If an ordered set has least upper bound property then it has greatest lower bound property. Lec-09

preview_player
Показать описание
pdf notes of these video lectures can be down loaded from our following google drive.
**************************************************************************************
To watch all videos of the playlist "Real Analysis I" visit the following:
************************************************************************************
For more educational videos of maths visit our channel
*********************************************************************************
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.
Рекомендации по теме
Комментарии
Автор

respected sir, i have enrolled for Msc Mathematics course. i find your method of teaching very interesting and endearing. your smooth and easy to understand talk makes learning easy. Prof like you are very rare and hard to find. thanks a lot from Mysore, Karnataka, India.

sovereignfoodspecialties
Автор

Bht achy sy explain kiya Thank you so much

areehaarif
Автор

Mashallah bahut khoob parhaty hain sr please aur lectures bhi send karen please maharbani ho gi

Mujahid
Автор

Sir yeah sari book tarteeb say parhain gy na

HamzaAli-xnge