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

Partial Differential Equations

MATH 642-001Spring 2019 | 3 Credit Hours


Shibin Dai

Contact Information

UA Campus Directory:

Office: GP 223A

Email: sdai4@ua.edu

Office Hours: MWF 8:15-9:00am, W 2:45-4:15 pm, F 1:45-3:00pm


UA Course Catalog Prerequisites:

MATH 238 and MATH 486 or permission of instructor

Math 541, and Math 486 or 586, or permission of instructor

Course Description

Course Description and Credit Hours

This is an introductory course in partial differential equations. It covers the theory, methods of solution as well as applications related to the three main equations of mathematical physics, namely the Laplace’s equation, the heat equation and the wave equation. This course serves as the second part of the sequence for the qualifying exam in partial differential equations.

This is an introductory course in partial differential equations. It covers the classical theory of the three important second order partial differential equations (Laplace's equation, the heat equation, and the wave equation), and the basic theory of nonlinear first order partial differential equations, especially conservation laws. This course serves as the second 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 solve the Laplace and Poisson equations using various techniques.

  2. Students will analyze properties of harmonic functions.

  3. Students will solve the heat and wave equations and analyze their properties.

  4. Students will solve first order partial differential equations using the method of characteristics.

  5. Students will analyze properties of conservation laws.

  6. If time permits, students will analyze properties of some other nonlinear PDEs.

Other Course Materials


Outline of Topics

Chapter 2. Four important linear PDE
Chapter 3. Nonlinear first order PDE
Chapter 4. Other ways to represent solutions

Exams and Assignments

ASSIGNMENTS: Homework will be assigned weekly.

EXAMS: There will be one midterm test and a comprehensive final exam.

Midterm: TBD
Final Exam: Aril 30, Tuesday 11:30-2:00.

Grading Policy

Grades will be determined by homework (30%), midterm test (30%), and the final examination (40%).

Policy on Missed Exams and Coursework

Makeup tests will be given only in the event of serious illness or other extreme cases, and only if timely notification is given.

Attendance Policy

You are expected to attend all the classes so that you can be informed about homework, exams, and other matters relevant to the course.

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.