Mathematics Videos

Lecture 1: Order on a Set, Ordered Set, Example 1

Lecture 2 : Example 2,3,4 (Examples of Ordered Sets)

Lecture 3: Field Axioms, Examples of Filed

Lecture 4 : Ordered Fileds, and their Properties

Lecture 5: Rational density theorem, its Corollary

Lecture 6 : Supremum and Infimum, Examples, Properties

Lecture 7 : Completeness property, Archimedian property and its corollary

Lecture 8 : Sequence and it's convergence

Lecture 9 : Example 2 and Example 3

Lecture 10: Example 4,5 and 6

Lecture 11: Theorem-1 (Uniqueness of Limit)

Lecture 12 : Theorem 2

Lecture 13 : Tail of a Sequence, Theorem-3

Lecture 14 : (Robert, G Bartle) Exercise 3.1 Q.4 to 7

Lecture 15 : Ex. 3.1 Q.8 to 10 (Robert G Bartle)

Lecture 16 : Ex 3.1, Q.11 To 14 (Robert G Bartle)

Lecture 17 : Ex 3.1 Q.15 To 18 (Robert G Bartle)

Lecture 18 : Exercise 2.1 (A J Kosmala) Q.18 And Theorem 2.1.13

Lecture 19 : Exercise 2.1 (A. J Kosmala) Q.17 and 19(a

Lecture 20 : Bounded Sequence (Definition and Examples), Theorems 1 and 2

Lecture 21 : Sum, Difference,Product,Quotient of sequences Theorem 03

Lecture 22 : Theorem 4 (Limit of Product of Sequences)

Lecture 23 : Theorem 5 (Limit of Quotient of two Sequences)

Lecture 24 : Theorem 6

Lecture 25 : Theorem 7 (Sandwich Theorem), Assignment

Lecture 26 : Theorem 8

Lecture 27 : Theorem 9

Lecture 28 : Example 1 to 6

Lecture 29 : Exercise Q.1 to 3

Lecture 30 : Q. 4 and Q.5

Lecture 31 : Q.6,7,8

Lecture 32 : Q.9 to Q. 11

Lecture 33 : Q.12 and Q.13

Lecture 34 : Q.14,15,16

Lecture 35 : Q.17,18

Lecture 36 : Monotone Sequence (definition And Examples)

Lecture 37 : Monotone Convergence Theorem

Lecture 38 : Example 1,2

Lecture 39 : Example3,4

Lecture 40 : Exercise Q.1,2,3

Exercise 41 : Q.4,5,6

Lecture 42 : Subsequece (definion And Examples), Theorem1

Lecture 43 : Divergence Criteria, Theorem 2

Lecture 44: Basics of Topology

Lecture 45 : Theorem 3

Lecture 46 : Sequential Compactness, Theorem (Optional)

Lecture 47 : Theorem 4 (Bolzano Weierstrass Theorem)-

Lecture 48 : Example 1, Example 2

Lecture 49 : Subsequential Limit, Example 1,2,3, Limit Superior, Limit Inferior of a sequence

Lecture 50 : Theorem5, Theorem 6

Lecture 51 : Definition of Cauchy Sequence, Example1,2

Lecture 52 : Theorem 1,2

Lecture 53 : Theorem 3

Lecture 54 : Contractive Sequence, Theorem 4

Lecture 55 ch. 1, Infinite Series, Its Convergence, Example 1

Lecture 56 : Example 2 and 3

Lecture 57 : Cauchy criterion for series convergence, example 4

Lecture 58 : Example-4, Example-5

Lecture 59 : Example-6, Example-7

Lecture 60 : Comparison Test

Lecture 61 : Limit Comparison Test

Lecture 62 : Example 8

Lecture 63 : Example 9 to 12 ( using comparison and limit comparison Tests)

Lecture 64 : Caunchy's Condensation Test

Lecture 65 : Example 13,14

Lecture 1 : Cluster point of a set, Example 1 to 4, Theorem 1

Lecture 2 : Definition Of Limit Of A Function, Its Negation, Example 1

Lecture 3 : Theorem 2 (sequential Criterion Of Limit), Theorem 03 Uniqueness Of Limit

Lecture 4 : Example 2,3,4 (limit Of A Function)

Lecture 5 : Real Exercise Q.1 to 3

Lecture 6 : Exercise Q.4 To 6

Lecture 7 : Exercise Q.7,8

Lecture 8 : Definition Of A Bounded Unction In A Nighborhood Of A Point, Theorem 01 (pu2019 Annual)

Lecture 9 : Theorem 2 And 3

Lecture 10 : Theorem 4, 5

Lecture 11 : Divergence Criterion, Example 1 to Example 6

Lecture 12 : Example 7,8

Lecture 13 : Continuous Functions, Theorem 1

Lecture 14 : Theorem 2,3 , Theorem 1 (corollary)

Lecture 15,16 : Uniform Continuity, Examples, Nonuniformity Criteria, Theorem 1

Lecture 17,18 : Lipschitz Condition, Examples, Theorem (Lipschitz Fuctions and Uniform continuity)

Lecture 19,20 : The continuous extension Theorem

Lecture 1 : Riemann integral, Riemann Stieltjes Integral (Definitions)

Lecture 2,3 : Refinement, Theorem1,2,3

Lecture 4,5 : Theorem 4,5,6

Lecture 6,7 Therem 7 (W.Rudin Theorem 6.10)

Lecture 8,9 : Theorem 8 (W.Rudin Th. 6.12 (a))

Lecture 10 11 Theorem 9,10 (T.Apostol Th. 7.2,7.3)

Lecture 12 Theorem 11 (T.Apostol Th. 7.4)

Lecture 13 Theorem 12 Integration By Parts (apostol Th. 7.6)

Lecture 14,15 Theorem 13 (Change of Varible, Apostol Th.7.8)

Lecture 16,17,18 Theorem 14 (Apostol Th. 7.8), Theorem 15 (W. Rudin Theorem 6.17)

Lecture 19,20 Theorem 16 (rudin Th.6.11)

Lecture 23,24,25 Theorem 19,20,21

Lecture 1,2,3,4 Pointwise convergence, Example 7.2, 7.3,7.4,7.5,7.6 (Walter Rudin)

Lecture 5,6,7,8 Uniform Convergence Of Sequece And Series Of Functions, Theorem 1,2,3,4 (from Rudin And Apostol)

Lecture 9,10 Theorem 5 (Rudin Th.7.11), Theorem 6 (Apostol Th.9.2)

Lecture 11,12 Theorem 7 (Walter Rudin Th. 7.13)

Lecture 13,14 Supremum norm and its property, Theorem 8 (The Complete Metric Space C(X)) Rudin Th. 7.15

Lecture 15,16 Uniform convergence and Integration, Theorem 9 (Rudin Th 7.16) and its corollary (Term by term integration of Series)

Lecture 17,18 Example 1,2 (Bartle Ex.8.2 Q.9,10)

lecture 19,20 Theorem 10 (Uniform convergence and differentiation)

Lecture 21 to 25 : Exercise Q.1 To 4 (rudin Q.7.1 To 7.4)

Lecture 26,27,28,29

Lecture 30,31,32 Q.8 To 12