Definitions of Least Upper Bound (Supremum) & Bounded Above Set. Real Analysis I, Rudin. Lec_04(Urdu

Notes Link
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• Real Analysis I
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In this part of lecture series course "Real Analysis I" Course of BS mathematics 5th Semester, we shall cover the following topics.
Real Number System
 Ordered sets, fields, the field of real numbers
 Completeness property of R
 The extended real number system
 Euclidean spaces
 Finite, countable and uncountable sets
Sequences and Series
 Sequences, subsequences, convergent sequences, Cauchy sequences
 Monotone and bounded sequences, Bolzano Weierstrass theorem
 Series, series of non-negative terms
 Partial sums, the root and ratio tests, integral test, comparison test
 Absolute and conditional convergence
Limit and Continuity
 The limit of a function
 Continuous functions
 Types of discontinuity
 Uniform continuity
 Monotone functions
Differentiation
 The derivative of a function
 Mean value theorems, the continuity of derivatives
 Taylor’s theorem
Functions of Several Variables
 Partial derivatives and differentiability, derivatives and differentials of composite functions
 Change in the order of partial derivative, implicit functions, inverse functions, Jacobians
 Maxima and minima
Recommended Books
1. W. Rudin, Principles of Mathematical Analysis, 3rd edition, (McGraw Hill, 1976)
2. R. G. Bartle, Introduction to Real Analysis, 3rd edition, (John Wiley and Sons, 2000)

[@mdabuzihad2000]

Its very helpful for me ,,,, thanks for this series ,,, respect from Bangladesh 😇

[@scholar-mj3om]

Excellent💯💯

[@ahmetsarboga3130]

it's very helpful for me too but ı wish to use English :) tnkx sir

[@hasnainnawaz7280]

Bahut kuch sekha aj💜❤️

[@HamzaAli-xn3ge]

Great work sir

[@junaidsabri9367]

Sir is chapter k bad plz sequence and series wala chapter ya differentiablity wala shuru kijiye ga plz

[@abdulwaheedyarik4396]

Sir g real analysis 2 bhi upload karna bartle say plZz sir

[@masumabarbhuiya6288]

I AM FROM INDIA

[@masumabarbhuiya6288]

Grateful work sir so much thanks

[@MathLogicpk]

thank u for watching.

[@raonaveednabeel657]

Sir upper bound and lower bound non-empty set k liye define hoty hn??

[@MathLogicpk]

Aap empty set k liay bhee krna chayeen to kr lain commonly zarorat nahee hotee....agar kahaeen zarorat ho to zarorat k mutabq define kr lain...

[@raonaveednabeel657]

@@MathLogicpk sir phir empty set k upper
Bounds,lower bounds,glb,lub Kya hoga??

[@MathLogicpk]

Main ny empty set k liay lub or glb nahee define karway or na hee karwany hain..

[@MathLogicpk]

Thats ur choice jo tum define kr loo