Faculty: Krishna Chowdary, Ph.D., Rachel Hastings, Ph.D., and Neil Switz, Ph.D.

The fall, winter, and spring quarters of Models of Motion integrated the study of calculus, physics, and the culture and history of science. This all-level program covered introductory topics in these subjects through lectures, workshops, seminars, and labs. Students used mathematical and scientific reasoning to improve their problem-solving abilities in calculus and physics. Students studied the cultural context and history of physics and math through reading, writing, and discussion in seminar. Students had the opportunity to develop hands-on skills with analog circuits along with related theory in spring and also to design and carry out independent projects in winter and spring. Student evaluations were based on in-class quizzes and exams, written and on-line homework, lab notebooks, papers, presentations, a portfolio of collected work, and on engagement in lectures, problem-solving workshops, laboratories, and seminars.

A unifying theme in the program involved attention to the relationship between physics and math, and the trajectory of thought that led to modern views of these subjects. Other program objectives for students included: improving ability to articulate and assume responsibility for their own work; improving oral and written communication skills; learning single and multivariable differential and integral calculus and some of its applications, particularly to physics; utilizing mathematical models that describe and explain motion in the natural world; using the main ideas of classical mechanics, special relativity, electricity & magnetism, thermodynamics, and waves & optics to solve fundamental and applied problems; and developing hands-on and practical skills through analog circuits.

**Calculus I, II with Laboratory, Calculus III**: We covered standard first year topics in single and multivariable calculus. We worked through chapters 0-14 in Strang’s *Calculus* (2^{nd} ed.) including the concepts of limit and derivative in connection with motion; the definitions of derivative and integral; techniques of differentiation and integration; calculus of trigonometric, exponential, and logarithmic functions; applications of differentiation and integration; polar coordinates and complex numbers; infinite series (particularly power series); vectors, planes, and motion along a curve; partial derivatives, and multiple integrals. In fall and winter, students participated in weekly computer labs to support their conceptual understanding, making considerable use of Desmos and GeoGebra.

**University Physics I, II, III with Laboratory**: We covered standard first year topics in calculus-based physics, with fall quarter focused on classical mechanics, winter on special relativity and electricity & magnetism, and spring on thermodynamics and waves & optics. Through reading, lectures, and workshops, students focused on developing conceptual understanding and problem-solving skills. These were reinforced by frequent hands-on activities and weekly lab exercises that involved data collection and analysis, frequently using Vernier data acquisition tools and LoggerPro software. Students worked through chapters 1-13, 15-17, 19-25, 27-30, and 33-34 in Mazur’s *Principles and Practice of Physics* (1^{st} ed.) along with customized readings on relativity, and submitted homework via the online system MasteringPhysics.

**Introductory Analog Circuits Lab**: Spring quarter included a weekly analog circuits lab with associated lecture. Texts were Horowitz and Hill’s *The Art of Electronics* (2^{nd} ed.), Chapters 1 and 4 (for Ch. 4, we covered 4.01-4.09 on basic op-amps circuits and parts of 4.11 on op-amp limitations), and labs from the affiliated lab manual by Horowitz and Hayes. Material covered included Ohm’s and Kirchhoff’s laws, Thevenin circuit equivalents, voltage dividers, complex impedance and gain for RC and LC filters, and basic op-amp circuits including inverting and non-inverting amplifiers. Labs included building and measuring these circuits, as well as constructing a basic AM radio with op-amp speaker driver.

**Seminar on the Cultural History of Physics**: Students participated in two discussion sessions per week based on Chapters 1-5 of Simonyi’s *A Cultural History of Physics*. The first session was a small group pre-seminar discussion together with peer review of writing assignments. The second session consisted of a larger group seminar discussion of the text and student-generated questions about the reading. Students wrote four 2-page papers in which they expanded on or filled in background for a particular passage or concept from the text. The essays were posted in our on-line forum, and students responded to peers’ papers both electronically and in in-class peer review groups. The papers were revised based on this feedback before being submitted to faculty.

**Seminar on Math in Society**: Our winter weekly seminar discussions were focused on Ascher’s *Mathematics Elsewhere*, which covered case studies of complex mathematics embedded in a wide variety of cultural contexts. Each student prepared to lead a discussion on one of the chapters in the book. For our winter writing project, students read a series of articles for a general audience by mathematician Steve Strogatz, and then worked in pairs to write a 4-5 page paper that explained a key concept from math or physics with accessibility to a broad audience in mind. Students submitted a prospectus, outline, and rough and final drafts of these papers, participated in peer review, and then gave a 15-minute final presentation of their project.

**Independent Project**: In spring, students working alone or in pairs designed and carried out independent projects based on their own interests. Students submitted a project prospectus and plan, submitted weekly updates, presented bi-weekly, gave final presentations to the entire class and at the 12^{th} annual Evergreen Science Carnival, and wrote a final paper that summarized their learning in the project.

In winter, students could choose a reduced credit option for seminar. In spring, students could choose to participate in any of the four program components: Calculus III, University Physics III with Lab, Introductory Analog Circuits Lab, or the Independent Project.

(Standard) Suggested Course Equivalencies

- 6 – Calculus I with Lab
- 6 – Calculus II with Lab
- 4 – Calculus III
- 6 – University Physics I with Lab
- 6 – University Physics II with Lab
- 5 – University Physics III with Lab
- 4 – Introductory Analog Circuits Lab
- 4 – Seminar on Cultural History of Physics
- 4 – Seminar on Math in Society
- 3 – Independent Project:

Solutions for Circuits Final are posted here.

Your class materials, with the exams, will be returned to you by Krishna during the eval conferences.

Best-

Neil

]]>– Week 7 solutions are here. Apologies.

– Do not grade Week 6, #6 – I made a mistake – that one was optional anyway. For finals study, do look over finding the magnitude of the response for the LC circuit in Problem 4 from the Midterm.

– The solution for Week 6, #2, the last sentence on p. 3 is incorrect; R1 = 10k, R2 = 1k. The Gain G is actually correct, as is everything else – I just reversed the resistors from the problem statement when writing them down (and, apparently, since I knew the result, still got the correct G…

Best-

Neil

]]>