APMA 2550: Finite Difference Schemes

The course intended for students who desire a rigorous development of the mathematical foundations of the methods used. This course provides further techniques of ordinary and partial differential equations, which are not covered by APMA 0330 and are of great importance in practice. Here are the main topics to be covered (syllabus):
 

• Topics from matrix algebra.
• Systems of linear ordinary differential equations.
• Nonlinear ordinary differential equations.
• Qualitative theory of ordinary differential equations.
• Sturm-Liouville problems and orthogonal expansions.
• Fourier series.
• Partial differential equations.

Software as a Learning Resource for Differential Equations


This course is designed to introduce numerical methods for partial differential equations. 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 periodic solutions, Fourier series 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/MuPad, Mathematica, or Maple) software in solving ordinary and partial differential equations during the semester.

Prerequisite: Elementary Calculus and APMA0330.
While previous knowledge of any computational solver is not a requirement for APMA 0340, students are expected to utilize one or more of available either free (Octave, wxMaxima, Sage, R, or SymPy) or commercial (Matlab/MuPad, 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.