Final Program Description and Suggested Course Equivalencies

Faculty: Krishna Chowdary and Vauhn Foster-Grahler

Physical Systems & Applied Mathematics was a full year interdisciplinary study of upper-division physics (classical mechanics, electrodynamics, quantum mechanics, and advanced lab) closely integrated with related applied mathematics (differential equations, linear algebra, and multivariable and vector calculus). Students could choose partial credit options or to switch out some element of the program for independent study in computer programming. Evaluation of student achievement was based on: quizzes, exams, and revisions; homework assignments; written and oral presentations; writing assignments; and workshop participation.

In addition to content coverage, program learning goals included: Improving ability to articulate and assume responsibility for personal work; Strengthening collaborative skills and the ability to respond in useful ways to the work of colleagues; Improving skills in clear communication of mathematical and scientific ideas, both orally and in writing; Improving reading of technical texts to develop conceptual understanding and procedural skills; Developing and utilizing increasingly sophisticated mathematical models that describe and explain physical systems; Using multiple representations to gain a firm understanding of the concepts and procedures of differential equations, linear algebra, and multivariable & vector calculus; Developing deep conceptual understanding and sophisticated problem-solving abilities related to classical mechanics, electricity & magnetism, and quantum mechanics; Using a computer based algebra system to visualize and solve complex problems in math and physics; Developing insight into the fundamental interplay between the experimental, computational, and theoretical aspects of physics through exposure to a variety of advanced laboratory experiments.

Electrodynamics: All 12 chapters of Introduction to Electrodynamics, 4th Edition (Griffiths) were covered in winter and spring, building heavily on foundational work in multivariable and vector calculus in fall. Topics included: vector analysis; electrostatics and magnetostatics in vacuum and matter (including forces, fields, and potentials); special techniques (method of images, Laplace’s equation, separation of variables); Maxwell’s equations; energy and momentum in fields; electromagnetic waves; time-delayed potentials and fields; radiation; and special relativity. Students completed 18 homework assignments totaling 180 textbook problems; for each assignment, students submitted one of their problem towards a collaborative solution set. In winter, students took 8 quizzes, a midterm exam, and a final exam. In spring, students took 5 exams.

Classical Mechanics: Chapters 1 – 9, 11, and 13 of Classical Mechanics (Taylor) were covered in fall, closely integrated with differential equations and multivariable and vector calculus. Students learned to use Mathematica for a wide variety of purposes, including visualization and to solve differential equations and integrals (analytically and numerically). Topics included: Newtonian mechanics in different coordinate systems; projectile and charged particle motion; momentum and angular momentum; energy; oscillations (including Fourier series); calculus of variations; Lagrangian mechanics (including the method of multipliers and constraints); central-force problems; non-inertial reference frames; coupled oscillations and normal modes; and Hamiltonian mechanics. Students completed 16 homework assignments totaling 94 problems. In addition, students produced high-quality solutions (either typeset or presented as narrated screencasts or videos) for 4 “three-star” level problems (Taylor’s challenge level problems) which were submitted for peer review and then revised for faculty. Students took 4 quizzes, a midterm exam, and a final exam.

Quantum Mechanics: Chapters 1 – 7 and 9 – 11 of A Modern Approach to Quantum Mechanics, 2nd Edition (Townsend) were covered in winter and spring; in winter, this was integrated closely with linear algebra. Using a spins-first approach, topics included: Stern-Gerlach experiments; Dirac notation; rotation of basis states and matrix mechanics; operators and expectation values; angular momentum; the Schrödinger equation and time evolution; systems of spin-1/2 particles, the EPR paradox and Bell’s inequalities; wave mechanics in one dimension for barriers, finite and infinite square wells, steps, and Gaussian wave packets; the one-dimensional harmonic oscillator with raising and lowering operators and in the position basis; orbital angular momentum and the rigid rotator; bound states for central potentials including the hydrogen atom and three-dimensional wells and harmonic oscillators; and time-independent perturbation theory. Students completed 15 homework assignments totaling 132 problems; for each assignment, students submitted one of their problem towards a collaborative solution set. In winter, students took 8 quizzes, a midterm exam, and a final exam. In spring, students took 5 exams.

Advanced Lab Projects: In winter, a seminar on experimental physics surveyed a variety of advanced physics lab experiments and apparatus that covered some of the breadth of physics. Students read apparatus manuals and found relevant primary source literature, historical accounts, textbook excerpts, and other technical material, which they read, annotated, and prepared for a weekly seminar conversation. Topics/apparatus included: Franck-Hertz experiment; gyroscopes; magnetic domains; mechanical chaos; microwave interference; physical (Fourier) optics; speed of light; superconductivity and magnetic susceptibility; and TeachSpin’s Faraday Rotation, Fourier Methods, Pulsed NMR, and Quantum Analogs. In spring, students chose to focus on one or two pieces of apparatus introduced in winter in order to experience the fundamental interplay between the experiment, computation, and theory. Students developed personalized learning goals which they were held accountable to and were required to include some technical writing. Students gave weekly presentations, culminating in a final presentation to the entire class and submitted their final technical writing for faculty review.

Differential Equations, Multivariable and Vector Calculus: Multivariable and Vector Calculus (Calculus: Multivariable, 6th Edition (Hughes-Hallett, et.al.), supplemented by Div, Grad, Curl, and All That, 4th ed (Schey)) was a rigorous study of the calculus of functions of several variables. Topics included Gradient Fields, Stokes’ Theorem, Green’s Theorem, Divergence, Curl, Line Integrals, calculus with Polar, Cylindrical and Spherical Coordinates, Directional Derivatives, operations with the del operator, along with the support skills of partial differentiation and multiple integration. 

Differential Equations (Elementary Differential Equations and Boundary Value Problems, 10th Edition (Boyce and DiPrima)) was a rigorous study of initial value problems and boundary value problems. Topics included:  First, second, and higher order linear differential equations, boundary value problems (heat conduction in a rod, wave equation), and Fourier Series. Most of the time was spent looking at homogeneous equations with constant coefficients. Students were asked to solve problems in a variety of ways and to identify patterns in solutions including complex and repeated roots to second order, linear, homogeneous equations. Students found and interpreted fundamental sets of solutions and used the Wronskian to determine linear independence. 

Students investigated problems symbolically, graphically, and, verbally. Mathematica was used to support visualization of functions in space, direction fields, and integral curves.

Linear Algebra: Chapters 1 – 6 of Linear Algebra and its Applications, 5th Edition (Lay, et.al.) were covered in winter, integrated very closely with quantum mechanics. Emphasis was on concepts, procedures, and applications of systems and solutions for linear equations, and topics included: linear transformations; matrix algebra; the Invertible Matrix Theorem; determinants; vector spaces, including null space and column space; change of basis; eigenvalues and eigenvectors; and orthogonality. Students completed 6 homework assignments totaling 100 problems; for each assignment, students submitted several of their problems towards a collaborative solution set. Students took 8 quizzes, a midterm exam, and a final exam.

Suggested Course Equivalencies (*upper-division science credits)

  • *12 – Electrodynamics
  • *8 – Classical Mechanics
  • *8 – Quantum Mechanics
  • *8 – Advanced Lab Projects
  • *4 – Differential Equations
  • *4 – Linear Algebra
  • *4 – Multivariable and Vector Calculus

Final! Conference sign-up sheet available

  • Conferences: Tue. June 13 and Wed. Jun. 14, in the Cave.
  • You can find a sign-up sheet for final program conferences here.
    • Note that you will need to be logged in to this site to access the sign-up sheet. If not logged-in, you can do so via this link.
  • Some reminders:
    • Sat. June 10, 9am: Quixam! Revisions due to box in Physics Cave.
    • Sat. June 10, noon: Final ALP papers due by email.
    • Mon. June 12, noon: Non-graduating-student Self-Evaluations posted and shared with faculty via your my.evergreen.edu by noon. (Graduating students in ALP should also submit Self-Evaluations)
    • Mon. June 12, noon: Final drafts of senior Academic Statements submitted to faculty, either by email or Google docs, by noon. We’ll go over senior Academic Statements in Conferences so that changes can be made in time for the Fri. June 16 due date.

Final Self-Evaluations

  • Non-graduating-student Self-Evaluations are due Mon. June 12 by noon via posting and sharing with faculty at your my.evergreen.edu. (Graduating students in ALP should also submit Self-Evaluations)
  • Your Self-Evaluations should address achievements in content learning and process skills, as well as areas for improvement, tied to your Individual Learning Goals, Program Learning Goals, and the Expectations of an Evergreen Graduate.
  • Program Learning Goals and Expectations for an Evergreen Graduate can be found here.

Quixam! 5E

  1. Quixam! 5E will be administered Tue. June 6 from 9am – 11am in the Cave. Students may opt to take it as a take-home version instead.
  2. If you opt for the take-home version, you must email Krishna before downloading the exam.
  3. In opting for the take-home version, you certify that that the only materials used to complete this exam (besides paper and writing implement) were your personally prepared 3 inch x 5 inch notecards for this and earlier quixams and your calculator or equivalent (except where specifically prohibited). You certify that you did not use any other resources (including but not limited to internet or on-line resources). You certify that you used no more than two hours to work on this quixam. You also certify that you did not discuss the questions on this exam with any other person in any way, with the possible exception of your program faculty.
  4. Your email to me opting for the take-home version (see 2. above) should acknowledge your certification of the above.
  5. After emailing me that your are opting for the take-home option and acknowledging your certification of the items in 3. above, you can download the exam here (link became active at 9am Tue. June 6).

Tuesday June 6: Quixam! 5E and afternoon open time

Campus is planned to be open on Tuesday June 6. I’m looking forward to seeing those of you who can come to class while supporting those of you who can’t.

We’ll have Quixam! 5E as scheduled from 9am – 11am in the Cave. Anyone may opt to take it as a take-home exam instead; it will become available at the program website starting at 9am. If you do plan to take it at home, I need no reason but do ask you to let me know by email so that I can know your plan.

If you do take the exam in person, please bring your EM and QM PSNs so I can do a final spot check. If you aren’t on campus on Tuesday, I’ll respond to your email (see previous paragraph) with an alternate plan for a PSN check.
 

A reminder that I will be available on Tuesday from noon – 3:30 for consultation on anything: ALP final presentations or papers, Academic Statement drafts, just to talk, etc.

A reminder that all PSAM students are expected to attend ALP Final Presentations on Wednesday from 9 – 1. I haven’t heard from anyone about legitimate scheduling conflicts (this should be expanded to include not feeling safe to come to campus), so please let me know right away if you won’t be attending all or part of the ALP Final Presentations.

Alternate Plan for Quixam! 4Q & 5Q

We will need to use our alternate plan for Quixam! 4Q & 5Q, since campus is again closed on Monday June 5. Instead of taking the quixam together from 9 – noon in the Cave, it will instead be administered as a take-home version.

At 9am Mon. June 5, the Quixam! will become available at the program web-site for you to download. You have up to three hours to work on the exam. If possible, I strongly encourage you to work on it from 9 – noon so at to closely replicate the original exam parameters. As much as possible in all the important ways, this should be treated as if it were the in-class exam session. I will do my best to provide clarity if you email me questions, but I can’t promise what the turn-around time for the responses will be.

Below is the text of what you will be asked to certify about the quixam:

“By signing below, I certify that the only materials I used to complete this exam (besides paper and writing implement) were my personally prepared 3 inch x 5 inch notecards for this and earlier quixams and my calculator or equivalent (except where specifically prohibited). I certify that I did not use any other resources (including but not limited to internet or on-line resources). I certify that I used no more than three hours to work on this quixam. I also certify that I did not discuss the questions on this exam with any other person in any way, with the possible exception of my program faculty.”

You will submit your Quixam at the very beginning of the very next class meeting we have together.

Week 30 and Conference Week Schedule

Here’s the planned schedule for our final week of class meetings. We’ll play by ear as necessary, so please continue to be flexible.

Please note that all class meetings this week are in the Physics Cave.Reminder: ALL PSAM students are expected to attend Wednesday’s ALP Final Presentations, from 9 – 1. I expect that if you have some legitimate scheduling conflict, you will contact me right away.

Week 30 and Conference Week Schedule:

  • Mon. June 5 (Cave)
    • 9 – 12: Qu¡xam 4Q and 5Q! (covers Ch. 10, Ch. 11). QM PSN check
  • Tue. June 6 (Cave)
    • 9 – 11: Qu¡xam 5E! (covers Ch. 12). EM PSN check.
    • 12 – 3:30 Open Time to help with ALP final presentations, review ALP papers, consult on Senior Academic Statements, etc.
  • Wed. June 7 (Cave)
    • 9 – 1: ALP Final Presentations (all PSAM students expected to attend)
  • Thu. June 8 (Cave)
    • 9 – ?: Breakfast Potluck, Qu¡xam Revision Session, Final Program Wrap and Look Forward, Special Surprise!
  • Sat. June 10:
    • Qu¡xam! revisions due by 9am to labeled box in Physics Cave.
    • ALP final papers due by noon via email.
  • Mon. June 12:
    • Non-graduating-student Self-Evaluations posted and shared with faculty via your my.evergreen.edu by noon.
    • Final drafts of senior Academic Statements submitted to faculty, either by email or Google docs, by noon.
  • Tue. June 13 and Wed. June 14: Final Conferences.
  • Fri. June 16: GRADUATION!

Week 30 room changes

Please note that any class meetings in week 30 will be in the Cave. I’ve released our CAL reservations this week so other programs can use them. So, all our class meetings this final week of the program will be in the Physics Cave.