Syllabus for 2021 AIMS Maxwell

Course name:
The Geometry of Maxwell's Equations
Course number:
AIMS 21.
Instructor:
Corinne Manogue and Tevian Dray
Office hours:
TBA
Course credits:
0
Class meeting times:
3 hours of lecture per week
Prerequisites:
Listed below is the background knowledge you should have for this course. Physics: We do not expect you to know any physics. We will motivate the mathematical techniques using physics examples and terminology, we will teach the necessary physics content as part of the course. For those of you who may have seen some of the physics topics before, there should still be plenty of new material. Mathematics: We expect that you have taken a first course in calculus, covering the basics of single-variable differentiation and integration. (It's OK if you need to refresh your memory.) Previous exposure to multivariable calculus (partial derivative and multiple integrals) would be an advantage, but is not necessary.
Course description:
Electromagnetism is beautifully described using vector calculus, yet most treatments of vector calculus emphasize algebraic manipulation, rather than the geometric reasoning that underpins Maxwell's equations. This course attempts to bridge that gap, providing a unified view of both electro- and magneto-statics and the underlying vector calculus.
Learning resources:

Online textbooks (see the course website for links): The Geometry of Mathematical Methods (GMM) The Geometry of Static Fields (GSF) The Geometry of Vector Calculus (GVC)

You may also see suggested reading from the following textbooks: Griffiths: Introduction to Electrodynamics (GEM) Schey: div, grad, curl and all that (Schey) We are checking to see if you have access to these resources.

Learning outcomes:
  • 1) Physics: Calculate electrostatic and magnetostatic fields from both discrete and continuous distributions of sources.
  • 2) Physics: Use Gauss's and Ampère's Laws in integral form to find electrostatic and magnetostatic fields in highly symmetric situations.
  • 3) Physics: Use Maxwell's equation in differential form to find sources from fields.
  • 4) Mathematics: Use the "chop, multiply, add" method to set up and analyze the structure of line, surface, flux, and volume integrals in rectangular, cylindrical, and spherical coordinates that represent sources and fields.
  • 5) Mathematics: Predict the gradient, divergence, and curl of fields from graphical representations.
  • 6) Mathematics: Use simple geometric arguments to prove the big vector calculus theorems (Divergence and Stokes') and then use them to transform the integral form of Maxwell's equations to the differential form.
  • 7) Sensemaking: Coordinate verbal, graphical, geometric, diagrammatic, and algebraic representations of sources and fields.
  • 8) Sensemaking: Use physical situations with simple geometries as idealized building blocks for more complicated physical situations.
  • 9) Sensemaking: Use the symmetries of physical situations to check the validity of symbolic and graphical representations of those situations.
  • 10) Sensemaking: Without panicking, break up a complicated algebraic problem into separate pieces related to the physical situation.
Course content:
  • 0) (nothng yet)
See also course schedule.
Evaluation of student performance:

The best way to learn the material of this course is to attend class, participate in the class activities, and do the exercises.

Your course mark will be determined by your marks on three required assignments which will be turned in on Gradescope (instructions will be shared in class).

In preparation for these assignments, we will provide daily practice exercises with solutions. You will NOT turn in these exercises.

Additional Guidance

  • You are strongly encouraged to work on assignments, including coding and plotting, collaboratively. Science is inherently a social and collaborative effort. So that we can best support your learning, you are required to turn in assignments that you have written up independently.
  • Appropriate resources on assignments include: working with each other, the course tutor(s0, or the course instructors; textbooks; other online materials, etc. Do not use homework solutions from Oregon State and do not share your completed homework solutions with other students (in other words, collaborate through discussion, not copying).
  • Document your resources appropriately. If you find a homework problem worked out somewhere (other than from Oregon State), you may certainly use that resource, just make sure you reference it properly. If someone else helps you solve a problem, reference that too. An appropriate reference might be "Corinne Manogue (private communication, 1/15/21)" or "I worked with Corinne Manogue on this problem". Representing someone else's work as your own without reference -- also known as plagiarism -- is unethical, but collaboration and exchange of ideas is healthy. You can avoid having collaborative efforts take on the look of plagiarism by acknowledging sources as described above and by writing up your work independently.
  • The problems in this course will likely take longer than problems you've seen in previous courses. If you find that you have worked on a problem for 1/2 hour WITHOUT MAKING FORWARD PROGRESS, it's time to pause, take a break, sleep, and seek help from classmates or the instructional team.

PLEASE IGNORE THE ITEMS BELOW, WHICH ARE THE OSU DEFAULTS

Academic calendar:
All students are subject to the registration and refund deadlines as stated in the Academic Calendar: https://registrar.oregonstate.edu/osu-academic-calendar
Statement regarding students with disabilities:
Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at http://ds.oregonstate.edu. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.
Expectations of student conduct:
Students are expected to comply with the University code of conduct, available at https://beav.es/codeofconduct.
Student bill of rights

OSU has twelve established student rights. They include due process in all university disciplinary processes, an equal opportunity to learn, and grading in accordance with the course syllabus: https://asosu.oregonstate.edu/advocacy/rights

Reach out for success:
University students encounter setbacks from time to time. If you encounter difficulties and need assistance, it’s important to reach out. Consider discussing the situation with an instructor or academic advisor. Learn about resources that assist with wellness and academic success at oregonstate.edu/ReachOut. If you are in immediate crisis, please contact the Crisis Text Line by texting OREGON to 741-741 or call the National Suicide Prevention Lifeline at 1-800-273-TALK (8255)