two examples)

Lecture 3 : L-infinity space is not seperable

Lecture 4 : Lp Space is seperable

Lecture 5,6 : Convergence in Metric Space

Lecture 7 : Cauchy sequence, Th.1.4-4,5.

Lecture 8,9 : Theorem 1.4-6, Theorem 1.4-7

Lecture 10,11 : Rn and Cn are complete (PU Annual)

Lecture 12,13 : Space L-infinity is complete (PU Annual)

Lecture 14,15 : sequence space c is complete

Lecture 16,17 : Lp-Space is complete

Lecture 18,19 : C[a,b] is complete, Q is not complete

Lecture 1,2 : Normed Space

Lecture 3,4 : Example 1, Example 2

Lecture 5,6 : Example 3,4

Lecture 7 : Example 2.2-8, Lemma 2.2-9(translation invariance)

Lecture 8: Convex Set, Example (Closed unit Ball B(1,0) is convex)

Lecture 9,10 : Subspace of a Normed Space, Sequential and Series Convergence in norm

Lecture 11,12 : Schauder Basis, Normed Space having Schauder Basis is Seperable

Lecture 13,14 : Theorem-Finite dimensionsional Normed space is complete

Lecture 15, 16 : Equivalent norms

Lecture 17,18 : Compactness in Metric space, Lemma 2

Lecture 19,20 : Theorem 2.5.3 (A subset of a fine dimensional norms space is compact if and only if it is closed and bounded) PU Annual

Lecture 21,22 : Reisz Lemma, Th.2.5-5 (A Normed space having compact closed unit Ball is finite dimensional) PU Annual