104018 Spring 2017

Instructor: Prof. Rom Pinchasi, Amado 607, room@math.technion.ac.il

Teaching assistant: Zilin Jiang, Amado 604, jiangzilin@technion.ac.il

Office hour for Zilin Jiang in Amado 604: Sunday 3:30PM – 4:30PM.

Recitations:

  • Recitation 1: Binomial theorem, Pascal (Yanghui) triangle, 1-1, onto and bounded functions, graphs of trig functions, trig formulas. March 23, 20117.
  • Recitation 2: Limit of function, trig functions have limits, limits do not compose, topologist’s sine curve, what happens when a function with 0 as its limit is multiplied by a bounded function? March 30, 2017.
  • Recitation 3: Application of sandwich theorem and pizza rule, supremum. April 6, 2017.
  • Recitation 4: Monotone increasing function has limit, convergent sequence is bounded, convergence of sequence is insensitive to finite changes, limit of \(n^{1/n}\) is 1. April 20, 2017.
  • Recitation 5: Harmonic series, pass limit to exponential, \(\lim_{n\to\infty}(1+1/n)^n = e\). April 27, 2017.
  • Recitation 6: \(e\) as limit of a function, application of the intermediate value theorem. May 4, 2017.
  • Recitation 7: Application of Bolzano–Weirstrass theorem, one-to-one continuous function is monotone, derivative can be discontinuous. May 11, 2017.
  • Recitation 8: Application of Heine’s theorem for non-existence of limit, find maximum and minimum by derivative, application of mean value theorem. May 17, 2017.
  • Recitation 9: Application of l’Hôpital’s rule and Taylor’s theorem. May 25, 2017.
  • Recitation 10: Integration by substitution, integration by parts. June 1, 2017.
  • Recitation 11: One more reduction formula, application of fundamental theorem of calculus, integration by substitution and integration by parts for definite integral, Newton–Leibniz formula, Euler substitution. June 5, 2017 and June 8, 2017.
  • Recitation 12: Improper integral and its convergence. June 15, 2017.
17 (this post is made with love)