Syllabus: MTH 324, Winter 2017
Vector Analysis via differential forms
| Instructor: | Jay Gopalakrishnan |
| Times: | Tue, Thu: 14:00-15:50 |
| Venue: | NH364 |
| Office hours: | NH309, Tue 16:00-17:00 |
Learning Outcomes
This elective course builds on student’s knowledge of multivariable calculus and introduces differential forms. Students will be guided to a vantage point where operations on vector fields will be seen as particular cases of operations on form fields. The focus is not on proof writing, but rather on calculational techniques. Applications in mechanics and electromagnetics are discussed.
Prerequisites
The official prerequisites are MTH 254 and MTH 261. Please do not take this course if you struggled with calculus, or if you have no patience for abstraction.
Topical outline
| Course notations. Sets and Functions. Determinants. |
| Abstract vector spaces. Dual basis. Double dual. |
| Exterior k-forms. |
| Permutations. Riffle shuffle. Counting forms. |
| Wedge product. A basis for k-forms. |
| Vector fields & Form fields. |
| Covariance & Contravariance. Einstein summation convention. |
| Derivations & Differentials. Curvilinear coordinate changes. |
| Kinematics of continua. Solids & Fluids. |
| Lagrangian & Eulerian descriptions. |
| Coriolis acceleration. Geostrophic manifestations. |
| Exterior derivative of form fields. |
| The Work form. The Flux form. The Mass form. |
| The Faraday form. The Maxwell form. |
| Electromagnetic applications. |
Learning methods
Lectures will be followed by problem solving sessions. Students are expected to present solutions to homework problems in the problem solving sessions.
Textbook: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by John Hubbard and Barbara Burke Hubbard, 5th Edition, September 2015.
Note that the learning material will not come from a single source. The textbook is to be used as a guide and reference, but not as a single source of all the discussed concepts. Further references will be given during the lectures. Therefore, in this course, it is particularly important to follow the class activities closely. Students missing classes will not be able to catch up using the textbook alone.
Evaluation of learning
- 20% of the grades are determined by class participation in the problem solving sessions. Students who never step up to solve a problem receive zero scores for this component. This participation grade is assigned by the instructor.
- 80% of the grades are determined by 4 one-hour quizzes held in class. Graduate Teaching Assistant Benjamin Parker will serve as grader for these quizzes and all questions on quiz grades should be first addressed to him at <bqp2@pdx.edu>. There is no make-up for missed quizzes. However, the lowest scoring quiz will be dropped.
Fine print
| Title IX Reporting Obligations: Every instructor at PSU has the responsibility to help create a safe learning environment for students and for the campus as a whole. Accordingly, the instructor must report any instances of sexual harassment, sexual violence and/or other forms of prohibited discrimination. If you would rather share information about sexual harassment, sexual violence or discrimination to a confidential employee who does not have this reporting responsibility, please use the online list of those individuals. For more information about Title IX please complete the student module Creating a Safe Campus in D2L. |
| Academic Misconduct: In the list of prohibited student behavior at PSU is plagiarism, buying and selling of course assignments, and obstruction of another student's success. Students are expected to know of and refrain from all proscribed conduct. |
| Disability Accommodations: The Disability Resource Center (DRC) provides reasonable accommodations for students who encounter barriers in the learning environment. If you have, or think you may have, a disability that may affect your work in this class and feel you need accommodations, contact the DRC to schedule an appointment and initiate a conversation about reasonable accommodations. The DRC is located in 116 Smith Memorial Student Union, 503-725-4150, drc@pdx.edu, https://www.pdx.edu/drc. Students who have testing accommodations must begin the test at the same time as the rest of the class. |
| Copyrighted Materials: All course materials handed out in class or placed in D2L are protected by copyright laws, and are for individual student's personal use only. Multiple copies or sale of these materials is prohibited. |
| Calculator Policy: Calculators, smart phones, and computers are not allowed during quizzes. |