Math 3413

Physical Mathematics I

Fall 2013

A praying mantis: this particular one is a European mantis (Mantis Religiosa), common in North America. European mantises were introduced to America as a means of controlling garden pests, and continue to be widely used for this purpose. They are also popular as pets. I saw one of these sitting on a flower in our front yard on an August afternoon a couple of days before class started this semester. It walked slowly away, stepping on a goldenrod crab spider as it went, without making any attempt to eat it.

Instructor: John Albert
Office: PHSC 1004
Office hours: Mondays and Fridays 12:30 to 1:30, Thursdays 9:30 to 10:30 (or by appointment)
Phone: 325-3782
E-mail: jalbert@ou.edu

Announcements

Assignments

Assignment 1 (due Fri, Aug 30)

  • 1.1 #23, 24 (For these, just verify the solution and find the correct value of C. No need to sketch the solutions.)
  • 1.1 #36
  • 1.2 #8, 9
  • 1.4 #1, 5, 12, 27
  • 1.5 #14, 15, 19, 20

    Assignment 2 (due Wed, Sept 11)

  • 1.6 #4, 8, 9, 20, 36, 38, 39, 64

    Assignment 3 (due Mon, Sept 16)

  • 1.6 #45, 46
  • 3.1 #5, 17, 35, 39, 41

    Assignment 4 (due Mon, Sept 30)

  • 3.3 #14, 16, 23
  • 3.5 #9, 33, 34

    Assignment 5 (due Mon, Oct 7)

  • 7.1 #5, 8, 19, 28

    Assignment 6 (due Wed, Oct 16)

  • 7.1 #38
  • 7.2 #2, 6, 9, 17
  • 7.3 #3, 5, 8, 14

    Assignment 7 (due Mon, Oct 21)

  • 7.4 #16
  • The problem from this sheet.

    Assignment 8 (due Mon, Nov 4)

  • 7.4 #2, 22, 23, 29
  • 7.5 #4, 6, 25

    Assignment 9 (due Mon, Nov 11)

  • 7.6 #5, 14
  • 8.1 #4
  • 9.1 #2, 9, 10

    Assignment 10 (due Fri, Nov 15)

  • 9.1 #13, 15, 27
  • 9.2 #12, 17

    Assignment 11 (due Wed, Dec 4)

  • 9.5 #3, 9, 13

    Links

  • Nov. 13: For a derivation of the equations of motion of a coupled pendulum, and a Java applet showing the behavior of the solutions, see this discussion by Annalisa Fusolino at Radboud Universiteit Nijmegen.
  • Oct. 18: When you take the Laplace transform of a function, you are viewing it in a parallel universe, where things are in a way the opposite of what they are here. When we take the derivative of a function in this universe, its counterpart in the parallel universe gets multiplied by the independent variable, and vice versa. When we multiply a function by an exponential in this universe, its counterpart in the parallel universe gets shifted to the left or right, and vice versa. The closest non-mathematical analogue that I can think of at the moment is the Bizarro world, where everything operates the reverse of the way it does here: when you get good grades, your parents punish you; when you read a mystery novel, the beginning is the best part; curing dizzy spells is problematic; and flying dishes are a good sign.
  • Oct. 4: Here is an explanation by Prof. Arthur Mattuck of MIT on "Where the Laplace transform comes from". It's in two parts: part two is here.
  • Sept. 13: The Wikipedia page on "Pendulum (mathematics)" contains a derivation of the ODE which describes a pendulum and of the formula T = 2 π √(l/g) for the time it takes to complete one oscillation. We verified this in class with a yo-yo. For a less technical but still interesting account, see also the article "Pendulum".
  • Sept. 11: This is a video of a demonstration showing, with a can of spray paint and a rolling sheet of paper, that an object at the end of a spring really does oscillate sinusoidally.
  • Sept. 9: Here is a graph of the data from the hot water experiment we conducted in class last week. From this data, what would you say the value of the thermal conductivity constant k is for this particular cup of water?
  • Aug. 23: the Wikipedia article I mentioned in class today concerning how Newton's Law of Cooling is actually used in engineering is titled "Lumped Capacitance Model".
  • Aug. 21: a discussion of how to reconcile the predictions of Torricelli's law with reality is in this article: Pin-Hole Water Flow from Cylindrical Bottles, by P. Murilo Castro de Oliveira et al.