\begin{definition}[Definition:Conjugate Point (Calculus of Variations)/Definition 1]
Let:
:$-\map {\dfrac \d {\d x} } {P h'} + Q h = 0$
with boundary conditions:
:$\map h a = 0, \quad \map h c = 0, \quad a < c \le b$
Suppose:
:$\map h x = 0 \quad \neg \forall x \in \closedint a b$
Suppose:
:$\map h a = 0, \quad \map h {\tilde a} = 0, \quad a \ne \tilde a$
Then the point $\tilde a$ is called '''conjugate''' to the point $a$ {{WRT}} solution to the aforementioned differential equation.
{{explain|Are both a and c conjugate?}}
\end{definition}