Day 04 - Mathematical Preliminaries

Day 04 - Mathematical Preliminaries#

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Announcements#

  • Homework 1 is due this Friday

  • Homework 2 is posted now

  • Help sessions start this week

    • DC today at 4pm; Friday at 3pm (1248 BPS)

  • Elisha (ULA) will join us Friday; additional help hours soon

Seminars this week (Tuesday and Wednesday)#

TUESDAY, January 21, 2025

  • High Energy Physics Theory Seminar

    • 11:00am, FRIB 1200 lab; Speaker: Alexei Bazavov, MSU-CMSE/PA

    • Title: Lattice QCD: From classical computation to quantum simulation

WEDNESDAY, January 22, 2025

  • Astronomy Seminar

    • 1:30 pm, 1400 BPS; Speaker: Allyson Bieryla, CfA | Harvard & Smithsonian

    • Title: Exoplanets and Solar Eclipses for Research and Community Engagement

Seminars this week (Wednesday, cont.)#

  • PER Seminar

    • 3:00 pm., BPS 1400; Speaker: Justin Gambrell, Assistant Professor, Department of Computational Mathematics, Science, and Engineering, Michigan State University - MSU PA ALUMNUS

    • Title: Computational Thinking Assessment for Introductory Physics: Design, Implementation, and Future Directions

  • FRIB Nuclear Science Seminar

    • 3:30pm., FRIB 1300 Auditorium; Speaker: Calem Hoffman of Argonne National Laboratory

    • Title: The Influence of Near-Threshold States on Nuclear Observables

Goals for this week#

Be able to answer the following questions.#

  • What are the essential physics models for single particles?

  • How do we setup problems in classical mechanics?

  • What mathematics do we need to get started?

  • How do we solve the equations of motion?

AI Policy Update#

Acceptable use cases proposed by y’all:#

  • All uses are OK

  • Brainstorming, getting ideas, finding information

  • Asking for help, clarifying concepts, elaborating on ideas

  • Outlining, structuring, and editing writing

  • Fixing errors, debugging code, checking solutions

AI Policy Update#

Unacceptable use cases proposed by y’all:#

  • No use is OK

  • Asking directly for answers and solutions

  • Using AI to complete the entire assignment

  • Using AI to write papers or reports

  • Turning in work that is not your own

AI Policy Update#

Ways of documenting AI use proposed by y’all:#

  • Summarizing the use of AI and how it helped

  • Documenting the use of AI in the assignment

  • Providing prompts, responses, and outcomes

  • Detailed documentation including screenshots and date/time of use

AI Policy Update#

Ways of collectively enforcing our policy:#

  • It is not possible.

  • Honor system; hold old your friends accountable

  • Collective policy helps us all; encourage honesty and integrity

  • Report violations to Danny

  • Fail the assignment if you violate the policy

  • Fail the course if you violate the policy

Ranked Choice Vote on our AI Policy#

  • Proposal 1: We adopt a policy that does not allow AI use at all.

    • Violation results in a failing grade on assignment.

    • Repeated violations result in failing the course.

  • Proposal 2: We adopt a policy that allows AI use for brainstorming, help, and editing.

    • AI cannot be used for direct answers or completion of assignments.

    • We expect documentation of AI use, but it can be informal.

    • Violations are discussed with Danny; the first violation requires a redo of the assignment, and repeated violations result in a failing grade.

Ranked Choice Vote on our AI Policy#

  • Proposal 3: We adopt a policy that allows AI for use in nearly any way.

    • We require detailed documentation of use; this means screenshots, prompts, responses, and outcomes.

    • Violations are discussed with Danny; the first violation requires a redo of the assignment, and repeated violations result in a failing grade.

  • Proposal 4: We adopt a policy that allows AI for use in any way with no documentation required.

    • Violations of the policy are limited to sharing answers or solutions with others.

Vote here: https://forms.office.com/r/PwfNQYJ2Rm

Reminders from Day 03#

  • In a Newtonian world, we start from a vector description of motion

  • Differential equations are mathematical models that describe the motion of particles

  • We can use different methods to solve these differential equations

Clicker Question 4-1#

Consider the generic position vector \(\vec{R}\) for a particle in 2D space. Which of the following describes the direction of the vector in plane polar coordinates (\(r\), \(\phi\))?

  1. \(\hat{R}\)

  2. \(\hat{r}\)

  3. \(\hat{\phi}\)

  4. Some combination of \(\hat{r}\) and \(\hat{\phi}\)

  5. I’m not sure.

Group Discussion 4-1#

We found the following expression for the equation of motion of a falling ball subject to air resistance:

\[m \ddot{y} = +mg - b \dot{y} - c \dot{y}^2\]

What are the units of the constants \(b\) and \(c\)?