Rohan Ghuge's Math 508 Notes  Fall 2017

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


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