Modules / Lectures

Name | Download | Download Size |
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Lecture Note | Download as zip file | 161M |

Module Name | Download |
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noc20_ma51_assignment_Week_1 | noc20_ma51_assignment_Week_1 |

noc20_ma51_assignment_Week_10 | noc20_ma51_assignment_Week_10 |

noc20_ma51_assignment_Week_11 | noc20_ma51_assignment_Week_11 |

noc20_ma51_assignment_Week_12 | noc20_ma51_assignment_Week_12 |

noc20_ma51_assignment_Week_2 | noc20_ma51_assignment_Week_2 |

noc20_ma51_assignment_Week_3 | noc20_ma51_assignment_Week_3 |

noc20_ma51_assignment_Week_4 | noc20_ma51_assignment_Week_4 |

noc20_ma51_assignment_Week_5 | noc20_ma51_assignment_Week_5 |

noc20_ma51_assignment_Week_6 | noc20_ma51_assignment_Week_6 |

noc20_ma51_assignment_Week_7 | noc20_ma51_assignment_Week_7 |

noc20_ma51_assignment_Week_8 | noc20_ma51_assignment_Week_8 |

noc20_ma51_assignment_Week_9 | noc20_ma51_assignment_Week_9 |

Sl.No | Chapter Name | MP4 Download |
---|---|---|

1 | 1.1 WEEK 1 INTRODUCTION | Download |

2 | 1.2 Why study Real Analysis | Download |

3 | 1.3 Square root of 2 | Download |

4 | 1.4 Wason's selection task | Download |

5 | 1.5 Zeno's Paradox | Download |

6 | 2.1 Basic set theory | Download |

7 | 2.2 Basic logic | Download |

8 | 2.3 Quantifiers | Download |

9 | 2.4 Proofs | Download |

10 | 2.5 Functions and relations | Download |

11 | 3.1 Axioms of Set Theory | Download |

12 | 3.2 Equivalence relations | Download |

13 | 3.3 What are the rationals | Download |

14 | 3.4 Cardinality | Download |

15 | WEEK 2 INTRODUCTION | Download |

16 | 4.1 Field axioms | Download |

17 | 4.2 Order axioms | Download |

18 | 4.3 Absolute value | Download |

19 | 5.1 The completeness axiom | Download |

20 | 5.2 Nested intervals property | Download |

21 | 6.1 NIP+AP⇒ Completeness | Download |

22 | 6.2 Existence of square roots | Download |

23 | 6.3 Uncountability of the real numbers | Download |

24 | 6.4 Density of rationals and irrationals | Download |

25 | WEEK 3 INTRODUCTION | Download |

26 | 7.1 Motivation for infinite sums | Download |

27 | 7.2 Definition of sequence and examples | Download |

28 | 7.3 Definition of convergence | Download |

29 | 7.4 Uniqueness of limits | Download |

30 | 7.5 Achilles and the tortoise | Download |

31 | 8.1 Deep dive into the definition of convergence | Download |

32 | 8.2 A descriptive language for convergence | Download |

33 | 8.3 Limit laws | Download |

34 | 9.1 Subsequences | Download |

35 | 9.2 Examples of convergent and divergent sequences | Download |

36 | 9.3 Some special sequences-CORRECT | Download |

37 | 10.1 Monotone sequences | Download |

38 | 10.2 Bolzano-Weierstrass theorem | Download |

39 | 10.3 The Cauchy Criterion | Download |

40 | 10.4 MCT implies completeness | Download |

41 | 11.1 Definition and examples of infinite series | Download |

42 | 11.2 Cauchy tests-Corrected | Download |

43 | 11.3 Tests for convergence | Download |

44 | 11.4 Erdos_s proof on divergence of reciprocals of primes | Download |

45 | 11.5 Resolving Zeno_s paradox | Download |

46 | 12.1 Absolute and conditional convergence | Download |

47 | 12.2 Absolute convergence continued | Download |

48 | 12.3 The number e | Download |

49 | 12.4 Grouping terms of an infinite series | Download |

50 | 12.5 The Cauchy product | Download |

51 | WEEK 5 - INTRODUCTION | Download |

52 | 13.1 The role of topology in real analysis | Download |

53 | 13.2 Open and closed sets | Download |

54 | 13.3 Basic properties of adherent and limit points | Download |

55 | 13.4 Basic properties of open and closed sets | Download |

56 | 14.1 Definition of continuity | Download |

57 | 14.2 Deep dive into epsilon-delta | Download |

58 | 14.3 Negating continuity | Download |

59 | 15.1 The functions x and x2 | Download |

60 | 15.2 Limit laws | Download |

61 | 15.3 Limit of sin x_x | Download |

62 | 15.4 Relationship between limits and continuity | Download |

63 | 15.5 Global continuity and open sets | Download |

64 | 15.6 Continuity of square root | Download |

65 | 15.7 Operations on continuous functions | Download |

66 | 16.1 Language for limits | Download |

67 | 16.2 Infinite limits | Download |

68 | 16.3 One sided limits | Download |

69 | 16.4 Limits of polynomials | Download |

70 | 17.1 Compactness | Download |

71 | 17.2 The Heine-Borel theorem | Download |

72 | 17.3 Open covers and compactness | Download |

73 | 17.4 Equivalent notions of compactness | Download |

74 | 18.1 The extreme value theorem | Download |

75 | 18.2 Uniform continuity | Download |

76 | 19.1 Connectedness | Download |

77 | 19.2 Intermediate Value Theorem | Download |

78 | 19.3 Darboux continuity and monotone functions | Download |

79 | 20.1 Perfect sets and the Cantor set | Download |

80 | 20.2 The structure of open sets | Download |

81 | 20.3 The Baire Category theorem | Download |

82 | 21.1 Discontinuities | Download |

83 | 21.2 Classification of discontinuities and monotone functions | Download |

84 | 21.3 Structure of set of discontinuities | Download |

85 | WEEK 8 & 9 - INTRODUCTION | Download |

86 | 22.1 Definition and interpretation of the derivative | Download |

87 | 22.2 Basic properties of the derivative | Download |

88 | 22.3 Examples of differentiation | Download |

89 | 23.1 Darboux_s theorem | Download |

90 | 23.2 The mean value theorem | Download |

91 | 23.3 Applications of the mean value theorem | Download |

92 | 24.1 Taylor's theorem NEW | Download |

93 | 24.2 The ratio mean value theorem and L_Hospital_s rule | Download |

94 | 25.1 Axiomatic characterisation of area and the Riemann integral | Download |

95 | 25.2 Proof of axiomatic characterization | Download |

96 | 26.1 The definition of the Riemann integral | Download |

97 | 26.2 Criteria for Riemann integrability | Download |

98 | 26.3 Linearity of integral | Download |

99 | 27.1 Sets of measure zero | Download |

100 | 27.2 The Riemann-Lebesgue theorem | Download |

101 | 27.3 Consequences of the Riemann-Lebesgue theorem | Download |

102 | WEEK 10 & 11 - INTRODUCTION | Download |

103 | 28.1 The fundamental theorem of calculus | Download |

104 | 28.2 Taylor's theorem-Integral form of remainder | Download |

105 | 28.3 Notation for Taylor polynomials | Download |

106 | 28.4 Smooth functions and Taylor series | Download |

107 | 29.1 Power series | Download |

108 | 29.2 Definition of uniform convergence | Download |

109 | 31.1 The exponential function | Download |

110 | 31.2 The inverse function theorem | Download |

111 | 31.3 The Logarithm | Download |

112 | 32.1 Trigonometric functions | Download |

113 | 32.2 The number Pi | Download |

114 | 32.3 The graphs of sin and cos | Download |

115 | 33.1 The Basel problem | Download |

116 | 34.1 Improper integrals | Download |

117 | 34.2 The Integral test | Download |

118 | 35.1 Weierstrass approximation theorem | Download |

119 | 35.2 Bernstein Polynomials | Download |

120 | 35.3 Properties of Bernstein polynomials | Download |

121 | 35.4 Proof of Weierstrass approximation theorem | Download |

Sl.No | Chapter Name | English |
---|---|---|

1 | 1.1 WEEK 1 INTRODUCTION | PDF unavailable |

2 | 1.2 Why study Real Analysis | PDF unavailable |

3 | 1.3 Square root of 2 | PDF unavailable |

4 | 1.4 Wason's selection task | PDF unavailable |

5 | 1.5 Zeno's Paradox | PDF unavailable |

6 | 2.1 Basic set theory | PDF unavailable |

7 | 2.2 Basic logic | PDF unavailable |

8 | 2.3 Quantifiers | PDF unavailable |

9 | 2.4 Proofs | PDF unavailable |

10 | 2.5 Functions and relations | PDF unavailable |

11 | 3.1 Axioms of Set Theory | PDF unavailable |

12 | 3.2 Equivalence relations | PDF unavailable |

13 | 3.3 What are the rationals | PDF unavailable |

14 | 3.4 Cardinality | PDF unavailable |

15 | WEEK 2 INTRODUCTION | PDF unavailable |

16 | 4.1 Field axioms | PDF unavailable |

17 | 4.2 Order axioms | PDF unavailable |

18 | 4.3 Absolute value | PDF unavailable |

19 | 5.1 The completeness axiom | PDF unavailable |

20 | 5.2 Nested intervals property | PDF unavailable |

21 | 6.1 NIP+AP⇒ Completeness | PDF unavailable |

22 | 6.2 Existence of square roots | PDF unavailable |

23 | 6.3 Uncountability of the real numbers | PDF unavailable |

24 | 6.4 Density of rationals and irrationals | PDF unavailable |

25 | WEEK 3 INTRODUCTION | PDF unavailable |

26 | 7.1 Motivation for infinite sums | PDF unavailable |

27 | 7.2 Definition of sequence and examples | PDF unavailable |

28 | 7.3 Definition of convergence | PDF unavailable |

29 | 7.4 Uniqueness of limits | PDF unavailable |

30 | 7.5 Achilles and the tortoise | PDF unavailable |

31 | 8.1 Deep dive into the definition of convergence | PDF unavailable |

32 | 8.2 A descriptive language for convergence | PDF unavailable |

33 | 8.3 Limit laws | PDF unavailable |

34 | 9.1 Subsequences | PDF unavailable |

35 | 9.2 Examples of convergent and divergent sequences | PDF unavailable |

36 | 9.3 Some special sequences-CORRECT | PDF unavailable |

37 | 10.1 Monotone sequences | PDF unavailable |

38 | 10.2 Bolzano-Weierstrass theorem | PDF unavailable |

39 | 10.3 The Cauchy Criterion | PDF unavailable |

40 | 10.4 MCT implies completeness | PDF unavailable |

41 | 11.1 Definition and examples of infinite series | PDF unavailable |

42 | 11.2 Cauchy tests-Corrected | PDF unavailable |

43 | 11.3 Tests for convergence | PDF unavailable |

44 | 11.4 Erdos_s proof on divergence of reciprocals of primes | PDF unavailable |

45 | 11.5 Resolving Zeno_s paradox | PDF unavailable |

46 | 12.1 Absolute and conditional convergence | PDF unavailable |

47 | 12.2 Absolute convergence continued | PDF unavailable |

48 | 12.3 The number e | PDF unavailable |

49 | 12.4 Grouping terms of an infinite series | PDF unavailable |

50 | 12.5 The Cauchy product | PDF unavailable |

51 | WEEK 5 - INTRODUCTION | PDF unavailable |

52 | 13.1 The role of topology in real analysis | PDF unavailable |

53 | 13.2 Open and closed sets | PDF unavailable |

54 | 13.3 Basic properties of adherent and limit points | PDF unavailable |

55 | 13.4 Basic properties of open and closed sets | PDF unavailable |

56 | 14.1 Definition of continuity | PDF unavailable |

57 | 14.2 Deep dive into epsilon-delta | PDF unavailable |

58 | 14.3 Negating continuity | PDF unavailable |

59 | 15.1 The functions x and x2 | PDF unavailable |

60 | 15.2 Limit laws | PDF unavailable |

61 | 15.3 Limit of sin x_x | PDF unavailable |

62 | 15.4 Relationship between limits and continuity | PDF unavailable |

63 | 15.5 Global continuity and open sets | PDF unavailable |

64 | 15.6 Continuity of square root | PDF unavailable |

65 | 15.7 Operations on continuous functions | PDF unavailable |

66 | 16.1 Language for limits | PDF unavailable |

67 | 16.2 Infinite limits | PDF unavailable |

68 | 16.3 One sided limits | PDF unavailable |

69 | 16.4 Limits of polynomials | PDF unavailable |

70 | 17.1 Compactness | PDF unavailable |

71 | 17.2 The Heine-Borel theorem | PDF unavailable |

72 | 17.3 Open covers and compactness | PDF unavailable |

73 | 17.4 Equivalent notions of compactness | PDF unavailable |

74 | 18.1 The extreme value theorem | PDF unavailable |

75 | 18.2 Uniform continuity | PDF unavailable |

76 | 19.1 Connectedness | PDF unavailable |

77 | 19.2 Intermediate Value Theorem | PDF unavailable |

78 | 19.3 Darboux continuity and monotone functions | PDF unavailable |

79 | 20.1 Perfect sets and the Cantor set | PDF unavailable |

80 | 20.2 The structure of open sets | PDF unavailable |

81 | 20.3 The Baire Category theorem | PDF unavailable |

82 | 21.1 Discontinuities | PDF unavailable |

83 | 21.2 Classification of discontinuities and monotone functions | PDF unavailable |

84 | 21.3 Structure of set of discontinuities | PDF unavailable |

85 | WEEK 8 & 9 - INTRODUCTION | PDF unavailable |

86 | 22.1 Definition and interpretation of the derivative | PDF unavailable |

87 | 22.2 Basic properties of the derivative | PDF unavailable |

88 | 22.3 Examples of differentiation | PDF unavailable |

89 | 23.1 Darboux_s theorem | PDF unavailable |

90 | 23.2 The mean value theorem | PDF unavailable |

91 | 23.3 Applications of the mean value theorem | PDF unavailable |

92 | 24.1 Taylor's theorem NEW | PDF unavailable |

93 | 24.2 The ratio mean value theorem and L_Hospital_s rule | PDF unavailable |

94 | 25.1 Axiomatic characterisation of area and the Riemann integral | PDF unavailable |

95 | 25.2 Proof of axiomatic characterization | PDF unavailable |

96 | 26.1 The definition of the Riemann integral | PDF unavailable |

97 | 26.2 Criteria for Riemann integrability | PDF unavailable |

98 | 26.3 Linearity of integral | PDF unavailable |

99 | 27.1 Sets of measure zero | PDF unavailable |

100 | 27.2 The Riemann-Lebesgue theorem | PDF unavailable |

101 | 27.3 Consequences of the Riemann-Lebesgue theorem | PDF unavailable |

102 | WEEK 10 & 11 - INTRODUCTION | PDF unavailable |

103 | 28.1 The fundamental theorem of calculus | PDF unavailable |

104 | 28.2 Taylor's theorem-Integral form of remainder | PDF unavailable |

105 | 28.3 Notation for Taylor polynomials | PDF unavailable |

106 | 28.4 Smooth functions and Taylor series | PDF unavailable |

107 | 29.1 Power series | PDF unavailable |

108 | 29.2 Definition of uniform convergence | PDF unavailable |

109 | 31.1 The exponential function | PDF unavailable |

110 | 31.2 The inverse function theorem | PDF unavailable |

111 | 31.3 The Logarithm | PDF unavailable |

112 | 32.1 Trigonometric functions | PDF unavailable |

113 | 32.2 The number Pi | PDF unavailable |

114 | 32.3 The graphs of sin and cos | PDF unavailable |

115 | 33.1 The Basel problem | PDF unavailable |

116 | 34.1 Improper integrals | PDF unavailable |

117 | 34.2 The Integral test | PDF unavailable |

118 | 35.1 Weierstrass approximation theorem | PDF unavailable |

119 | 35.2 Bernstein Polynomials | PDF unavailable |

120 | 35.3 Properties of Bernstein polynomials | PDF unavailable |

121 | 35.4 Proof of Weierstrass approximation theorem | PDF unavailable |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |