Math 441 - Introduction to Analysis I - Fall 2024

Class Information

Instructor: Tuan Pham
Class meetings: M, W, F: 11:00 - 11:50 AM at SCB 209
[Syllabus]   [Class schedule]   [Canvas]   [Textbook]  

Office Hours

Monday, Wednesday, Friday: 12:00 - 1:30 PM at SCB 316, or by appointment

Assignments

  • Homework problems are to be turned in in class.
  • Homework 1.1, 1.2: Problems 1.1.1, 1.1.3, 1.1.4, 1.1.9, 1.2.1, 1.2.9
  • Homework 1.3, 2.1: Problems 1.3.1, 1.3.2, 1.3.3, 1.3.9, 2.1.21, 2.1.22
  • Homework 2.2: Problems 2.2.4, 2.2.5, 2.2.7, 2.2.12, 2.2.13, 2.2.14
  • Homework 2.3, 2.4: Problems 2.3.6, 2.3.7, 2.3.18, 2.4.1, 2.4.4, 2.4.6
  • Homework 2.5, 3.1: Problems 2.5.4, 2.5.11, 2.5.14, 3.1.1 (d) and (e), 3.1.12, 3.1.13
  • Homework 3.2, 3.3: Problems 3.2.3, 3.2.11, 3.2.15, 3.3.10, 3.3.12, 3.3.13
  • Homework 3.4, 3.5: Problems 3.4.3, 3.4.4, 3.4.8, 3.4.12, 3.5.2, 3.5.6
  • Homework 4.1, 4.2: Problems 4.1.5, 4.1.6, 4.1.11, 4.1.16, 4.2.3, 4.2.10
  • Homework 4.3, 5.1: Problems 4.3.2, 4.3.10, 5.1.1, 5.1.2, 5.1.5, 5.1.15
  • Homework 5.2: Problems 5.2.5, 5.2.6, 5.2.10, 5.2.17
  • Homework 5.3, 5.5: Problems 5.3.1, 5.3.7, 5.3.10, 5.3.11, 5.5.8, 5.5.9
  • Homework 6.1: Problems 6.1.2, 6.1.5, 6.1.6, 6.1.10, 6.1.12, 6.1.13
  • See the class schedule above for a schedule of presentations.

    • Lecture notes

  • Lecture 33 (Dec 2): uniform convergence of a sequence of functions
  • Lecture 32 (Nov 27): pointwise convergence of a sequence of functions
  • Lecture 31 (Nov 25): improper integral (cont.)
  • Lecture 30 (Nov 20): derivative of \(\int_{g(x)}^{h(x)}f(t)dt\), improper integral
  • Lecture 29 (Nov 18): Fundamental Theorem of Calculus
  • Lecture 28 (Nov 15): compute \(\int_0^1\sqrt{x}dx\)
  • Lecture 27 (Nov 13): sum of two Riemann integrable functions
  • Lecture 26 (Nov 11): Lebesgue-Vitali theorem (or Riemann-Lebesgue theorem)
  • Lecture 25 (Nov 8): Cauchy's characterization of Riemann integrable functions
  • Lecture 24 (Nov 6): define Riemann integral using Darboux sums
  • Lecture 23 (Nov 4): Cauchy's Mean Value Theorem (algebraic and geometric form)
  • Lecture 22 (Oct 30): Mean Value Theorem, Darboux's theorem
  • Lecture 21 (Oct 28): simple form of L'Hospital rule; Rolle's theorem
  • Lecture 20 (Oct 25): derivatives, product rule; prove quotient rule for extra credit
  • Lecture 19 (Oct 23): Lipschitz continuity; infinite limit; limit at infinity
  • Lecture 18 (Oct 21): continuity and uniform continuity
  • Lecture 17 (Oct 14): Bolzano's Intermediate Value Theorem
  • Lecture 16 (Oct 11): continuous functions are bounded
  • Lecture 15 (Oct 9): continuous and discontinuous functions; Thomae's functions
  • Lecture 14 (Oct 7): another example of showing limits using definition; cluster points
  • Lecture 13 (Oct 4): epsilon-delta definition of limit
  • Lecture 12 (Oct 2): application of Root test and Ratio test; limit of a function
  • Lecture 11 (Sep 30): series, Root test and Ratio test in terms of \(\limsup\)
  • Lecture 10 (Sep 25): Cauchy sequence (cont.)
  • Lecture 9 (Sep 25): Bolzano-Weierstrass theorem, Cauchy sequence
  • Lecture 8 (Sep 23): two equivalent definitions of \(\limsup\) and \(\liminf\)
  • Lecture 7 (Sep 18): convergence of monotone sequence and recursive sequence
  • Lecture 6 (Sep 16): sequence, limit, subsequence
  • Lecture 5 (Sep 13): sup and inf of any set; how to show \(\sup A\le M\ ,\inf A\ge m\) ?
  • Lecture 4 (Sep 11): absolute values, bounded functions
  • Lecture 3 (Sep 9): supremum and infimum
  • Lecture 2 (Sep 6): prove properties of real numbers using axioms
  • Lecture 1 (Sep 4): introduction; define real numbers axiomatically

    • Supplement materials

  • Proof of Riemann-Lebesgue's theorem
  • limsup f(n) where f is periodic

    • Links

    Joseph F. Smith Library, Math Lab
    This page was last modified on Tuesday, Dec 10, 2024.