Course11110113472 lectures
Basic Real Analysis
Prof. I. K. Rana · IIT Bombay
Lectures
Week 1
- Lecture 1 : Real Numbers and Sequences - Part I
- Lecture 2 : Real Numbers and Sequences - Part II
- Lecture 3 : Real Numbers and Sequences - Part III
- Lecture 4 : Convergence of Sequences - Part I
- Lecture 5 : Convergence of Sequences - Part II
- Lecture 6 : Convergence of Sequences - Part III
Week 2
- Lecture 7 : The LUB Property and Consequences - Part I
- Lecture 8 : The LUB Property and Consequences - Part II
- Lecture 9 : The LUB Property and Consequences - Part III
- Lecture 10 : Topology of Real Numbers: Closed Sets - Part I
- Lecture 11 : Topology of Real Numbers: Closed Sets - Part II
- Lecture 12 : Topology of Real Numbers: Closed Sets - Part III
Week 3
- Lecture 13 : Topology of Real Numbers: Limit Points, Interior Points, Open Sets and Compact Sets - Part I
- Lecture 14 : Topology of Real Numbers: Limit Points, Interior Points, Open Sets and Compact Sets - Part II
- Lecture 15 : Topology of Real Numbers: Limit Points, Interior Points, Open Sets and Compact Sets - Part III
- Lecture 16 : Topology of Real Numbers: Compact Sets and Connected Sets - Part I
- Lecture 17 : Topology of Real Numbers: Compact Sets and Connected Sets - Part II
- Lecture 18 : Topology of Real Numbers: Compact Sets and Connected Sets - Part III
Week 4
- Lecture 19 : Topology of Real Numbers: Connected Sets; Limits and Continuity - Part I
- Lecture 20 : Topology of Real Numbers: Connected Sets; Limits and Continuity - Part II
- Lecture 21 : Topology of Real Numbers: Connected Sets; Limits and Continuity - Part III
- Lecture 22 : Continuity and Uniform continuity - Part I
- Lecture 23 : Continuity and Uniform continuity - Part II
- Lecture 24 : Continuity and Uniform continuity - Part III
Week 5
- Lecture 25 : Uniform continuity and connected sets - Part I
- Lecture 26 : Uniform continuity and connected sets - Part II
- Lecture 27 : Uniform continuity and connected sets - Part III
- Lecture 28 : Connected sets and continuity - Part I
- Lecture 29 : Connected sets and continuity - Part II
- Lecture 30 : Connected sets and continuity - Part III
Week 6
- Lecture 31 : Differentiability - Part I
- Lecture 32 : Differentiability - Part II
- Lecture 33 : Differentiability - Part III
- Lecture 34 : Differentiability - Part IV
- Lecture 35 : Differentiability - Part V
- Lecture 36 : Differentiability - Part VI
Week 7
- Lecture 37 : Riemann Integration - Part I
- Lecture 38 : Riemann Integration - Part II
- Lecture 39 : Riemann Integration - Part III
- Lecture 40 : Riemann Integration - Part IV
- Lecture 41 : Riemann Integration - Part V
Week 8
- Lecture 42 : Riemann Integration - Part VI
- Lecture 43 : Riemann Sum and Riemann Integrals - Part I
- Lecture 44 : Riemann Sum and Riemann Integrals - Part II
- Lecture 45 : Riemann Sum and Riemann Integrals - Part III
Week 9
- Lecture 46 : Optimization in several variables - Part I
- Lecture 47 : Optimization in several variables - Part II
- Lecture 48 : Optimization in several variables - Part III
- Lecture 49 : Integration in several variables - Part I
- Lecture 50 : Integration in several variables - Part II
- Lecture 51 : Integration in several variables - Part III
Week 10
- Lecture 52 : Change of variables - Part I
- Lecture 53 : Change of variables - Part II
- Lecture 54 : Change of variables - Part III
- Lecture 55 : Change of variables - Part IV
- Lecture 56 : Metric Spaces - Part I
- Lecture 57 : Metric Spaces - Part II
Week 11
- Lecture 58 : Metric Spaces - Part III
- Lecture 59 : L^p Metrics - Part I
- Lecture 60 : L^p Metrics - Part II
- Lecture 61 : L^p Metrics - Part III
- Lecture 62 : Pointwise and Uniform convergence - Part I
- Lecture 63 : Pointwise and Uniform convergence - Part II
Week 12
- Lecture 64 : Pointwise and Uniform convergence - Part III
- Lecture 65 : Pointwise and Uniform convergence - Part IV
- Lecture 66 : Series of Numbers - Part I
- Lecture 67 : Series of Numbers - Part II
- Lecture 68 : Series of Numbers - Part III
- Lecture 69 : Alternating Series and Power Series
Live Session
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Bombay
- Department
- Mathematics
- Teacher
- Prof. I. K. Rana
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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