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Intro to Differential Equations
Taught by Catherine Williams. Meets 6:30pm-7:50pm T/Th in MEB 246. Homework
Intro and scope
There are two general classes of Differential Equations- Ordinary Differential Equations? (⚠ ODEs) and Partial Differential Equations? (⚠ PDEs). We will deal only with ⚠ ODEs.
When we speak of the order of an equation in the context of ⚠ DEs, we are referring to differential orders- i.e. first order of u is {$u’$}, second order is {$u$}, and so on. We will deal mostly with first and second order equations, with a few third-order exceptions. In other words, we will not see {$u’ + \cos(u’)u′ + \sin t = 0$} or anything like it.
The term homogeneous? refers to equations that do not have constant elements in them- i.e. if you were to stick everything with a variable on the LHS of the equation, the RHS would be 0. If this cannot be done, an equation is non-homogeneous. We will deal with both.
There is, finally, one more dichotomy- linear and nonlinear equations. Linear equations do not perform nonlinear operations on the unknowns, as expected. We will deal with both.