Day 30 - Calculus of Variations

Announcements

  • Midterm 2 is posted
  • Look for feedback from DC on projects

Seminars this Week

MONDAY, March 31, 2025

  • Condensed Matter Seminar 4:10 pm,1400 BPS, Justin Wilson, Louisiana State University, Title: Measurement and Feedback Driven Adaptive Dynamics in the Classical and Quantum Kicked Top

TUESDAY, April 1, 2025

  • Theory Seminar, 11:00am., FRIB 1200, Kazuyuki Ogata, Kyushu University, Title: “Knock It Out of the Nucleus -Structure of Nuclei Revealed by Knockout Reactions”
  • High Energy Physics Seminar, 1:00 pm, 1400 BPS, Manel Errando, Washington University in St. Louis, Title: Extracting Meson Distribution Amplitudes from Nonlocal Euclidean Correlations at Next-to-Next-to-Leading Order

Seminars this Week

WEDNESDAY, April 2, 2025

  • Astronomy Seminar, 1:30 pm, 1400 BPS, Andy Tzandikas, Univ. of Washington, Title: Searching for the Rarest Stellar Occultations

  • PER Seminar, 3:00 pm., BPS 1400, Abigail Daane, Professor of Physics, South Seattle College, Title: The obstacles, stumbles, and growth in examining the “decolonization” of physics education

THURSDAY, April 3, 2025

  • Colloquium, 3:30 pm, 1415 BPS, Alex Sushkov, Boston University, Title: Nuclear magnetic resonance at the quantum sensitivity limit

Clicker Question 30-1

The generic segment, , of a curve in 2D Cartesian coordinates is given by

The integral of from to gives the length of the curve, . What is the correct expression for ?

  5. More than one of the above

Clicker Question 30-2

I can explain why:

where , the true path plus an error term.

  1. Yes, I can explain why
  2. I think I can explain why
  3. I'm having trouble seeing why
  4. I don't think I can explain why

Clicker Question 30-3

For the function , where is the true path, is a small error term, and is a small parameter, what is the derivative of with respect to ?

Clicker Question 30-4

For the function , what is the derivative of with respect to ?

Clicker Question 30-5

The "surface term" that we computed for is:

I can explain why this surface term is equal to zero:

  1. Yes, I can explain why
  2. I think I can explain why
  3. I'm having trouble seeing why
  4. I don't think I can explain why
  5. I don't know what a surface term is

Clicker Question 30-6

We completed this derivation with the following mathematical statement:

where is an arbitrary function. What does this imply about the term in square brackets?

  1. The term in square brackets must be a pure function of .
  2. The term in square brackets must be a pure function of .
  3. The term in square brackets must be a pure function of .
  4. The term in square brackets must be zero.
  5. The term in square brackets must be a non-zero constant.