Master Boundary Value Problems in Differential Equations – Lecture 6.6 📘

Differential Equations, Lecture 6.6: Boundary value problems. An initial value problem (IVP) is an ODE involving a function y(t) of time, with initial conditions. A boundary value problem (BVP) is an ODE involving a function y(x) of position, with boundary conditions. An example might be where y(x) measures the temperature of a rod, and the temperature at the endpoints is fixed. The theory of IVPs (existence and uniqueness of solutions) is well-understood, whereas BVPs are more mysterious. We give an 3 examples of an ODE with slightly different boundary conditions, yielding infinitely many, one, and no solutions, respectively. We conclude by solving a few variants of a classic BVP that will be very useful in our study of PDEs. In doing so, we revisit the hyperbolic trig functions: cosh and sinh. Course webpage (with lecture notes, worksheets, etc.): http://www.math.clemson.edu/~macaule/math2080-online.html