Course Content:
Required Texts: Applied Partial Differential Equations
with Fourier Series and Boundary Value Problems, by Richard Haberman,
Prentice-Hall, 2004.
This is the second half of a two-semester course on the
application of analytical methods to partial differential equations, which is
the arena where many of these applications were developed. This will be a
thorough treatment of the solution of initial and boundary value problems of
partial differential equations. Topics for the full year will include
classification of partial differential equations, the method of characteristics,
separation of variables, Fourier analysis, integral
transforms, generalized functions, Green's functions, Sturm–Liouville theory,
the calculus of complex functions,
and numerical methods. In the second half of the course we will cover a variety of material in
Chapters 8-13 of the text.
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 40% of your grade.
Exams and Grades: There will be a midterm and a final for this course. The exams will cover the material up to the date of the exam. The tentative dates for the exams are below.
| Midterm
| First Half
| Mar 3
|
| Final
| Second Half
| May 9, 7:00 PM
|
Your final grade will be based on the following
| Homework
| 40%
|
| Midterm
| 30%
|
| Final
| 30%
|
| 89.5-100
| A
|
| 79.5-89.5
| B
|
| 69.5-79.5
| C
|
| 59.5-69.5
| D
|
In some cases borderline grades may be modified by a plus, or a minus, if the instructor determines that such grades are earned.
Supplemental Materials:
As you have gathered from the overview, we will follow the main text for most of the course and you will need supplemental readings. Of course, all of this material is covered in other texts and you are strongly encouraged to go to the library and find readings suitable to your tastes. In particular, you will need additional material on complex analysis and Green's
functions. Specialized topics can be found in books on mathematical physics, Fourier analysis, complex analysis, engineering mathematics and partial differential equations.
In particular, some of these topics will be found in my online texts found at
http://people.uncw.edu/hermanr/teaching.htm.
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Examples:
- Weinberger, A First Course in Partial Differential Equations with Complex Variables and Transform Methods. This is the text that has been used most often by current members of the department. It has a good chapter on complex variables, as well as everything else in the course except first order partial differential equations and numerical methods.
- Arfken, Mathematical Methods for Physicists. This text has two readable chapters on complex analysis and is a good reference for special functions, Fourier series, and numerous other topics.
- Keener, Principles of Applied Mathematics.
- Churchill and Brown, Complex Variables and Applications.
- Jerri, Introduction to Integral Equations with Applications.
_____________________________________________________
Further material will be placed at the course website:
http://people.uncw.edu/hermanr/pde2/
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Academic Honor Code: "The University of North Carolina at Wilmington is committed to the proposition that the pursuit of truth requires the presence of honesty among all involved. It is therefore the institution's stated policy that no form of dishonesty among its faculty or students will be tolerated. Although all members of the university community are encouraged to report occurrences of dishonesty, each individual is principally responsible for his or her own honesty." Student Handbook.
(This includes plagiarism, bribery and cheating.)
Student Disabilities: UNCW Disability Services supplies
information about disability law, documentation procedures and accommodations
that can be found at
http://www.uncw.edu/stuaff/disability/ . To obtain accommodations the
student should first contact Disability Services and present their documentation
to the coordinator for review and verification.
THIS SYLLABUS IS SUBJECT TO CHANGE!