Welcome to the homepage for Math 2700! This course studies differential equations, which are equations involving the derivative of an unknown function. For example, a classical differential equation is
f”(x) = -f(x)
To solve the differential equation, we find a function (or family of functions) with this property: the second derivative of the function is equal to the negative of the function. If you remember your calculus well, you can guess that sin(x) is a solution, since if f(x) = sin(x), then f'(x) = cos(x) and f”(x) = -sin(x).
But cos(x) is also a solution, by similar reasoning. Are these all the solutions?
In this class, we develop a framework for studying these kinds of equations, learning plenty of tricks for finding specific solutions to special classes of equations, and also some general methods for gaining insight into the properties of solutions to equations that we can’t solve explicitly.
This course is especially useful for students interested in applying mathematics to problems in biology, finance, engineering, and physics.