Course:  Math 175/275: Numerical Methods for Partial Differential Equations

Class meet time and location:  MWF 4pm-4:50pm, APM 2402
Office hours:  Wednesday 12-1 pm, Friday 3-4pm, location: APM 5755
Discussion sections:  Thursday 5:00-5:50 pm, location: MANDE B-104
TA office hours:  Qihao Ye, Thursday 6-8 pm, location: APM 5720

Credit Hours:  4
Prerequisites:  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.

Required materials :

  • Textbook:
    Partial Differential Equations with Numerical Methods by Stig Larsson and Vidar Thomee. (PDF access on campus Wi-Fi)
  • MATLAB:
    MATLAB (from "matrix laboratory") is a programming language and numerical computing environment commonly used in applied mathematics and other fields of application. Many assignments will involve writing short programs for MATLAB.
    You can install MATLAB on your personal computer or access it directly through the online version. For more information, please visit the website.
    An introduction to MATLAB can be found here .
Additional reading:
Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, by Randall J. LeVeque, published by SIAM, 2007
Numerical Solution of Partial Differential Equations by the Finite Element Method, by Claes Johnson, published by Dover Publications, 2009.
Lecture notes on Numerical Analysis of Partial Differential Equations, by Douglas N. Arnold.
The Mathematical Theory of Finite Element Methods, by Susanne C. Brenner and Ridgway Scott, published by Springer, 2008.

Lecture:   Lectures will be held in person at APM 2402. Attending the lecture 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.

Piazza:    A discussion forum for MATH 175/275. We encourage you to ask questions on Piazza.

Homework:  All homework is due on Fridays 11:59pm (Pacific Time) online, with a late submission deadline on Saturdays 11:59pm. Submission is through Gradescope. If you submit after the regular deadline (Fridays), please include a brief explanation of why you needed additional time. The two lowest scores will be dropped in the end.
Coding Policy
  1. Please specify your MATLAB version (and add-ons, if any), such as R2023b, within your code as a comment. Alternatively, ensure that your code can be executed using the online MATLAB environment, such as https://www.mathworks.com/products/matlab-online.html or https://octave-online.net. This approach will greatly assist TAs in the review and execution of your code in their own environments.
   2. If the primary objective function in your assignment can be easily solved using built-in MATLAB functions without specification, you are encouraged to create your own code implementation. However, you can use built-in functions as verification tools for your code.
   3. We urge you to refrain from submitting programs without explanations. The inclusion of comments is highly appreciated. You are expected to elucidate the method/algorithm employed to solve the problem. Additionally, please specify the input/output requirements and the parameters used.
   4. You are allowed to use other programming languages (e.g., Python, Julia, C++) for coding assignments. Please be sure to follow the above instructions and provide clear instructions on how to run your code. Homework solutions will be provided only in MATLAB.

Collaboration policy:   You are encouraged to collaborate with other students. However, you must type every line of code and write up all solutions independently.
What's encouraged:
   1. Discuss homework problems with classmates in person or online.
   2. Form study groups to brainstorm ideas and learn together.
What’s not allowed:
   1. Copying any part of another student’s solution or code.
   2. Letting others copy your work.
   3. Submitting solutions or code you did not write yourself.

Use of AI Tools (e.g., ChatGPT):   AI can be helpful, but only if used responsibly.
What's allowed:
   1. Review background concepts.
   2. Check explanations or get hints after attempting the problem.
   3. Debug your own code after writing it.
   4. Generate extra practice examples to deepen understanding.
What’s not allowed:
   1. Submitting AI-generated solutions or code as your own.
   2. Copying and pasting answers directly into your submission.
   3. Using AI to complete homework without understanding the solution.
If you use an AI tool to help you understand a concept, acknowledge it briefly in your submission (e.g., “I used ChatGPT to clarify the definition of column space.”)
For more information, visit the UCSD Academic Integrity website.

Exams and grading (for 175 students):
There will be a one in-class midterm exam on Monday, February 9 and a final exam on Friday, March 20.
Your final grade will be calculated using whichever of the two methods below gives you a higher score:
Method 1: (25% HW) + (35% Midterm) + (40% Final).
Method 2: (25% HW) + (25% Midterm) + (50% Final).
Extra Credit: 5% bonus for a final project with a class presentation.

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.