Mod-06 Lec-08 Finite, Infinite, Countable and Uncountable Sets of Real Numbers

Course Lectures

• Mod-01 Lec-01 Rational Numbers and Rational Cuts

  Prof. P.D. Srivastava

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• Mod-02 Lec-02 Irrational numbers, Dedekind's Theorem

  Prof. P.D. Srivastava

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• Mod-03 Lec-03 Continuum and Exercises

  Prof. P.D. Srivastava

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• Mod-03 Lec-04 Continuum and Exercises (Contd.)

  Prof. P.D. Srivastava

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• Mod-04 Lec-05 Cantor's Theory of Irrational Numbers

  Prof. P.D. Srivastava

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• Mod-04 Lec-06 Cantor's Theory of Irrational Numbers (Contd.)

  Prof. P.D. Srivastava

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• Mod-05 Lec-07 Equivalence of Dedekind and Cantor's Theory

  Prof. P.D. Srivastava

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• Mod-06 Lec-08 Finite, Infinite, Countable and Uncountable Sets of Real Numbers

  Prof. P.D. Srivastava

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• Mod-07 Lec-09 Types of Sets with Examples, Metric Space

  Prof. P.D. Srivastava

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• Mod-08 Lec-10 Various properties of open set, closure of a set

  Prof. P.D. Srivastava

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• Mod-09 Lec-11 Ordered set, Least upper bound, greatest lower bound of a set

  Prof. P.D. Srivastava

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• Mod-10 Lec-12 Compact Sets and its properties

  Prof. P.D. Srivastava

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• Mod-11 Lec-13 Weiersstrass Theorem, Heine Borel Theorem, Connected set

  Prof. P.D. Srivastava

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• Mod-12 Lec-14 Tutorial - II

  Prof. P.D. Srivastava

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• Mod-13 Lec-15 Concept of limit of a sequence

  Prof. P.D. Srivastava

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• Mod-14 Lec-16 Some Important limits, Ratio tests for sequences of Real Numbers

  Prof. P.D. Srivastava

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• Mod-15 Lec-17 Cauchy theorems on limit of sequences with examples

  Prof. P.D. Srivastava

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• Mod-16 Lec-18 Fundamental theorems on limits, Bolzano-Weiersstrass Theorem

  Prof. P.D. Srivastava

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• Mod-17 Lec-19 Theorems on Convergent and divergent sequences

  Prof. P.D. Srivastava

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• Mod-18 Lec-20 Cauchy sequence and its properties

  Prof. P.D. Srivastava

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• Mod-19 Lec-21 Infinite series of real numbers

  Prof. P.D. Srivastava

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• Mod-20 Lec-22 Comparison tests for series, Absolutely convergent and Conditional convergent series

  Prof. P.D. Srivastava

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• Mod-21 Lec-23 Tests for absolutely convergent series

  Prof. P.D. Srivastava

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• Mod-22 Lec-24 Raabe's test, limit of functions, Cluster point

  Prof. P.D. Srivastava

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• Mod-23 Lec-25 Some results on limit of functions

  Prof. P.D. Srivastava

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• Mod-24 Lec-26 Limit Theorems for functions

  Prof. P.D. Srivastava

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• Mod-25 Lec-27 Extension of limit concept (one sided limits)

  Prof. P.D. Srivastava

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• Mod-26 Lec-28 Continuity of Functions

  Prof. P.D. Srivastava

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• Mod-27 Lec-29 Properties of Continuous Functions

  Prof. P.D. Srivastava

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• Mod-28 Lec-30 Boundedness Theorem, Max-Min Theorem and Bolzano's theorem

  Prof. P.D. Srivastava

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• Mod-29 Lec-31 Uniform Continuity and Absolute Continuity

  Prof. P.D. Srivastava

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• Mod-30 Lec-32 Types of Discontinuities, Continuity and Compactness

  Prof. P.D. Srivastava

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• Mod-31 Lec-33 Continuity and Compactness (Contd.), Connectedness

  Prof. P.D. Srivastava

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• Mod-32 Lec-34 Differentiability of real valued function, Mean Value Theorem

  Prof. P.D. Srivastava

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• Mod-33 Lec-35 Mean Value Theorem (Contd.)

  Prof. P.D. Srivastava

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• Mod-34 Lec-36 Application of MVT , Darboux Theorem, L Hospital Rule

  Prof. P.D. Srivastava

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• Mod-35 Lec-37 L'Hospital Rule and Taylor's Theorem

  Prof. P.D. Srivastava

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• Mod-36 Lec-38 Tutorial - III

  Prof. P.D. Srivastava

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• Mod-37 Lec-39 Riemann/Riemann Stieltjes Integral

  Prof. P.D. Srivastava

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• Mod-38 Lec-40 Existence of Reimann Stieltjes Integral

  Prof. P.D. Srivastava

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• Mod-39 Lec-41 Properties of Reimann Stieltjes Integral

  Prof. P.D. Srivastava

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• Mod-39 Lec-42 Properties of Reimann Stieltjes Integral (Contd.)

  Prof. P.D. Srivastava

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• Mod-40 Lec-43 Definite and Indefinite Integral

  Prof. P.D. Srivastava

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• Mod-41 Lec-44 Fundamental Theorems of Integral Calculus

  Prof. P.D. Srivastava

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• Mod-42 Lec-45 Improper Integrals

  Prof. P.D. Srivastava

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• Mod-43 Lec-46 Convergence Test for Improper Integrals

  Prof. P.D. Srivastava

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