Capstone: Mathematical Methods
PH 461: Capstones in Physics: Mathematical Methods meets 3 hours per week (MWF for 1 hour) for ten weeks for a total of 3 credits.
Prerequisites, Co-requisites and Enforced Prerequisites
Prereq: PH 424/524, MTH 256
A complete list of required texts and other resources for the the entire year of Paradigms courses can be found on the Paradigms website. For this course, the required text is Boas (B).
This Capstone will cover mathematical methods of physics, including complex algebra and functions, analyticity, special functions, ordinary differential equations including series solutions, and partial differential equations including Sturm-Liouville theory.
Student Learning Outcomes
Evaluation of Student Performance
- 30% required homework, quizzes, and other assignments.
- 30% midterm
- 40% final exam.
- Practice problems provide simple examples for you to check whether or not you understand the material as you go along. They will not be graded. Sometimes solutions will be posted. At a minimum, you should read each practice problem and make sure that you know how to do it. If you can't, ask for help!
- Required problems will be graded. Solutions will be posted online. Assignments turned in after solutions are posted can earn at most 50% of the total points. Very late assignments will earn less. It is a good idea to turn in what you have done by the due date, and, if necessary, the rest later. Please consult the instructor for special circumstances.
- In 400/500 level classes, some of the required problems and probably one problem on the final exam will be marked as "Challenge" problems. 500-level students are required to do these Challenge problems. 400-level students are not necessarily expected to do them. However, those students who hope to get an A are encouraged to do so. While it may be possible for a 400-level student to get an A without doing any Challenge problems, it may be difficult. (In PH 320, they are optional and don't count for anything--just fun.) Grading of the Challenge problems will be quite strict; we won't even look at them unless they seem to be clearly written, coherent, complete, and essentially correct.
Statement of Expectations for Student Conduct
Students will be expected to abide by all university rules regarding student conduct and academic honesty, in particular, see: link to University Rules.
Additional Ground Rules
Science is inherently a social and collaborative effort, each scientist building on the work of others. Nevertheless, each student must ultimately be responsible for his or her own education. Therefore, you will be expected to abide by a number of Ground Rules:
- We strongly encourage students to work with each other, more advanced students, the TA, and the professor, on assignments. However, each student is expected to turn in assignments that have been independently written up. In other words, the final synthesis must be entirely your own. This applies also to, and especially to, computer generated worksheets. If you work with someone on a computer project, do not get locked into writing the solution together. You will end up turning in the sameassignment.
- Homework solutions from previous years are very strictly off limits. You are on your honor not to use them, and not to share your homework solutions with other students. Allow faculty to use their time interacting with you, rather than continually thinking up new assignments. Besides, if you don't do the work yourself, it will show up very clearly on exams later. Likewise, the solutions are for your use only. You may make one copy and keep it in your personal files.
- Sources must be appropriately documented. If you find a homework problem worked out somewhere (other than homework solutions from previous years), you may certainly use that resource, just make sure you reference it properly. If someone else helps you solve a problem, reference that too. In a research paper, the appropriate reference would be:
Jane Doe, (private communication).
- Plagiarism – representing someone else’s work as your own – 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 and by writing up your work independently.
- If you find that you have worked on a problem for 1/2 hour without making any forward progress, it would be a good idea to stop and seek help.
Statement Regarding Students with Disabilities
Accommodations are collaborative efforts between students, faculty and Disability Access Services (DAS). Students with accommodations approved through DAS are responsible for contacting the faculty member in charge of the course prior to or during the first week of the term to discuss accommodations. Students who believe they are eligible for accommodations but who have not yet obtained approval through DAS should contact DAS immediately at 737-4098.