Modules / Lectures
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Lecture NoteDownload as zip file161M
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noc20_ma51_assignment_Week_1noc20_ma51_assignment_Week_1
noc20_ma51_assignment_Week_10noc20_ma51_assignment_Week_10
noc20_ma51_assignment_Week_11noc20_ma51_assignment_Week_11
noc20_ma51_assignment_Week_12noc20_ma51_assignment_Week_12
noc20_ma51_assignment_Week_2noc20_ma51_assignment_Week_2
noc20_ma51_assignment_Week_3noc20_ma51_assignment_Week_3
noc20_ma51_assignment_Week_4noc20_ma51_assignment_Week_4
noc20_ma51_assignment_Week_5noc20_ma51_assignment_Week_5
noc20_ma51_assignment_Week_6noc20_ma51_assignment_Week_6
noc20_ma51_assignment_Week_7noc20_ma51_assignment_Week_7
noc20_ma51_assignment_Week_8noc20_ma51_assignment_Week_8
noc20_ma51_assignment_Week_9noc20_ma51_assignment_Week_9


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
164.1 Field axiomsDownload
174.2 Order axiomsDownload
184.3 Absolute valueDownload
195.1 The completeness axiomDownload
205.2 Nested intervals propertyDownload
216.1 NIP+AP⇒ CompletenessDownload
226.2 Existence of square rootsDownload
236.3 Uncountability of the real numbersDownload
246.4 Density of rationals and irrationalsDownload
25WEEK 3 INTRODUCTIONDownload
267.1 Motivation for infinite sumsDownload
277.2 Definition of sequence and examplesDownload
287.3 Definition of convergenceDownload
297.4 Uniqueness of limitsDownload
307.5 Achilles and the tortoiseDownload
318.1 Deep dive into the definition of convergenceDownload
328.2 A descriptive language for convergenceDownload
338.3 Limit lawsDownload
349.1 SubsequencesDownload
359.2 Examples of convergent and divergent sequencesDownload
369.3 Some special sequences-CORRECTDownload
3710.1 Monotone sequencesDownload
3810.2 Bolzano-Weierstrass theoremDownload
3910.3 The Cauchy CriterionDownload
4010.4 MCT implies completenessDownload
4111.1 Definition and examples of infinite seriesDownload
4211.2 Cauchy tests-CorrectedDownload
4311.3 Tests for convergenceDownload
4411.4 Erdos_s proof on divergence of reciprocals of primesDownload
4511.5 Resolving Zeno_s paradoxDownload
4612.1 Absolute and conditional convergenceDownload
4712.2 Absolute convergence continuedDownload
4812.3 The number eDownload
4912.4 Grouping terms of an infinite seriesDownload
5012.5 The Cauchy productDownload
51WEEK 5 - INTRODUCTIONDownload
5213.1 The role of topology in real analysisDownload
5313.2 Open and closed setsDownload
5413.3 Basic properties of adherent and limit pointsDownload
5513.4 Basic properties of open and closed setsDownload
5614.1 Definition of continuityDownload
5714.2 Deep dive into epsilon-deltaDownload
5814.3 Negating continuityDownload
5915.1 The functions x and x2Download
6015.2 Limit lawsDownload
6115.3 Limit of sin x_xDownload
6215.4 Relationship between limits and continuityDownload
6315.5 Global continuity and open setsDownload
6415.6 Continuity of square rootDownload
6515.7 Operations on continuous functionsDownload
6616.1 Language for limitsDownload
6716.2 Infinite limitsDownload
6816.3 One sided limitsDownload
6916.4 Limits of polynomialsDownload
7017.1 CompactnessDownload
7117.2 The Heine-Borel theoremDownload
7217.3 Open covers and compactnessDownload
7317.4 Equivalent notions of compactnessDownload
7418.1 The extreme value theoremDownload
7518.2 Uniform continuityDownload
7619.1 ConnectednessDownload
7719.2 Intermediate Value TheoremDownload
7819.3 Darboux continuity and monotone functionsDownload
7920.1 Perfect sets and the Cantor setDownload
8020.2 The structure of open setsDownload
8120.3 The Baire Category theoremDownload
8221.1 DiscontinuitiesDownload
8321.2 Classification of discontinuities and monotone functionsDownload
8421.3 Structure of set of discontinuitiesDownload
85WEEK 8 & 9 - INTRODUCTIONDownload
8622.1 Definition and interpretation of the derivativeDownload
8722.2 Basic properties of the derivativeDownload
8822.3 Examples of differentiationDownload
8923.1 Darboux_s theoremDownload
9023.2 The mean value theoremDownload
9123.3 Applications of the mean value theoremDownload
9224.1 Taylor's theorem NEWDownload
9324.2 The ratio mean value theorem and L_Hospital_s ruleDownload
9425.1 Axiomatic characterisation of area and the Riemann integralDownload
9525.2 Proof of axiomatic characterizationDownload
9626.1 The definition of the Riemann integralDownload
9726.2 Criteria for Riemann integrabilityDownload
9826.3 Linearity of integralDownload
9927.1 Sets of measure zeroDownload
10027.2 The Riemann-Lebesgue theoremDownload
10127.3 Consequences of the Riemann-Lebesgue theoremDownload
102WEEK 10 & 11 - INTRODUCTIONDownload
10328.1 The fundamental theorem of calculusDownload
10428.2 Taylor's theorem-Integral form of remainderDownload
10528.3 Notation for Taylor polynomialsDownload
10628.4 Smooth functions and Taylor seriesDownload
10729.1 Power series Download
10829.2 Definition of uniform convergenceDownload
10931.1 The exponential functionDownload
11031.2 The inverse function theoremDownload
11131.3 The LogarithmDownload
11232.1 Trigonometric functionsDownload
11332.2 The number PiDownload
11432.3 The graphs of sin and cosDownload
11533.1 The Basel problemDownload
11634.1 Improper integralsDownload
11734.2 The Integral testDownload
11835.1 Weierstrass approximation theoremDownload
11935.2 Bernstein PolynomialsDownload
12035.3 Properties of Bernstein polynomialsDownload
12135.4 Proof of Weierstrass approximation theoremDownload

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
164.1 Field axiomsDownload
Verified
174.2 Order axiomsDownload
Verified
184.3 Absolute valueDownload
Verified
195.1 The completeness axiomDownload
Verified
205.2 Nested intervals propertyDownload
Verified
216.1 NIP+AP⇒ CompletenessDownload
Verified
226.2 Existence of square rootsDownload
Verified
236.3 Uncountability of the real numbersDownload
Verified
246.4 Density of rationals and irrationalsDownload
Verified
25WEEK 3 INTRODUCTIONDownload
Verified
267.1 Motivation for infinite sumsDownload
Verified
277.2 Definition of sequence and examplesDownload
Verified
287.3 Definition of convergenceDownload
Verified
297.4 Uniqueness of limitsDownload
Verified
307.5 Achilles and the tortoiseDownload
Verified
318.1 Deep dive into the definition of convergenceDownload
Verified
328.2 A descriptive language for convergenceDownload
Verified
338.3 Limit lawsDownload
Verified
349.1 SubsequencesDownload
Verified
359.2 Examples of convergent and divergent sequencesDownload
Verified
369.3 Some special sequences-CORRECTDownload
Verified
3710.1 Monotone sequencesDownload
Verified
3810.2 Bolzano-Weierstrass theoremDownload
Verified
3910.3 The Cauchy CriterionDownload
Verified
4010.4 MCT implies completenessDownload
Verified
4111.1 Definition and examples of infinite seriesDownload
Verified
4211.2 Cauchy tests-CorrectedDownload
Verified
4311.3 Tests for convergenceDownload
Verified
4411.4 Erdos_s proof on divergence of reciprocals of primesDownload
Verified
4511.5 Resolving Zeno_s paradoxDownload
Verified
4612.1 Absolute and conditional convergenceDownload
Verified
4712.2 Absolute convergence continuedDownload
Verified
4812.3 The number eDownload
Verified
4912.4 Grouping terms of an infinite seriesDownload
Verified
5012.5 The Cauchy productDownload
Verified
51WEEK 5 - INTRODUCTIONDownload
Verified
5213.1 The role of topology in real analysisDownload
Verified
5313.2 Open and closed setsDownload
Verified
5413.3 Basic properties of adherent and limit pointsDownload
Verified
5513.4 Basic properties of open and closed setsDownload
Verified
5614.1 Definition of continuityDownload
Verified
5714.2 Deep dive into epsilon-deltaDownload
Verified
5814.3 Negating continuityDownload
Verified
5915.1 The functions x and x2Download
Verified
6015.2 Limit lawsDownload
Verified
6115.3 Limit of sin x_xDownload
Verified
6215.4 Relationship between limits and continuityDownload
Verified
6315.5 Global continuity and open setsDownload
Verified
6415.6 Continuity of square rootDownload
Verified
6515.7 Operations on continuous functionsDownload
Verified
6616.1 Language for limitsDownload
Verified
6716.2 Infinite limitsDownload
Verified
6816.3 One sided limitsDownload
Verified
6916.4 Limits of polynomialsDownload
Verified
7017.1 CompactnessDownload
Verified
7117.2 The Heine-Borel theoremDownload
Verified
7217.3 Open covers and compactnessDownload
Verified
7317.4 Equivalent notions of compactnessDownload
Verified
7418.1 The extreme value theoremDownload
Verified
7518.2 Uniform continuityDownload
Verified
7619.1 ConnectednessDownload
Verified
7719.2 Intermediate Value TheoremDownload
Verified
7819.3 Darboux continuity and monotone functionsDownload
Verified
7920.1 Perfect sets and the Cantor setDownload
Verified
8020.2 The structure of open setsDownload
Verified
8120.3 The Baire Category theoremDownload
Verified
8221.1 DiscontinuitiesDownload
Verified
8321.2 Classification of discontinuities and monotone functionsDownload
Verified
8421.3 Structure of set of discontinuitiesDownload
Verified
85WEEK 8 & 9 - INTRODUCTIONDownload
Verified
8622.1 Definition and interpretation of the derivativeDownload
Verified
8722.2 Basic properties of the derivativeDownload
Verified
8822.3 Examples of differentiationDownload
Verified
8923.1 Darboux_s theoremDownload
Verified
9023.2 The mean value theoremDownload
Verified
9123.3 Applications of the mean value theoremDownload
Verified
9224.1 Taylor's theorem NEWDownload
Verified
9324.2 The ratio mean value theorem and L_Hospital_s ruleDownload
Verified
9425.1 Axiomatic characterisation of area and the Riemann integralDownload
Verified
9525.2 Proof of axiomatic characterizationDownload
Verified
9626.1 The definition of the Riemann integralDownload
Verified
9726.2 Criteria for Riemann integrabilityDownload
Verified
9826.3 Linearity of integralDownload
Verified
9927.1 Sets of measure zeroDownload
Verified
10027.2 The Riemann-Lebesgue theoremDownload
Verified
10127.3 Consequences of the Riemann-Lebesgue theoremDownload
Verified
102WEEK 10 & 11 - INTRODUCTIONDownload
Verified
10328.1 The fundamental theorem of calculusDownload
Verified
10428.2 Taylor's theorem-Integral form of remainderDownload
Verified
10528.3 Notation for Taylor polynomialsDownload
Verified
10628.4 Smooth functions and Taylor seriesDownload
Verified
10729.1 Power series Download
Verified
10829.2 Definition of uniform convergenceDownload
Verified
10931.1 The exponential functionDownload
Verified
11031.2 The inverse function theoremDownload
Verified
11131.3 The LogarithmDownload
Verified
11232.1 Trigonometric functionsDownload
Verified
11332.2 The number PiDownload
Verified
11432.3 The graphs of sin and cosDownload
Verified
11533.1 The Basel problemDownload
Verified
11634.1 Improper integralsDownload
Verified
11734.2 The Integral testDownload
Verified
11835.1 Weierstrass approximation theoremDownload
Verified
11935.2 Bernstein PolynomialsDownload
Verified
12035.3 Properties of Bernstein polynomialsDownload
Verified
12135.4 Proof of Weierstrass approximation theoremDownload
Verified


Sl.No Language Book link
1EnglishDownload
2BengaliNot Available
3GujaratiNot Available
4HindiNot Available
5KannadaNot Available
6MalayalamNot Available
7MarathiNot Available
8TamilNot Available
9TeluguNot Available