The purpose of this lab is to use a CAS to find the Wronskians of given sets of functions.
Definitions of linear independence and linear dependence are given to the students. Students are also introduced to the concept of the solution space of an nth order linear ordinary differential equation. The Wronskian is defined. Finally, theorems concerning the relationship between the Wronskian and arbitrary sets of functions and the Wronskian a solution space of a differential equation are presented.
Students are asked to use a CAS to compute the Wronskian of several sets of functions. They are also given two functions whose Wronskian at a specified point is zero and are asked if the functions are linear independent.
Return to Differential Equations: Explorations
Through Technology.