1. Contact Information
  2. Prerequisites
  3. Course Description and Credit Hours
  4. Required Texts
  5. Course Objectives
  6. Student Learning Outcomes
  7. Other Course Materials
  8. Outline Of Topics
  9. Exams and Assignments
  10. Grading Policy
  11. Policy on Missed Exams and Coursework
  12. Attendance Policy
  13. Notification of Changes
  14. Custom Sections
  15. Statements on Academic Misconduct
  16. Statement On Disability Accommodations
  17. Severe Weather Protocol
  18. Pregnant Student Accommodations
  19. Religious Observances
  20. UAct Statement

Boundary Value Problems

MATH 541-001Fall 2019 | 3 Credit Hours


Shibin Dai

Contact Information

UA Campus Directory:

Office Hours: Monday 9:00-9:50 am, and by appointment.


UA Course Catalog Prerequisites:

MATH 343 and MATH 486 or MATH 586.

Math 486/586, and Math 343.

Course Description

Course Description and Credit Hours

Emphasis on boundary value problems for classical partial differential equations of physical sciences and engineering. Other topics include Fourier series, Fourier transforms, asymptotic analysis of integrals and boundary-value problems for ordinary differential equations.

This course serves as the first part of the sequence for the qualifying exam in boundary value problems and partial differential equations.

Required Texts

Required Texts from UA Supply Store:

Course Objectives

Student Learning Outcomes

  1. Students will lean analytical methods for solving boundary value problems.

  2. Students will learn how to classify linear partial differential equations and learn their distinguishing qualitative properties.

  3. Students will learn the use of physical principles to derive some common partial differential equations that are prominent in the physical science.

  4. Students will be introduced to the theory of Fourier series and the method of eigenfunctions expansion.

  5. Students will be introduced to the Sturm-Liouville theory.

Other Course Materials

Outline of Topics

Chapter 1. Where PDEs come from (1.1-1.5) (1 week)

Chapter 2. Waves and Diffusion (2.1-2.5) (2 weeks)

Chapter 4. Boundary problems (4.1-4.3) (3 weeks)

Chapter 5. Fourier Series (5.1-5.6) (4 weeks)

Chapter 6. Harmonic Functions (6.1-6.4) (3 weeks)

Chapter 10. Boundaries in the Plane and in Space (10.1-10.3) (1 week)

Exams and Assignments

Midterm Exam: Wednesday October 16, in class. (Chapters 1,2,4: first order linear equations, diffusion and wave equations, energy estimates, separation of variables, spectral analysis for boundary problems.)

Cumulative Final: Wednesday December 11, 11:30 am -1:30 pm.

Homework will be assigned weekly and will be due on Wednesday in class.

Grading Policy

homework 30%;

Exams 30%;

Final 40%.

Policy on Missed Exams and Coursework

No late homework will be accepted, unless there is a documented legitimate reason.

There will be no makeup for the midterm exams or the final, unless there is a documented legitimate reason. The only allowed excuses for a makeup are

  • documented illnesses

  • university sponsored events

  • a religious holiday

  • a family emergency

Unless there is a true emergency, makeup exams should be arranged at least two weeks before the exam date.

Attendance Policy

Attendance is required. It is the students' responsibility to attend every class and actively participate in class activities.

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.

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.

Religious Observances

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.

UAct Statement

The University of Alabama is committed to an ethical, inclusive community defined by respect and civility.  The UAct website (www.ua.edu/uact)  provides extensive information on how to report or obtain assistance with a variety of issues, including issues related to dating violence, domestic violence, stalking, sexual assault, sexual violence or other Title IX violations, illegal discrimination, harassment, hate or bias incidents, child abuse or neglect, hazing, threat assessment, retaliation, and ethical violations or fraud.