A Basic Course in Real Analysis (USB)

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SKU
111105069



Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. P.D. Srivastava

NPTEL Co-ordinating Institute : IIT Kharagpur

NPTEL Lecture Count : 46

NPTEL Course Size : 15 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)


Lecture Titles:

Lecture 1 - Rational Numbers and Rational Cuts
Lecture 2 - Irrational numbers, Dedekind's Theorem
Lecture 3 - Continuum and Exercises
Lecture 4 - Continuum and Exercises (Continued.)
Lecture 5 - Cantor's Theory of Irrational Numbers
Lecture 6 - Cantor's Theory of Irrational Numbers (Continued.)
Lecture 7 - Equivalence of Dedekind and Cantor's Theory
Lecture 8 - Finite, Infinite, Countable and Uncountable Sets of Real Numbers
Lecture 9 - Types of Sets with Examples, Metric Space
Lecture 10 - Various properties of open set, closure of a set
Lecture 11 - Ordered set, Least upper bound, greatest lower bound of a set
Lecture 12 - Compact Sets and its properties
Lecture 13 - Weiersstrass Theorem, Heine Borel Theorem, Connected set
Lecture 14 - Tutorial - II
Lecture 15 - Concept of limit of a sequence
Lecture 16 - Some Important limits, Ratio tests for sequences of Real Numbers
Lecture 17 - Cauchy theorems on limit of sequences with examples
Lecture 18 - Fundamental theorems on limits, Bolzano-Weiersstrass Theorem
Lecture 19 - Theorems on Convergent and divergent sequences
Lecture 20 - Cauchy sequence and its properties
Lecture 21 - Infinite series of real numbers
Lecture 22 - Comparison tests for series, Absolutely convergent and Conditional convergent series
Lecture 23 - Tests for absolutely convergent series
Lecture 24 - Raabe's test, limit of functions, Cluster point
Lecture 25 - Some results on limit of functions
Lecture 26 - Limit Theorems for functions
Lecture 27 - Extension of limit concept (one sided limits)
Lecture 28 - Continuity of Functions
Lecture 29 - Properties of Continuous Functions
Lecture 30 - Boundedness Theorem, Max-Min Theorem and Bolzano's theorem
Lecture 31 - Uniform Continuity and Absolute Continuity
Lecture 32 - Types of Discontinuities, Continuity and Compactness
Lecture 33 - Continuity and Compactness (Continued.), Connectedness
Lecture 34 - Differentiability of real valued function, Mean Value Theorem
Lecture 35 - Mean Value Theorem (Continued.)
Lecture 36 - Application of MVT , Darboux Theorem, L Hospital Rule
Lecture 37 - L'Hospital Rule and Taylor's Theorem
Lecture 38 - Tutorial - III
Lecture 39 - Riemann/Riemann Stieltjes Integral
Lecture 40 - Existence of Reimann Stieltjes Integral
Lecture 41 - Properties of Reimann Stieltjes Integral
Lecture 42 - Properties of Reimann Stieltjes Integral (Continued.)
Lecture 43 - Definite and Indefinite Integral
Lecture 44 - Fundamental Theorems of Integral Calculus
Lecture 45 - Improper Integrals
Lecture 46 - Convergence Test for Improper Integrals

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