Math 2.0

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A Basic Course in Real Analysis R0F1RAZGZ7

URIm2://res/R0F1RAZGZ7
Kindcourse
CreatorsP.D. Srivastava (instructor)
Date2013-07-02
MSC26-XX
Scopein
Idscourse 03w5sq511:111105069

Expressions

e1: edition

Languageen
Date2013-07-02
Contents
  • part 1: Rational Numbers and Rational Cuts
  • session 1: Rational Numbers and Rational Cuts
  • part 2: Irrational numbers, Dedekind\'s Theorem
  • session 2: Irrational numbers, Dedekind's Theorem
  • part 3: Continuum and Exercises
  • session 3: Continuum and Exercises
  • session 4: Continuum and Exercises (Contd.)
  • part 4: Cantor\\\'s Theory of Irrational Numbers
  • session 5: Cantor's Theory of Irrational Numbers
  • session 6: Cantor's Theory of Irrational Numbers (Contd.)
  • part 5: Equivalence of Dedekind and Cantor\'s Theory
  • session 7: Equivalence of Dedekind and Cantor's Theory
  • part 6: Finite, Infinite, Countable and Uncountable Sets of Real Numbers
  • session 8: Finite, Infinite, Countable and Uncountable Sets of Real Numbers
  • part 7: Types of Sets with Examples, Metric Space
  • session 9: Types of Sets with Examples, Metric Space
  • part 8: Various properties of open set, closure of a set
  • session 10: Various properties of open set, closure of a set
  • part 9: Ordered set, Least upper bound, greatest lower bound of a set
  • session 11: Ordered set, Least upper bound, greatest lower bound of a set
  • part 10: Compact Sets and its properties
  • session 12: Compact Sets and its properties
  • part 11: Weiersstrass Theorem, Heine Borel Theorem, Connected set
  • session 13: Weiersstrass Theorem, Heine Borel Theorem, Connected set
  • part 12: Tutorial - II
  • session 14: Tutorial - II
  • part 13: Concept of limit of a sequence
  • session 15: Concept of limit of a sequence
  • part 14: Some important limits, Ratio tests for sequences of Real Numbers
  • session 16: Some Important limits, Ratio tests for sequences of Real Numbers
  • part 15: Cauchy theorems on limit of sequences with examples
  • session 17: Cauchy theorems on limit of sequences with examples
  • part 16: Fundamental theorems on limits, Bolzano-Weiersstrass Theorem
  • session 18: Fundamental theorems on limits, Bolzano-Weiersstrass Theorem
  • part 17: Theorems on Convergent and Divergent sequences
  • session 19: Theorems on Convergent and divergent sequences
  • part 18: Cauchy sequence and its properties
  • session 20: Cauchy sequence and its properties
  • part 19: Infinite series of real numbers
  • session 21: Infinite series of real numbers
  • part 20: Comparison tests for series, Absolutely convergent and Conditional convergent series
  • session 22: Comparison tests for series, Absolutely convergent and Conditional convergent series
  • part 21: Tests for absolutely convergent series
  • session 23: Tests for absolutely convergent series
  • part 22: Raabe\\\'s test, limit of functions, Cluster point
  • session 24: Raabe's test, limit of functions, Cluster point
  • part 23: Some results on limit of functions
  • session 25: Some results on limit of functions
  • part 24: Limit Theorems for functions
  • session 26: Limit Theorems for functions
  • part 25: Extension of limit concept (one sided limits)
  • session 27: Extension of limit concept (one sided limits)
  • part 26: Continuity of Functions
  • session 28: Continuity of Functions
  • part 27: Properties of Continuous Functions
  • session 29: Properties of Continuous Functions
  • part 28: Boundedness Theorem, Max-Min Theorem, and Bolzano\'s Theorem
  • session 30: Boundedness Theorem, Max-Min Theorem and Bolzano's theorem
  • part 29: Uniform Continuity and Absolute Continuity
  • session 31: Uniform Continuity and Absolute Continuity
  • part 30: Types of Discontinuities, Continuity and Compactness
  • session 32: Types of Discontinuities, Continuity and Compactness
  • part 31: Continuity and Compactness (Contd.), Connectedness
  • session 33: Continuity and Compactness (Contd.), Connectedness
  • part 32: Differentiability of real valued function, Mean Value Theorem
  • session 34: Differentiability of real valued function, Mean Value Theorem
  • part 33: Mean Value Theorem (Contd.)
  • session 35: Mean Value Theorem (Contd.)
  • part 34: Application of MVT, Darboux Theorem, L Hospital Rule
  • session 36: Application of MVT , Darboux Theorem, L Hospital Rule
  • part 35: L\' Hospital Rule and Taylor\'s Theorem
  • session 37: L'Hospital Rule and Taylor's Theorem
  • part 36: Tutorial - III
  • session 38: Tutorial - III
  • part 37: Riemann/Riemann Stieltjes Integral
  • session 39: Riemann/Riemann Stieltjes Integral
  • part 38: Existence of Reimann Stieltjes Integral
  • session 40: Existence of Reimann Stieltjes Integral
  • part 39: Properties of Reimann Stieltjes Integral
  • session 41: Properties of Reimann Stieltjes Integral
  • session 42: Properties of Reimann Stieltjes Integral (Contd.)
  • part 40: Definite and Indefinite Integral
  • session 43: Definite and Indefinite Integral
  • part 41: Fundamental Theorems of Integral Calculus
  • session 44: Fundamental Theorems of Integral Calculus
  • part 42: Improper Integrals
  • session 45: Improper Integrals
  • part 43: Convergence Test for Improper Integrals
  • session 46: Convergence Test for Improper Integrals

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