MATH 331: Partial Differential Equations

Spring 2026

Course Syllabus and Class Policies

1. Course Topics:

• Review of ordinary differential equations (Sections 0.1 - 0.2)

• Boundary value problems for ODE (Sections 0.3 - 0.4)

• Fourier series; Fourier integral; convergence (Chapter 1)

• Heat equation; the product method (Sections 2.1 - 2.6)

• Sturm-Liouville problems; eigenfunctions series (Sections 2.7 - 2.13)

• Wave equation: product method solution; D’Alembert’s solution (Chapter 3)

• Potential equation; harmonic functions (Chapter 4)

• Higher dimensions, other coordinates, applications (selected sections of Chapter 5)

• Laplace and Fourier transform methods (Chapter 6 and handouts)

• Numerical methods; Monte-Carlo method (selected sections of Chapter 7)

The tentative detailed schedule of the course has been posted on my website; see https://home.sandiego.edu/~pruski/m331s26schedule.html

2. Course Learning Outcomes:

Upon successful completion of this course, the student will:

• Demonstrate a working knowledge of the theory of second-order linear partial differential equations, including the knowledge of theorems with assumptions.

• Be able to:

• solve simple boundary value problems for ordinary differential equations,

• determine Fourier series and Fourier integral of simple functions,

• apply the product method, transform method, and selected numerical methods to solve standard initial-boundary value problems for heat, wave, and potential equations.

• Demonstrate the ability to:

• solve problems in the topics listed above, including applications from the field of physics and engineering,

• use a computer environment to solve differential equations and visualize and interpret the solutions,

• understand simple proofs and write elementary proofs,

• communicate mathematical ideas clearly.

3. Regular Attendance is really necessary. It is quite difficult to catch up with the material when you miss a class. It may become virtually impossible, if you miss several classes.

4. Proofs: One of the most important tasks in mathematics is proving that certain statements are true. We will be doing proofs in class and you will be required to do simple proofs in your assignments and during the exams.

5. Textbook: Powers, Boundary Value Problems and Partial Differential Equations. Sixth Edition. This is one of the best textbooks I have used in my life: serious yet accessible to students. There is not enough time to lecture on everything in class, so you will have to learn some material on your own. Reading the assigned material is absolutely essential!

6. Office hours (Dr. Lukasz Pruski, Saints 147, x. 4035):

Monday	11:00 - 12:00
Tuesday	1:45 - 3:45
Wednesday	3:30 – 4:30
Friday	11:00 - 12:00

and at other times, by appointment (I am not on campus on Thursdays).

7. Contact: The best way to contact me is by using e-mail (pruski@sandiego.edu or lukaszpruski@gmail.com). I read e-mail many times a day. If for some reason you are unable to contact me, try calling our departmental Executive Assistant, Laney Green, at extension 4706.

8. Homework Assignments will be assigned and collected weekly. The total homework assignment score will count for 20% of the course grade. Late assignments will not be accepted unless you have a valid reason and you arrange it with me in advance.

9. Research Project requiring team research will be assigned in late March to be completed by May 7. Each project requires a brief write-up. The projects will be presented in class at the end of the course. The project counts for 10% of the course grade.

10. Eight Quizzes will be announced; the quiz questions will refer to the recently covered material and to the new material you were supposed to read. Two lowest quiz scores will be dropped, and the remaining scores will count for 25% of the course grade. Quizzes cannot be made up unless you have a valid reason for not taking the quiz and you notify me in advance of your absence.

11. Midterm (Friday, March 13). Closed-book, no advanced calculators, smart phones, iPads, iPods or similar gadgets are allowed. The test score will count for 15% of the course grade. A test can be made up only if you have an actual emergency and if you notify me in advance about your absence.

12. The Final Exam (Thursday, May 20, 2:00 – 4:30) will be cumulative and its score will count for 30% of the course grade. The final exam will also be closed book, and no advanced calculators will be allowed.

13. Grading criteria are as follows:

Total percentage	Grade
90% and above	A
80% - 90%	B
60% - 80%	C
50% - 60%	D

15. The Mathematics and Computer Science Department strongly promotes Academic Integrity. I hope issues related to academic integrity will not arise in our course. There have been some cases of cheating in math courses in the past – mainly the cases of submitting someone else’s work as well as cases of cheating during exams. Depending on the severity of the case, the possible consequences include: assigning the score of 0 on the given assignment, lowering the course grade, or even assigning an F in the course. The USD academic integrity policy can be found at https://www.sandiego.edu/conduct/documents/Honor-Code.pdf). 

15. Accommodations: Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. A student attempting to access Disability Services for the first time should begin by contacting the Disability and Learning Difference Resource Center (DLDRC) in SH, Room 300 (619/260-4655), e-mail: disabilityservices@sandiego.edu , website: www.sandiego.edu/disability/ It is the student's responsibility to schedule an "intake" meeting with the DLDRC Director as soon as possible. 

15. Health Resources: If you feel sick, please stay home to keep others healthy. The following USD resources are available to students

    a) Student Health Center https://www.sandiego.edu/health-center/ (non-urgent email: usdhealthcenter@sandiego.edu)

    b) MyWellness Portal: https://mywellness.sandiego.edu/