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UA Course Catalog Prerequisites:
No prereqs found
This course has two prerequisites.
1. Basic knowledge of PDE (Math 541 or 642).
2. Real Analysis (Math 580 and 681).
Course Description and Credit Hours
No description found
MODERN THEORY OF PARTIAL DIFFERENTIAL EQUATIONS
This course concerns the modern theory of partial differential equations (PDE). The classical approach of PDE is the search for explicit formulas for the solutions. However, many times formulas do not provide as much useful information as we hope. What’s more, most PDEs do not possess a formula for their solutions. Hence it is essential to understand the properties of their solutions without a formula.
In this course, we will abandon the search for explicit solutions. Instead we will concentrate on modern techniques in the theoretical study of linear and nonlinear PDEs. This is a course that provides students the opportunity to learn PDE in topics beyond the classical theory covered in Math 541 and 642. And students will be prepared for research in PDE-related areas. In his now definitive textbook Partial Differential Equations, L. Craig Evans described six principles:
PDE theory is (mostly) not restricted to two independent variables.
Many interesting equations are nonlinear.
Understanding generalized solutions is fundamental.
PDE theory is not a branch of functional analysis.
Notation is a nightmare.
Good theory is (almost) as useful as exact formulas.
These principles are also the guidelines for our course.
Required Texts from UA Supply Store:
- EVANS / PARTIAL DIFFERENTIAL EQUATIONS (V19)* (Required)
- EVANS (RENTAL) / (RENTAL) PARTIAL DIFFERENTIAL EQUATIONS (V19)* (RENTAL)
- EVANS / (eBook) Partial Differential Equations (E - Book)
Student Learning Outcomes
Students will analyze the properties of PDEs.
Other Course Materials
Weak Convergence Methods for Nonlinear Partial Differential Equations, (Regional Conference Seriess in Mathematics, No 74) CBMS/74, by Lawrence C. Evans, 1990
Elliptic Partial Differential Equations, Second Edition, by Qing Han and Fanghua Lin
Outline of Topics
Sobolev spaces; weak solutions (existence, uniqueness, and regularity) for linear and nonlinear PDEs; calculus of variations; non variational techniques for nonlinear PDEs.
Exams and Assignments
There will be no written homework or written exam. Rather, each student will give a presentation on some problems chosen from the textbook.
The grade will be determined by class participation, and the quality of each student's presentation.
Policy on Missed Exams and Coursework
Each student will give at least one presentation on topics from the textbook. If a student has to miss a scheduled presentation due to legitimate reasons or emergencies, he/she should inform the instructor as soon as possible.
Attendance is required.
Notification of Changes
The instructor will make every effort to follow the guidelines of this syllabus as listed; however, the instructor reserves the right to amend this document as the need arises. In such instances, the instructor will notify students in class and/or via email and will endeavor to provide reasonable time for students to adjust to any changes.
Department of Mathematics Academic Misconduct Policy
- During tests you may only use a calculator that has been specifically approved by the instructor. Using or being in possession of an unauthorized calculator will be considered academic misconduct.
- Taking a test for another student will be treated as academic misconduct by both parties. In particular, showing an instructor a fake ID or another student’s ACT card will be treated as academic misconduct.
- Receiving or providing assistance of any kind during an exam will be treated as academic misconduct by both parties.
- Cellphones must be turned completely off and placed with other belongings on the floor. All watches must be taken off and put away. DO NOT put your phone or watch in your lap or on your chair or desk. Physically holding or concealing on your person a phone, watch or other unauthorized technological device (including but not limited to headsets, earphones, earbuds, microphones, cameras, or scanning pens) will be treated as academic misconduct.
- If you are seen using an unauthorized device, the instructor may request that you turn it over. It will be returned at the end of the exam. However, the instructor does not have to request your device in order to charge you with academic misconduct.
- If for any reason you must have access to your phone while taking a test, you must inform an instructor prior to accessing your phone. The instructor must be present while you use the phone. Failure to do so will be treated as academic misconduct.
- If necessary, scratch paper will be provided. No other paper is allowed; being in possession of any unauthorized papers will be treated as academic misconduct.
- You may review your test before leaving the exam. You may not photograph your exam or write down or copy any information pertaining to the test, nor may you share any information about the test with anyone by any means. This includes sharing information by word of mouth, written correspondence, electronic device or any type of social media. Providing information about the test to other students will be treated as academic misconduct. Also, having in your possession information about any test prior to the test that was not given to you by the instructor will be treated as academic misconduct.
- You may not leave your place during a test for any reason. This includes getting water or going to the restroom. You must take care of these things before the start of the test. If you leave your test without permission, your test will be collected and you will not be allowed to continue working on it.
- Interrupting the exam or creating a disturbance to cause a distraction during the exam will be treated as academic misconduct.
- In order to enforce these rules, an instructor may require you to do any of the following. Failure to comply will be treated as academic misconduct.
- Remove hats, hoods, scarves, or other head coverings.
- Remove bulky coats, sweaters or other over-garments.
- Roll up sleeves.
- Remove anything seen in your ears or on your person.
- Empty your pockets and display the contents.
- Sit in assigned seats prior to the start of the exam.
- Require you to move to a new seat during the exam.
If you wear a hat, head covering or long-sleeved garment for religious reasons, the instructor may still request to examine under them. If you would prefer to have this done privately, or by an instructor or staff member of the same sex, you will be accommodated. To ensure accommodation, you must discuss this with your instructor prior to the test.
If you use a hearing aid or other adaptive technology that could be mistaken for an earbud or other unauthorized electronic device, please notify your instructor prior to the test. You may be asked to provide documentation of your need to use such a device.
MTLC Specific Policies
- In the MTLC, you may only use either the Casio fx-SOLAR SCHOOL or the Casio fx-260 SOLAR II.
- In the MTLC, swiping another student’s ACT card will be treated as academic misconduct.
- In the MTLC having any other website other than the test open during a test will be treated as academic misconduct.
- In the MTLC, if you leave your computer during a test without permission, your exam will be closed and you will forfeit any remaining exam time.
Statement on Academic Misconduct
Students are expected to be familiar with and adhere to the official Academic Misconduct Policy provided in the Online Catalog.
Statement On Disability Accommodations
Contact the Office of Disability Services (ODS) as detailed in the Online Catalog.
Severe Weather Protocol
Please see the latest Severe Weather Guidelines in the Online Catalog.
Pregnant Student Accommodations
Title IX protects against discrimination related to pregnancy or parental status. If you are pregnant and will need accommodations for this class, please review the University’s FAQs on the UAct website.
Under the Guidelines for Religious Holiday Observances, students should notify the instructor in writing or via email during the first two weeks of the semester of their intention to be absent from class for religious observance. The instructor will work to provide reasonable opportunity to complete academic responsibilities as long as that does not interfere with the academic integrity of the course. See full guidelines at Religious Holiday Observances Guidelines.
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Statement on COVID-19
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