Other Resources:

• Introduction to the Mathematical Theory of Waves, by Roger Knobel, American Mathematical Society, 2000.
• Applied Partial Differential Equations,4 ed., by R. Haberman, Prentice-Hall, 2004.
• Partial Differential Equations for Scientists and Engineers, by Stanley J. Farlow, Dover, 1993.
• A First Course in Partial Differential Equations with Complex Variables and Transform Methods, by H.F. Weinberger, Dover Publications, 1995

In this course we will mostly study analytical methods for solving partial differential equations. This will be a thorough treatment of the solution of initial and boundary value problems of partial differential equations. Topics for this semester will include the classification of partial differential equations, separation of variables, Fourier series, Sturm–Liouville theory, first order partial differential equations, the method of characteristics, and numerical methods. We will cover the chapters in the online course notes, though these topics can also be found in standard texts on partial differential equations.

Besides a maturity in mathematics, you are expected to review your analytical skills and introductory differential equations. Undergraduate students will do a subset of the homework and exams. 

Learning Outcomes:

At the conclusion of the course, the successful undergraduate student will be able to

• demonstrate proficiency at solving partial differential equations.
• solve linear second order partial differential equations using separation of variables.
• find Fourier series expansions of given functions.
• identify generic differential equations such as the heat, wave, Laplace's equations and classify second order equations as elliptic, hyperbolic, or parabolic.
• understand how to solve initial-boundary value problems
• understand the linear algebra underlying boundary value problems.
• solve homogeneous partial differential in different geometries.
• demonstrate and understanding of finite difference methods for solving partial differential equations.
• solve first order differential equations using the method of characteristics.

Graduate students should be able to do the above plus demonstrate a higher level of understanding and proficiency in several other areas as demonstrated in the homework and projects.

More information will be posted on the web related to the topics we are studying. Links can be found with summaries to the material, study suggestions, homework assignments, etc. These will be accessible through the instructor's homepage at  http://www.uncwil.edu/people/hermanr/pde1  

Some of the more important partial differential equations can only be solved numerically. Therefore, there will be a section on numerical techniques and the assignments for that section will consist mostly of doing a group project. More information on this part of the course will be provided at a later time. This part of the course will count 10% of your grade.

Advice for Success:  

In order to learn the material in this course and earn a good grade, you need to put in some effort. Do not put off assignments or reading. If you do not understand something, ask the instructor. Come to office hours, use the email, ask knowledgeable students, or go to the library/internet and find supplementary material. Additional material will be placed at the course website. The instructor can only cover the basics in class. You are not expected to know the material by only listening to the lectures. You need to work problems and think about what you are doing.

Course Requirements:

Homework: Homework problems will be assigned periodically and you will be told when the work is due. As doing homework is important in understanding the material, it will count 50% of your grade.  Late homework is subject to a 10% penalty.

Attendance: YOU ARE EXPECTED TO ATTEND ALL OF THE CLASSES! After two excused absences there will be a penalty of 2% for each absence from your total grade.

Project: There will be at least one group project, which will have several pieces. This will make up 10% of the course grade.

Exams and Grades: There will be a midterm and a final exam. The exams will cover the basic material up to the date of the exam. The tentative dates for the exams are below.

Your final grade will be based on the following

In some cases borderline grades may be modified by a plus, or a minus, if the instructor determines that such grades are earned.

You are required to turn in all of the assigned problems for grading on the due date. All work is expected to be neat, in order and with all work provided. The Homework Assignments are listed at the course website.

This syllabus is subject to change!
 

Academic Honor Code:

All members of UNCW’s community are expected to follow the academic Honor Code. Please read the UNCW Honor Code carefully (as covered in the UNCW Student Handbook). Academic dishonesty in any form will not be tolerated in this class. Please be especially familiar with UNCW’s position on plagiarism as outlined in the UNCW Student Handbook. Plagiarism is a form of academic dishonesty in which you take someone else’s ideas and represent them as your own.

Student Disabilities: UNCW Disability Services supplies information about disability law, documentation procedures and accommodations that can be found at http://uncw.edu/disability/. To obtain accommodations the student should first contact Disability Services and present their documentation to the coordinator for review and verification.