# 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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