Mathematical techniques involving differential equations used in the analysis of physical, biological and economic phenomena. Emphasis is placed on the use of established methods, rather than rigorous foundations.

    First and second order differential equations.
    Variable coefficient second order linear differential equations.
    The Laplace transform.
    Numerical methods.
   Software as a Learning Resource for DiffEqs (click on red links for software resources)
   This course in elementary differential equations 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 not only elementary analytical techniques that lead to exact solutions of certain classes of problems, but also include approximations based on numerical algorithms or series expansions, as well as qualitative or geometrical methods. The problem sets will be assigned and discussed in subsequent class sessions. A student is expected to learn how to use a software package (commercial or free) in solving ordinary differential equations. Workload:

Prerequisite: Elementary Calculus.
While previous knowledge of any computational solver is not a requirement for APMA 0330, students are expected to learn one or more of available either free (Octave, wxMaxima/Maxima, Sage, R, or SymPy/Python) or commercial (Matlab/MuPad/Live Editor, 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.