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Calculus of One Real Variable - Introduction - Prof.Joydeep Dutta
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Calculus of One Real Variable
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- 1 Calculus of One Real Variable - Introduction - Prof.Joydeep Dutta
- 2 Introduction to Numbers
- 3 Countability and Uncountability
- 4 Examples of Irrational numbers
- 5 Functions
- 6 Limits of Functions-I
- 7 Limit of Functions- II
- 8 Continuous Functions
- 9 Intermediate Value Theorem
- 10 Maximum Value Theorem
- 11 Supremum and Infimum
- 12 Rules of Differentiation
- 13 Monotonic Functions and Inverse Functions
- 14 Maxima and Minima
- 15 Rolle's Theorem and Lagrange Mean Value Theorem (MVT)
- 16 Derivative of a Function
- 17 Newton's Method for solving Equations
- 18 Optimization Problems
- 19 Integration-III : Newton and Leibnitz Style
- 20 Integration-I : In the style of Newton and Leibnitz
- 21 Integration-II : In the spirit of Newton and Leibnitz
- 22 Integration theory of Riemann-I
- 23 Integration theory of Riemann-II
- 24 Integration Rule
- 25 Fundamental Theorem of Calculus (in Riemann style)
- 26 The Kurzweil-Henstock Integral (K-H Integral)
- 27 Improper Integral-II
- 28 Improper Integral-I
- 29 Calculating Indefinite Integrals
- 30 Application of Definite Integral-I
- 31 Application of definite Integral-II
- 32 Application of definite Integral-III
- 33 Application of definite Integral-III (Contd.)
- 34 Numerical Integration-I
- 35 Numerical Integration-II
- 36 Sequences
- 37 Sequence (continued)
- 38 Infinite Series
- 39 Taylors Theorem, other issues and end of the course-I
- 40 infinite series (continued)
- 41 Taylors Theorem, other issues and end of the course-II
