Class meetings: Class meetings will be held in person. If the classroom allows it, class meetings will be recorded for those who are not able to attend or would like to review the recorded class material later.
Problem-solving sessions: These mandatory sessions (one of which is offered unscheduled for self-study if you have a time conflict with the scheduled sessions or prefer to work by yourself) focus on going through worksheets to deepen our understanding of the material and to work on applications and modeling scenarios.
To support your learning, we will provide the following:
Handwritten lectures notes for each class;
Brief video reviews and other reference materials posted on Canvas;
Office hours: we will offer multiple open office hours throughout the week;
Q&A through Ed Discussions;
Optional textbooks (available as free PDFs through Brown's library: see below).
No textbook is required. Books that are available for free through the Brown Library and that cover similar material include
J David Logan "Applied Partial Differential Equations" (available as a free PDF through Brown)
Peter J Olver "Introduction to Partial Differential Equations" (also available as a free PDF through Brown).
If your Brown undergraduate financial aid package includes the Book/Course Material Support Pilot Program (BCMS), concerns or questions about the cost of books and course materials for this or any other Brown course (including RISD courses via cross-registration) can be addressed to bcms@brown.edu. For all other concerns related to non-tuition course-related expenses, whether or not your Brown undergraduate financial aid package includes BCMS, please visit the Academic Emergency Fund in E-GAP (within the umbrella of "E-Gap Funds" in UFunds) to determine options for financing these costs, while ensuring your privacy.
Our goal is that you develop an understanding and appreciation of the theory of partial differential equations and achieve mastery of modeling real-world problems using partial differential equations, solving them using a range of mathematical methods, and connecting model outcomes and applications. Except for the midterm exams, you can collaborate on assignments.
Rubrics: We will provide rubrics for the assignments. Generally, grading will focus on understanding and not on algebra and non-essential mistakes. We would like to see explanations that justify your answers (instead of only lines of formulas), full sentences that summarize your answers (instead of just a formula), and discussions of the assumptions you made when you design a model.
Weekly problem sets: These problem sets will allow you to deepen your understanding of the class materials and to apply the techniques we covered in class.
Weekly reflections/check-ins: The reflections give you an opportunity to reflect on your learning and to communicate to me if concepts or techniques were not explained clearly. I will read all of your responses but may not respond to most of them.
Midterm exam: The midterm exams will be held in class.
Final group projects: The final group projects will involve 2-5 students in each group. I will help you find groups based on your project preferences and strengths, and you are also free to form your own groups. The goal of these projects is to learn more about a specific application or topics that we did not cover in class. The end product will be a 10-15 page written single-spaced report that is accessible to anyone in the class. I will provide a list of topics, but you can also choose your own. For instance, you could pick a chapter in the textbook that we did not cover and expand on the textbook presentation by adding more details, examples, and explanations. Or you can identify an application that involves PDEs and report on this application and how PDEs have been used to help gain insights into it.
Your overall course grade will be calculated according to the following breakdown:
30% weekly problem sets – submitted through Gradescope
10% weekly reflections/check-ins – submitted through Canvas
10% weekly problem-solving worksheets – during session or submitted through Gradescope
20% two midterm exams (10% each) – conducted in class
30% final group project – submitted through Gradescope
Problem sets (30% of the grade):
We will drop the lowest score of the regular homework assignments when calculating the 30% homework grade contribution.
Reflections/check-ins:
The reflections/check-ins are graded for completion.
Problem-solving worksheets:
The problem-solving worksheets are graded for completion.
I will use the following minimum cut-offs:
90-100% or higher is guaranteed an A
80-89% or higher is guaranteed a B
65% or higher is guaranteed a C.
For students taking this course S/NC, a minimum grade of 65% is required to guarantee a grade of S.
Although specific out-of-class time investments may vary for individual students, I estimate that students will spend
36 hours on lectures (approximately 3 hours per week)
12 hours on problem-solving sessions
84 hours on review of material, problem sets, and reflections (approximately 7 hours per week)
16 hours on preparations for midterm exams
35 hours on the final project
during the semester for a total of approximately 183 hours.
If possible, I will record class meetings so that everyone can use the recordings to review lectures at their own pace. The recordings can be accessed by all students enrolled in this course at any time. If you have questions or concerns about this protocol, please contact me so that we can talk through those to also ensure your full participation in this course.
Lectures and other course materials are copyrighted. Students are prohibited from reproducing, making copies, publicly displaying, selling, or otherwise distributing the recordings or transcripts of the materials. The only exception is that students with disabilities may have the right to record for their private use if that method is determined to be a reasonable accommodation by Student Accessibility Services. Disregard of the University's copyright policy and federal copyright law is a Student Code of Conduct violation.
This course will use the following technological platforms:
I am committed to ensuring access to online course resources by students. If you have any concerns or questions about access or the privacy of any of these platforms, please reach out to me.
The IT Service Center provides many services including remote assistance, phones, tickets, and chat. Please also see the Online and Hybrid Learning Student Guide.