Cauchy's Root Test (Statement & Proof). Real Analysis I, Bartle, Rudin. Lec-65. (Urdu/Hindi) скачать в хорошем качестве

Cauchy's Root Test (Statement & Proof). Real Analysis I, Bartle, Rudin. Lec-65. (Urdu/Hindi)

pdf notes of these video lectures can be down loaded from our google drive. https://drive.google.com/drive/folder... ************************************************************************************** To watch all videos of the playlist "Real Analysis I" visit the following:    • Real Analysis  I   ************************************************************************************ For more educational videos of maths visit our channel    / mathlogicpk   ********************************************************************************* 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