Ordered set, upper bound. Real Analysis I, Rudin, Lec-03(Urdu/Hindi)

Notes Link
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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)

We shall be thankful to all those, who will comment and message us on our channels whatsapp number (092)03154414993.

[MuhammadNawaz-imzf]

Respected sir. Many mistakes and concepts have been cleared from your lectures in real analysis but sir your new lectures are not coming plz sir continue your lectures

[sajidmunir]

Sir relation to SxS Ka subset hai
ISS sense Mai nhi understand kr sktay
Plus Differential geometry k next part b upload kray

[alibajwa]

Sir Does Order defined on a set Of complex Number??

[muhammadnazir]

Order sirf <ho skta >order my b to likh skty k y>x...x>y

[ejazhussain]

Sir real analysis per mazeed vedio upload kr dy

[mathematicswithexcelacadem]

Asalamualikum sir, I want to ask that "If a set has one upper bound, then it has infinitely many upper bounds"Sir please guide whether this statement does not hold in case of finite superset.

[amnakousar]

Sir is irrational numbers are in order set or not?

[ejazhussain]

Sir specialy continuous and uniform continuous function