Modules / Lectures
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Lecture NoteDownload as zip file161M
Module NameDownload


Sl.No Chapter Name MP4 Download
11.1 WEEK 1 INTRODUCTIONDownload
21.2 Why study Real AnalysisDownload
31.3 Square root of 2Download
41.4 Wason's selection taskDownload
51.5 Zeno's ParadoxDownload
62.1 Basic set theoryDownload
72.2 Basic logicDownload
82.3 QuantifiersDownload
92.4 ProofsDownload
102.5 Functions and relationsDownload
113.1 Axioms of Set TheoryDownload
123.2 Equivalence relationsDownload
133.3 What are the rationalsDownload
143.4 CardinalityDownload
15WEEK 2 INTRODUCTIONDownload
164.2 Order axiomsDownload
174.3 Absolute valueDownload
185.1 The completeness axiomDownload
195.2 Nested intervals propertyDownload
206.1 NIP+AP⇒ CompletenessDownload
216.2 Existence of square rootsDownload
226.3 Uncountability of the real numbersDownload
236.4 Density of rationals and irrationalsDownload
24WEEK 3 INTRODUCTIONDownload
257.2 Definition of sequence and examplesDownload
267.3 Definition of convergenceDownload
277.4 Uniqueness of limitsDownload
287.5 Achilles and the tortoiseDownload
298.1 Deep dive into the definition of convergenceDownload
308.2 A descriptive language for convergenceDownload
318.3 Limit lawsDownload
329.1 SubsequencesDownload
339.2 Examples of convergent and divergent sequencesDownload
349.3 Some special sequences-CORRECTDownload
3510.1 Monotone sequencesDownload
3610.2 Bolzano-Weierstrass theoremDownload
3710.3 The Cauchy CriterionDownload
3810.4 MCT implies completenessDownload
3911.1 Definition and examples of infinite seriesDownload
4011.2 Cauchy tests-CorrectedDownload
4111.3 Tests for convergenceDownload
4211.4 Erdos_s proof on divergence of reciprocals of primesDownload
4311.5 Resolving Zeno_s paradoxDownload
4412.1 Absolute and conditional convergenceDownload
4512.2 Absolute convergence continuedDownload
4612.3 The number eDownload
4712.4 Grouping terms of an infinite seriesDownload
4812.5 The Cauchy productDownload
49WEEK 5 - INTRODUCTIONDownload
5013.1 The role of topology in real analysisDownload
5113.2 Open and closed setsDownload
5213.3 Basic properties of adherent and limit pointsDownload
5313.4 Basic properties of open and closed setsDownload
5414.1 Definition of continuityDownload
5514.2 Deep dive into epsilon-deltaDownload
5614.3 Negating continuityDownload
5715.1 The functions x and x2Download
5815.2 Limit lawsDownload
5915.3 Limit of sin x_xDownload
6015.4 Relationship between limits and continuityDownload
6115.5 Global continuity and open setsDownload
6215.6 Continuity of square rootDownload
6315.7 Operations on continuous functionsDownload
6416.1 Language for limitsDownload
6516.2 Infinite limitsDownload
6616.3 One sided limitsDownload
6716.4 Limits of polynomialsDownload
6817.1 CompactnessDownload
6917.2 The Heine-Borel theoremDownload
7017.3 Open covers and compactnessDownload
7117.4 Equivalent notions of compactnessDownload
7218.1 The extreme value theoremDownload
7318.2 Uniform continuityDownload
7419.1 ConnectednessDownload
7519.2 Intermediate Value TheoremDownload
7619.3 Darboux continuity and monotone functionsDownload
7720.1 Perfect sets and the Cantor setDownload
7820.2 The structure of open setsDownload
7920.3 The Baire Category theoremDownload
8021.1 DiscontinuitiesDownload
8121.2 Classification of discontinuities and monotone functionsDownload
8221.3 Structure of set of discontinuitiesDownload

Sl.No Chapter Name English
11.1 WEEK 1 INTRODUCTIONDownload
Verified
21.2 Why study Real AnalysisDownload
Verified
31.3 Square root of 2Download
Verified
41.4 Wason's selection taskDownload
Verified
51.5 Zeno's ParadoxDownload
Verified
62.1 Basic set theoryDownload
Verified
72.2 Basic logicDownload
Verified
82.3 QuantifiersDownload
Verified
92.4 ProofsDownload
Verified
102.5 Functions and relationsDownload
Verified
113.1 Axioms of Set TheoryDownload
Verified
123.2 Equivalence relationsDownload
Verified
133.3 What are the rationalsDownload
Verified
143.4 CardinalityDownload
Verified
15WEEK 2 INTRODUCTIONDownload
Verified
164.2 Order axiomsDownload
Verified
174.3 Absolute valueDownload
Verified
185.1 The completeness axiomDownload
Verified
195.2 Nested intervals propertyDownload
Verified
206.1 NIP+AP⇒ CompletenessDownload
Verified
216.2 Existence of square rootsDownload
Verified
226.3 Uncountability of the real numbersDownload
Verified
236.4 Density of rationals and irrationalsDownload
Verified
24WEEK 3 INTRODUCTIONDownload
Verified
257.2 Definition of sequence and examplesDownload
Verified
267.3 Definition of convergenceDownload
Verified
277.4 Uniqueness of limitsDownload
Verified
287.5 Achilles and the tortoiseDownload
Verified
298.1 Deep dive into the definition of convergenceDownload
Verified
308.2 A descriptive language for convergenceDownload
Verified
318.3 Limit lawsDownload
Verified
329.1 SubsequencesDownload
Verified
339.2 Examples of convergent and divergent sequencesDownload
Verified
349.3 Some special sequences-CORRECTDownload
Verified
3510.1 Monotone sequencesPDF unavailable
3610.2 Bolzano-Weierstrass theoremPDF unavailable
3710.3 The Cauchy CriterionPDF unavailable
3810.4 MCT implies completenessPDF unavailable
3911.1 Definition and examples of infinite seriesPDF unavailable
4011.2 Cauchy tests-CorrectedPDF unavailable
4111.3 Tests for convergencePDF unavailable
4211.4 Erdos_s proof on divergence of reciprocals of primesPDF unavailable
4311.5 Resolving Zeno_s paradoxPDF unavailable
4412.1 Absolute and conditional convergencePDF unavailable
4512.2 Absolute convergence continuedPDF unavailable
4612.3 The number ePDF unavailable
4712.4 Grouping terms of an infinite seriesPDF unavailable
4812.5 The Cauchy productPDF unavailable
49WEEK 5 - INTRODUCTIONPDF unavailable
5013.1 The role of topology in real analysisPDF unavailable
5113.2 Open and closed setsPDF unavailable
5213.3 Basic properties of adherent and limit pointsPDF unavailable
5313.4 Basic properties of open and closed setsPDF unavailable
5414.1 Definition of continuityPDF unavailable
5514.2 Deep dive into epsilon-deltaPDF unavailable
5614.3 Negating continuityPDF unavailable
5715.1 The functions x and x2PDF unavailable
5815.2 Limit lawsPDF unavailable
5915.3 Limit of sin x_xPDF unavailable
6015.4 Relationship between limits and continuityPDF unavailable
6115.5 Global continuity and open setsPDF unavailable
6215.6 Continuity of square rootPDF unavailable
6315.7 Operations on continuous functionsPDF unavailable
6416.1 Language for limitsPDF unavailable
6516.2 Infinite limitsPDF unavailable
6616.3 One sided limitsPDF unavailable
6716.4 Limits of polynomialsPDF unavailable
6817.1 CompactnessPDF unavailable
6917.2 The Heine-Borel theoremPDF unavailable
7017.3 Open covers and compactnessPDF unavailable
7117.4 Equivalent notions of compactnessPDF unavailable
7218.1 The extreme value theoremPDF unavailable
7318.2 Uniform continuityPDF unavailable
7419.1 ConnectednessPDF unavailable
7519.2 Intermediate Value TheoremPDF unavailable
7619.3 Darboux continuity and monotone functionsPDF unavailable
7720.1 Perfect sets and the Cantor setPDF unavailable
7820.2 The structure of open setsPDF unavailable
7920.3 The Baire Category theoremPDF unavailable
8021.1 DiscontinuitiesPDF unavailable
8121.2 Classification of discontinuities and monotone functionsPDF unavailable
8221.3 Structure of set of discontinuitiesPDF unavailable


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