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 | Download Verified |
2 | 1.2 Why study Real Analysis | Download Verified |
3 | 1.3 Square root of 2 | Download Verified |
4 | 1.4 Wason's selection task | Download Verified |
5 | 1.5 Zeno's Paradox | Download Verified |
6 | 2.1 Basic set theory | Download Verified |
7 | 2.2 Basic logic | Download Verified |
8 | 2.3 Quantifiers | Download Verified |
9 | 2.4 Proofs | Download Verified |
10 | 2.5 Functions and relations | Download Verified |
11 | 3.1 Axioms of Set Theory | Download Verified |
12 | 3.2 Equivalence relations | Download Verified |
13 | 3.3 What are the rationals | Download Verified |
14 | 3.4 Cardinality | Download Verified |
15 | WEEK 2 INTRODUCTION | Download Verified |
16 | 4.1 Field axioms | Download Verified |
17 | 4.2 Order axioms | Download Verified |
18 | 4.3 Absolute value | Download Verified |
19 | 5.1 The completeness axiom | Download Verified |
20 | 5.2 Nested intervals property | Download Verified |
21 | 6.1 NIP+AP⇒ Completeness | Download Verified |
22 | 6.2 Existence of square roots | Download Verified |
23 | 6.3 Uncountability of the real numbers | Download Verified |
24 | 6.4 Density of rationals and irrationals | Download Verified |
25 | WEEK 3 INTRODUCTION | Download Verified |
26 | 7.1 Motivation for infinite sums | Download Verified |
27 | 7.2 Definition of sequence and examples | Download Verified |
28 | 7.3 Definition of convergence | Download Verified |
29 | 7.4 Uniqueness of limits | Download Verified |
30 | 7.5 Achilles and the tortoise | Download Verified |
31 | 8.1 Deep dive into the definition of convergence | Download Verified |
32 | 8.2 A descriptive language for convergence | Download Verified |
33 | 8.3 Limit laws | Download Verified |
34 | 9.1 Subsequences | Download Verified |
35 | 9.2 Examples of convergent and divergent sequences | Download Verified |
36 | 9.3 Some special sequences-CORRECT | Download Verified |
37 | 10.1 Monotone sequences | Download Verified |
38 | 10.2 Bolzano-Weierstrass theorem | Download Verified |
39 | 10.3 The Cauchy Criterion | Download Verified |
40 | 10.4 MCT implies completeness | Download Verified |
41 | 11.1 Definition and examples of infinite series | Download Verified |
42 | 11.2 Cauchy tests-Corrected | Download Verified |
43 | 11.3 Tests for convergence | Download Verified |
44 | 11.4 Erdos_s proof on divergence of reciprocals of primes | Download Verified |
45 | 11.5 Resolving Zeno_s paradox | Download Verified |
46 | 12.1 Absolute and conditional convergence | Download Verified |
47 | 12.2 Absolute convergence continued | Download Verified |
48 | 12.3 The number e | Download Verified |
49 | 12.4 Grouping terms of an infinite series | Download Verified |
50 | 12.5 The Cauchy product | Download Verified |
51 | WEEK 5 - INTRODUCTION | Download Verified |
52 | 13.1 The role of topology in real analysis | Download Verified |
53 | 13.2 Open and closed sets | Download Verified |
54 | 13.3 Basic properties of adherent and limit points | Download Verified |
55 | 13.4 Basic properties of open and closed sets | Download Verified |
56 | 14.1 Definition of continuity | Download Verified |
57 | 14.2 Deep dive into epsilon-delta | Download Verified |
58 | 14.3 Negating continuity | Download Verified |
59 | 15.1 The functions x and x2 | Download Verified |
60 | 15.2 Limit laws | Download Verified |
61 | 15.3 Limit of sin x_x | Download Verified |
62 | 15.4 Relationship between limits and continuity | Download Verified |
63 | 15.5 Global continuity and open sets | Download Verified |
64 | 15.6 Continuity of square root | Download Verified |
65 | 15.7 Operations on continuous functions | Download Verified |
66 | 16.1 Language for limits | Download Verified |
67 | 16.2 Infinite limits | Download Verified |
68 | 16.3 One sided limits | Download Verified |
69 | 16.4 Limits of polynomials | Download Verified |
70 | 17.1 Compactness | Download Verified |
71 | 17.2 The Heine-Borel theorem | Download Verified |
72 | 17.3 Open covers and compactness | Download Verified |
73 | 17.4 Equivalent notions of compactness | Download Verified |
74 | 18.1 The extreme value theorem | Download Verified |
75 | 18.2 Uniform continuity | Download Verified |
76 | 19.1 Connectedness | Download Verified |
77 | 19.2 Intermediate Value Theorem | Download Verified |
78 | 19.3 Darboux continuity and monotone functions | Download Verified |
79 | 20.1 Perfect sets and the Cantor set | Download Verified |
80 | 20.2 The structure of open sets | Download Verified |
81 | 20.3 The Baire Category theorem | Download Verified |
82 | 21.1 Discontinuities | Download Verified |
83 | 21.2 Classification of discontinuities and monotone functions | Download Verified |
84 | 21.3 Structure of set of discontinuities | Download Verified |
85 | WEEK 8 & 9 - INTRODUCTION | Download Verified |
86 | 22.1 Definition and interpretation of the derivative | Download Verified |
87 | 22.2 Basic properties of the derivative | Download Verified |
88 | 22.3 Examples of differentiation | Download Verified |
89 | 23.1 Darboux_s theorem | Download Verified |
90 | 23.2 The mean value theorem | Download Verified |
91 | 23.3 Applications of the mean value theorem | Download Verified |
92 | 24.1 Taylor's theorem NEW | Download Verified |
93 | 24.2 The ratio mean value theorem and L_Hospital_s rule | Download Verified |
94 | 25.1 Axiomatic characterisation of area and the Riemann integral | Download Verified |
95 | 25.2 Proof of axiomatic characterization | Download Verified |
96 | 26.1 The definition of the Riemann integral | Download Verified |
97 | 26.2 Criteria for Riemann integrability | Download Verified |
98 | 26.3 Linearity of integral | Download Verified |
99 | 27.1 Sets of measure zero | Download Verified |
100 | 27.2 The Riemann-Lebesgue theorem | Download Verified |
101 | 27.3 Consequences of the Riemann-Lebesgue theorem | Download Verified |
102 | WEEK 10 & 11 - INTRODUCTION | Download Verified |
103 | 28.1 The fundamental theorem of calculus | Download Verified |
104 | 28.2 Taylor's theorem-Integral form of remainder | Download Verified |
105 | 28.3 Notation for Taylor polynomials | Download Verified |
106 | 28.4 Smooth functions and Taylor series | Download Verified |
107 | 29.1 Power series | Download Verified |
108 | 29.2 Definition of uniform convergence | Download Verified |
109 | 31.1 The exponential function | Download Verified |
110 | 31.2 The inverse function theorem | Download Verified |
111 | 31.3 The Logarithm | Download Verified |
112 | 32.1 Trigonometric functions | Download Verified |
113 | 32.2 The number Pi | Download Verified |
114 | 32.3 The graphs of sin and cos | Download Verified |
115 | 33.1 The Basel problem | Download Verified |
116 | 34.1 Improper integrals | Download Verified |
117 | 34.2 The Integral test | Download Verified |
118 | 35.1 Weierstrass approximation theorem | Download Verified |
119 | 35.2 Bernstein Polynomials | Download Verified |
120 | 35.3 Properties of Bernstein polynomials | Download Verified |
121 | 35.4 Proof of Weierstrass approximation theorem | Download Verified |
Sl.No | Language | Book link |
---|---|---|
1 | English | Download |
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 |