APMA 0360: Partial Differential Equations
The course APMA0360 intended for students who desire a rigorous development of the mathematical foundations of the methods used. This course provides further techniques of partial differential equations, which are not covered by APMA 0340 and are of great importance in practice. Here are the main topics to be covered:
- Basic partial differential equations.
- Sturm--Liuville problems and orthogonal expansions.
- Integral transformations.
- Heat equations.
- Wave equations.
- Elliptic equations.
- Elements of Potential theory.
- Introduction to numerical methods.
Software as a Learning Resource for Differential Equations
This is the fourth course in elementary differential equations and it is designed to introduce the student for displaying the interrelations between mathematics and physical sciences or engineering. The principal attention is given to those methods that are capable of broad applications and that can be extended to various problems.
The methods discussed here include applications of separation of variables, Sturm-Liouville problems, Fourier series and integrals, potential theory, and numerical methods in partial differential equations. The problem sets will be assigned and discussed in subsequent class sessions. A student is expected to use one or more of available either free (Octave, wxMaxima/Maxima, Sage, R, or SymPy/Python) or commercial (Matlab, Mathematica, or Maple) software in solving partial differential equations during the semester.
| Hours per week | Number of weeks | Hours (total) | |
| Class meetings | 3 | 13 | 39 |
| Recitations | 1 | 13 | 13 |
| Reviewing material | 3 | 13 | 39 |
| Homework | 4 | 13 | 52 |
| Midterms exams | 8 | 2 | 16 |
| Project | 2 | 1 | 2 |
| Final exam | 22 | 1 | 22 |
| TOTAL | 183 |
Prerequisite: APMA0330 and APMA0340.
While previous knowledge of any computational solver is not a requirement for APMA 0360, students are expected to utilize one or more of available either free (Octave, wxMaxima, Sage, R, or SymPy) or commercial (Matlab, Mathematica, or Maple) software in some applications during the semester. Therefore, students without software experience may need to take initiative in learning simple software techniques (click on "Computing" button on this page) to ensure success in the course. TA's and the instructor are usually available to provide mathematical software help for all students.
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