A Basic Course in Real Analysis Video Lectures

A Basic Course in Real Analysis
'A Basic Course in Real Analysis' Video Lectures by Prof. P.D. Srivastava from IIT Kharagpur
"A Basic Course in Real Analysis" - Video Lectures
1. Rational Numbers and Rational Cuts
2. Irrational numbers, Dedekind's Theorem
3. Continuum and Exercises
4. Continuum and Exercises (Contd.)
5. Cantor's Theory of Irrational Numbers
6. Cantor's Theory of Irrational Numbers (Contd.)
7. Equivalence of Dedekind and Cantor's Theory
8. Finite, Infinite, Countable and Uncountable Sets of Real Numbers
9. Types of Sets with Examples, Metric Space
10. Various properties of open set, closure of a set
11. Ordered set, Least upper bound, greatest lower bound of a set
12. Compact Sets and its properties
13. Weiersstrass Theorem, Heine Borel Theorem, Connected set
14. Tutorial - II
15. Concept of limit of a sequence
16. Some Important limits, Ratio tests for sequences of Real Numbers
17. Cauchy theorems on limit of sequences with examples
18. Fundamental theorems on limits, Bolzano-Weiersstrass Theorem
19. Theorems on Convergent and divergent sequences
20. Cauchy sequence and its properties
21. Infinite series of real numbers
22. Comparison tests for series, Absolutely convergent and Conditional convergent series
23. Tests for absolutely convergent series
24. Raabe's test, limit of functions, Cluster point
25. Some results on limit of functions
26. Limit Theorems for functions
27. Extension of limit concept (one sided limits)
28. Continuity of Functions
29. Properties of Continuous Functions
30. Boundedness Theorem, Max-Min Theorem and Bolzano's theorem
31. Uniform Continuity and Absolute Continuity
32. Types of Discontinuities, Continuity and Compactness
33. Continuity and Compactness (Contd.), Connectedness
34. Differentiability of real valued function, Mean Value Theorem
35. Mean Value Theorem (Contd.)
36. Application of MVT , Darboux Theorem, L Hospital Rule
37. L'Hospital Rule and Taylor's Theorem
38. Tutorial - III
39. Riemann/Riemann Stieltjes Integral
40. Existence of Reimann Stieltjes Integral
41. Properties of Reimann Stieltjes Integral
42. Properties of Reimann Stieltjes Integral (Contd.)
43. Definite and Indefinite Integral
44. Fundamental Theorems of Integral Calculus
45. Improper Integrals
46. Convergence Test for Improper Integrals
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