MAT 519 Syllabus

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Course Content:

Required Text: A First Course in Partial Differential Equations , by R. L. Herman, online, 2021.

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 7-10 of the text.

Learning Outcomes:

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

  • solve first order partial differential equations.
  • demonstrate proficiency at solving partial differential equations.
  • solve ordinary differential equations using initial value or boundary value Green's functions.
  • solve partial differential equations using initial value or boundary value Green's functions.
  • solve partial differential equations using integral transforms.
  • apply numerical techniques in the solution of partial differential equations.
  • differentiate and integrate complex functions.
  • solve Laplace's equation in 2D using complex variable methods.
  • use Fourier and Laplace transforms to solve PDEs.

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.

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: Some interesting problems take a group effort. So, there will be at least one such project assigned. More information will be provided later in the course. This will make up 10% of the course 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 Ch 7-8Mar 3
Final Ch 9-endMay 5, 8:00 AM

Your final grade will be based on the following

Homework
40%
Project10%
Midterm
25%
Final
25%

89.5-100 A
79.5-89.5 B
69.5-79.5 C

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:

  1. 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.
  2. 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.
  3. Keener, Principles of Applied Mathematics.
  4. Churchill and Brown, Complex Variables and Applications.
  5. Jerri, Introduction to Integral Equations with Applications.
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Further material will be placed at the course website: http://people.uncw.edu/hermanr/pde2/  
 
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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.

Campus Respect Compact.  UNCW has recently instituted a Respect Compact to affirm our commitment to a civil community, characterized by mutual respect.  That Compact will soon be affixed to the wall of each classroom and can be accessed at: http://uncw.edu/diversity/documents/ApprovedSeahawkRespectCompact8x10.08.09.pdf

COVID Guidelines

Following CDC Guidelines, UNC System directives, and out of mutual respect as outlined in the UNCW Seahawk Respect Compact, all faculty, staff, and students will wear face coverings while inside buildings. Students who are unprepared or unwilling to wear protective face coverings will not be permitted to participate in face-to-face sessions and will need to leave the building. Noncompliant students will be referred to the Dean of Students for an Honor Code Violation. Any student who has a medical concern with wearing a face covering should contact the Disability Resource Center at (910) 962-7555.

Students who experience COVID-19 symptoms should immediately contact the Abrons Student Health Center at (910) 962-3280.

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E-Mail: Dr. Russell Herman Last Updated: April 19, 2021