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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 INTRODUCTIONPDF unavailable
21.2 Why study Real AnalysisPDF unavailable
31.3 Square root of 2PDF unavailable
41.4 Wason's selection taskPDF unavailable
51.5 Zeno's ParadoxPDF unavailable
62.1 Basic set theoryPDF unavailable
72.2 Basic logicPDF unavailable
82.3 QuantifiersPDF unavailable
92.4 ProofsPDF unavailable
102.5 Functions and relationsPDF unavailable
113.1 Axioms of Set TheoryPDF unavailable
123.2 Equivalence relationsPDF unavailable
133.3 What are the rationalsPDF unavailable
143.4 CardinalityPDF unavailable
15WEEK 2 INTRODUCTIONPDF unavailable
164.1 Field axiomsPDF unavailable
174.2 Order axiomsPDF unavailable
184.3 Absolute valuePDF unavailable
195.1 The completeness axiomPDF unavailable
205.2 Nested intervals propertyPDF unavailable
216.1 NIP+AP⇒ CompletenessPDF unavailable
226.2 Existence of square rootsPDF unavailable
236.3 Uncountability of the real numbersPDF unavailable
246.4 Density of rationals and irrationalsPDF unavailable
25WEEK 3 INTRODUCTIONPDF unavailable
267.1 Motivation for infinite sumsPDF unavailable
277.2 Definition of sequence and examplesPDF unavailable
287.3 Definition of convergencePDF unavailable
297.4 Uniqueness of limitsPDF unavailable
307.5 Achilles and the tortoisePDF unavailable
318.1 Deep dive into the definition of convergencePDF unavailable
328.2 A descriptive language for convergencePDF unavailable
338.3 Limit lawsPDF unavailable
349.1 SubsequencesPDF unavailable
359.2 Examples of convergent and divergent sequencesPDF unavailable
369.3 Some special sequences-CORRECTPDF unavailable
3710.1 Monotone sequencesPDF unavailable
3810.2 Bolzano-Weierstrass theoremPDF unavailable
3910.3 The Cauchy CriterionPDF unavailable
4010.4 MCT implies completenessPDF unavailable
4111.1 Definition and examples of infinite seriesPDF unavailable
4211.2 Cauchy tests-CorrectedPDF unavailable
4311.3 Tests for convergencePDF unavailable
4411.4 Erdos_s proof on divergence of reciprocals of primesPDF unavailable
4511.5 Resolving Zeno_s paradoxPDF unavailable
4612.1 Absolute and conditional convergencePDF unavailable
4712.2 Absolute convergence continuedPDF unavailable
4812.3 The number ePDF unavailable
4912.4 Grouping terms of an infinite seriesPDF unavailable
5012.5 The Cauchy productPDF unavailable
51WEEK 5 - INTRODUCTIONPDF unavailable
5213.1 The role of topology in real analysisPDF unavailable
5313.2 Open and closed setsPDF unavailable
5413.3 Basic properties of adherent and limit pointsPDF unavailable
5513.4 Basic properties of open and closed setsPDF unavailable
5614.1 Definition of continuityPDF unavailable
5714.2 Deep dive into epsilon-deltaPDF unavailable
5814.3 Negating continuityPDF unavailable
5915.1 The functions x and x2PDF unavailable
6015.2 Limit lawsPDF unavailable
6115.3 Limit of sin x_xPDF unavailable
6215.4 Relationship between limits and continuityPDF unavailable
6315.5 Global continuity and open setsPDF unavailable
6415.6 Continuity of square rootPDF unavailable
6515.7 Operations on continuous functionsPDF unavailable
6616.1 Language for limitsPDF unavailable
6716.2 Infinite limitsPDF unavailable
6816.3 One sided limitsPDF unavailable
6916.4 Limits of polynomialsPDF unavailable
7017.1 CompactnessPDF unavailable
7117.2 The Heine-Borel theoremPDF unavailable
7217.3 Open covers and compactnessPDF unavailable
7317.4 Equivalent notions of compactnessPDF unavailable
7418.1 The extreme value theoremPDF unavailable
7518.2 Uniform continuityPDF unavailable
7619.1 ConnectednessPDF unavailable
7719.2 Intermediate Value TheoremPDF unavailable
7819.3 Darboux continuity and monotone functionsPDF unavailable
7920.1 Perfect sets and the Cantor setPDF unavailable
8020.2 The structure of open setsPDF unavailable
8120.3 The Baire Category theoremPDF unavailable
8221.1 DiscontinuitiesPDF unavailable
8321.2 Classification of discontinuities and monotone functionsPDF unavailable
8421.3 Structure of set of discontinuitiesPDF unavailable
85WEEK 8 & 9 - INTRODUCTIONPDF unavailable
8622.1 Definition and interpretation of the derivativePDF unavailable
8722.2 Basic properties of the derivativePDF unavailable
8822.3 Examples of differentiationPDF unavailable
8923.1 Darboux_s theoremPDF unavailable
9023.2 The mean value theoremPDF unavailable
9123.3 Applications of the mean value theoremPDF unavailable
9224.1 Taylor's theorem NEWPDF unavailable
9324.2 The ratio mean value theorem and L_Hospital_s rulePDF unavailable
9425.1 Axiomatic characterisation of area and the Riemann integralPDF unavailable
9525.2 Proof of axiomatic characterizationPDF unavailable
9626.1 The definition of the Riemann integralPDF unavailable
9726.2 Criteria for Riemann integrabilityPDF unavailable
9826.3 Linearity of integralPDF unavailable
9927.1 Sets of measure zeroPDF unavailable
10027.2 The Riemann-Lebesgue theoremPDF unavailable
10127.3 Consequences of the Riemann-Lebesgue theoremPDF unavailable
102WEEK 10 & 11 - INTRODUCTIONPDF unavailable
10328.1 The fundamental theorem of calculusPDF unavailable
10428.2 Taylor's theorem-Integral form of remainderPDF unavailable
10528.3 Notation for Taylor polynomialsPDF unavailable
10628.4 Smooth functions and Taylor seriesPDF unavailable
10729.1 Power series PDF unavailable
10829.2 Definition of uniform convergencePDF unavailable
10931.1 The exponential functionPDF unavailable
11031.2 The inverse function theoremPDF unavailable
11131.3 The LogarithmPDF unavailable
11232.1 Trigonometric functionsPDF unavailable
11332.2 The number PiPDF unavailable
11432.3 The graphs of sin and cosPDF unavailable
11533.1 The Basel problemPDF unavailable
11634.1 Improper integralsPDF unavailable
11734.2 The Integral testPDF unavailable
11835.1 Weierstrass approximation theoremPDF unavailable
11935.2 Bernstein PolynomialsPDF unavailable
12035.3 Properties of Bernstein polynomialsPDF unavailable
12135.4 Proof of Weierstrass approximation theoremPDF unavailable


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3GujaratiNot Available
4HindiNot Available
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