Syllabus
Updated 1/2/22 The details listed in the syllabus are subject to change during the term.
Course: Math 175/275
Title: Numerical Methods for Partial Differential Equations
Credit Hours: 4
Prerequisite: Math 174/274 and knowledge of programming
Catalog Description: Mathematical background for working with partial differential equations. Survey of finite difference, finite element, and other numerical methods for the solution of elliptic, parabolic, and hyperbolic partial differential equations.
Textbook: Stig Larsson and Vidar Thomee, Partial Differential Equations with Numerical Methods.
Additional reading:
Lawrence C. Evans, Partial Differential Equations.
Lloyd N. Trefethen and David Bau, Numerical Linear Algebra.
Robert Plato, Concise Numerical Mathematics.
Lecture: We are starting the quarter with two weeks of remote instruction and are currently targeting Tuesday, Jan. 18 as the start of in-person instruction. During the time of remote instruction, lectures will be held live via zoom and will be recorded and made available on Canvas. The in-person lectures will be delivered at APM 2402 and will also be recorded and made available on Canvas and Podcast. Attending the lecture (or reviewing the recording) is a fundamental part of the course; you are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.
Homework: All homework is due on Wednesdays 11:59pm (Pacific Time) online. Submission is through Gradescope.
Late homework will not be accepted. Two lowest scores will be dropped in the end.
Each homework will contain a mix of analytical and programming problems. You are allowed to use any preferred programming languages. Code used in class and provided for homework solutions will be in
Matlab. Please read the homework assignments guidelines below.
- Programming problem requirements:
1. Describe the method/algorithm used to solve the problem.
2. Discuss the numerical experiments conducted(specify input/output and the parameters used).
3. Report the key observations of the numerical experiments. Provide some analysis (performance, results) and offer a conclusion
4. Use table/graphics to summarize the data/output from experiments to support the analysis and conclusion.
5. Attach the computer program written for the project as supplementary materials.
Note:
a. Please avoid turning in pages of computer programs output without explanation.
b. Please provide captions to tables, legends for picture/plots. - Collaboration policy:
1. It is okay to discuss the problems with others, but you must write your sown solutions.
2. For the programming problems, it is okay to work on the development and debugging with others, but you must do your own runs, make your own plots, etc.
3. If you worked together with someone on a homework assignment, you must write down who you worked with.
Exams: There will be a 50-min midterm exam and one 2-hour final exam given on the days specified in the course calendar. Exams will take place in APM 2402. There will be no makeup exams.
Regrade Policy: Your exams will be graded using Gradescope. You will be able to request a regrade via Gradescope for a specified window of time. Be sure to make your request within the specified window of time; no regrade requests will be accepted after the deadline.
Grading:
Graduate students (in Math 275) are required to complete a final project and do a short in-class
presentation of their work during the last week of classes. The topic of your project should be decided in consultation with the instructor.
Undergraduate students (in Math 175) may also elect
to do a final project, although this is not required. The grades for this course will be
determined as follows, and undergraduates may elect either option.
Math 175: Homework (35%) + Midterm (25%) + Final (40%).
Math 275: Homework (25%) + Final Project (15%) + Midterm (25%) + Final (35%).
Your letter grade will be
determined up to some minor adjustment according to the following scale::
A+ | A | A- | B+ | B | B- | C+ | C | C- |
97 | 93 | 90 | 87 | 83 | 80 | 76 | 70 | 65 |
You are guaranteed this scale, that means that your grade will not be worse than specified by the above scale. Your instructor reserves the right to adjust the above scale to be more generous if warranted by the class's performance.
Academic Integrity: Academic integrity is highly valued at UCSD and academic dishonesty is considered a serious offense. Students involved in an academic integrity violation will face an administrative sanction which may include suspension or, in very serious cases, expulsion from the university. Your integrity has great value: Cultivate and protect your academic integrity. For more about academic integrity and its value, visit the UCSD Academic Integrity Website.