Learn · Calculus of One Real Variable
Lecture 24 of 40Week 5
Fundamental Theorem of Calculus (in Riemann style)
Prof. Joydeep Dutta · IIT Kanpur
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- Calculus of One Real Variable, IIT Kanpur (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Introduction to Numbers
- Countability and Uncountability
- Examples of Irrational numbers
- Functions
- Limits of Functions-I
- Limit of Functions- II
- Continuous Functions
- Intermediate Value Theorem
- Maximum Value Theorem
- Supremum and Infimum
- Derivative of a Function
- Rules of Differentiation
- Maxima and Minima
- Rolle's Theorem and Lagrange Mean Value Theorem (MVT)
- Monotonic Functions and Inverse Functions
- Newton’s Method for solving Equations
- Optimization Problems
- Integration-I : In the style of Newton and Leibnitz
- Integration-II : In the spirit of Newton and Leibnitz
- Integration-III : Newton and Leibnitz Style
- Integration theory of Riemann-I
- Integration theory of Riemann-II
- Integration Rule
- Fundamental Theorem of Calculus (in Riemann style)
- The Kurzweil-Henstock Integral (K-H Integral)
- Calculating Indefinite Integrals
- Improper Integral-I
- Improper Integral-II
- Application of Definite Integral-I
- Application of definite Integral-II
- Application of definite Integral-III
- Application of definite Integral-III
- Numerical Integration-I
- Numerical Integration-II
- Sequences
- Sequence (continued)
- Infinite Series
- infinite series (continued)
- Taylor's Theorem, other issues and end of the course-I
- Taylor's Theorem, other issues and end of the course-II