Rohan Ghuge's Math 508 Notes Fall 2017
- Lecture 3, September 5, 2017 -- The natural numbers and countability
- Lecture 4, September 7, 2017 -- Axioms for the real numbers, the least upper bound property
- Lecture 5, September 12,
2017 -- The rationals in the reals
- Lecture
6, September 14, 2017 -- nth roots
- Lecture
7, September 19, 2017 -- irrational numbers
- Lecture
8, September 21, 2017 -- limits and subsequences
- Lecture 9, September 26, 2017 -- limsups, liminfs and the Bolzano-Weierstrass theorem
- Lecture 10, September 28,
2017 -- Cauchy sequences and the construction of the real numbers (see
also these additional notes).
- Lecture 11, October 3,
2017 -- Summing infinite series.
- Lecture 12, October 10,
2017 --Conditional convergence, partial sum formula.
- Lecture 13, October 12,
2017 --Open and closed sets.
- Lecture 14, October 17, 2017 --Limit points and the Cantor set
- Lecture 15, October 24, 2017 --Continuous functions
- Lecture 16, October 26, 2017 --The IVT and comtinuous functions on compact sets (thanks to Luv Iyer)
- Lecture 17, October 31, 2017 --Monotone functions. The derivative.
- Lecture 18, November 2, 2017 --The Mean Value Theorem and the Inverse Function Theorem
- Lecture 19, November 7, 2017 -- Inverse FunctionTheorem and Higher Order Derivatives
- Lecture 20, November 9, 2017 -- Taylor's Theorem and Remainder Formulae
- Lecture 21, November 14, 2017 -- Integration of continuous functions and the F.T.C. (thanks to Neda Saleem)
- Lecture 22, November 16, 2017 -- Introduction to the Riemann Integration
- Lecture 25, November 30, 2017 -- Convergence of Sequences of Functions
- Lecture 26, December 5, 2017 -- Convolution, Approximate Identities
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