MATH521 Boundary Value Problems and Partial Differential Equations Spring 2021

Details: Written by Changhui Tan; Category: Teaching; Published: 07 January 2021; Hits: 5360

Course Information

Instructor	Dr. Changhui Tan
Lectures	Tu Th 2:50pm - 4:05pm, via Blackboard Collaborate Ultra
Office	LeConte 402
Office Hours	M W 11:00am - 12:00pm, or by appointment, via Blackboard Collaborate Ultra
Textbooks	Walter A. Strauss, Partial Differential Equations: An Introduction. (ISBN: 978-0470054567)
References	Lawrence C. Evans, Partial Differential Equations. (ISBN: 978-0821849743)
	J. David Logan, Applied Partial Differential Equations. (ISBN: 978-3319124933)
Syllabus	Click Here

A partial differential equation (PDE) is an equation that contains unknown multivariable functions and their partial derivatives. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. In this course, we will address many of the mathematical issues on various types of PDEs. We will also discuss boundary value problems on PDE, and related applications in physics and other natural sciences. A brief outline of topics to be covered is as follows.
List of Topics:
- An introduction to PDEs and associated applications.
- First-order linear and nonlinear PDE:
  - Linear transport equations, the Burgers equation, and other first-order nonlinear PDE.
  - Local existence theory on initial/boundary value problems of first-order PDE.
  - Method of characteristics.
- Second-order linear PDE, 3 basic equations:
  - The wave equation and the heat equation (diffusion).
  - Boundary conditions, the Fourier method.
  - The Laplace equation: fundamental solution, Green's function in unbounded and bounded domains.
- Other selected topics will be covered if time permits.

Due to the coronavirus pandemic, online lectures will be offered via Blackboard Collaborate Ultra. You can access the virtual classroom from the course page at Blackboard (Click "Online Lectures") at normal lecture time. A microphone is recommended for in-class communication. Lectures will be recorded for future access.
Office hours will also be offered via the internet. A session has been created in the Blackboard system. Other than the regular office hours, appointments can be made via email.
Download Notes for Online Lectures.

Homework assignments will be assigned via blackboard and collected each week. The tentative due date is on Tuesday at 2pm.
The homework is not pledged. You are encouraged to discuss the problems. However, each student is responsible for the final preparation of his/her own homework papers.
Download Homework Assignments and Solutions.

There will be a 75 minutes take-home midterm exam. The date will be announced later (at least 10 days before the exam is released). There will be a 150 minutes take-home cumulative final exam.
In both exams, you can use the textbook, your own lecture notes, and your own homework assignments. Other communications and help are not allowed.
Download Exams and Solutions.

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