Lec-109 Approximating a continuous function by a step function. Real Analysis I. Bartle. (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 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)3154414993.

Lec-110 Approximating a continuous funtion by a piecewise linear and continuous function. Bartle.

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