'Irrational numbers, Dedekind's Theorem' Video Lecture

Irrational numbers, Dedekind's Theorem

  • Course: A Basic Course in Real Analysis
  • Discipline: Mathematics
  • Faculty: Prof. P.D. Srivastava
  • Institute: IIT Kharagpur

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    Course Video Lectures Rational Numbers and Rational Cuts Irrational numbers, Dedekind's Theorem Continuum and Exercises Continuum and Exercises (Contd.) Cantor's Theory of Irrational Numbers Cantor's Theory of Irrational Numbers (Contd... Equivalence of Dedekind and Cantor's Theory Finite, Infinite, Countable and Uncountable S.. Types of Sets with Examples, Metric Space Various properties of open set, closure of a .. Ordered set, Least upper bound, greatest lowe.. Compact Sets and its properties Weiersstrass Theorem, Heine Borel Theorem, Co.. Tutorial - II Concept of limit of a sequence Some Important limits, Ratio tests for sequen.. Cauchy theorems on limit of sequences with ex.. Fundamental theorems on limits, Bolzano-Weier.. Theorems on Convergent and divergent sequence.. Cauchy sequence and its properties Infinite series of real numbers Comparison tests for series, Absolutely conve.. Tests for absolutely convergent series Raabe's test, limit of functions, Cluster poi.. Some results on limit of functions Limit Theorems for functions Extension of limit concept (one sided limits) Continuity of Functions Properties of Continuous Functions Boundedness Theorem, Max-Min Theorem and Bolz.. Uniform Continuity and Absolute Continuity Types of Discontinuities, Continuity and Comp.. Continuity and Compactness (Contd.), Connecte.. Differentiability of real valued function, Me.. Mean Value Theorem (Contd.) Application of MVT , Darboux Theorem, L Hospi.. L'Hospital Rule and Taylor's Theorem Tutorial - III Riemann/Riemann Stieltjes Integral Existence of Reimann Stieltjes Integral Properties of Reimann Stieltjes Integral Properties of Reimann Stieltjes Integral (Con.. Definite and Indefinite Integral Fundamental Theorems of Integral Calculus Improper Integrals Convergence Test for Improper Integrals
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