A graph of states which is closed and connected.

Also relating to this is a derived variable. One way to prove reaching any state is via Floyd’s Invariant Method.

A finite-dimensional vector space is a vector space where some actual list (which remember, has finite length) of vectors spans the space.

An infinite-demensional vector space is a vector space that’s not a finite-dimensional vector space.

additional information

every finite-dimensional vector space has a basis

Begin with a spanning list in the finite-dimensional vector space you are working with. Apply the fact that all spanning lists contains a basis of which you are spanning. Therefore, some elements of that list form a basis of the finite-dimensional vector space you are working with. \(\blacksquare\)

Fireside Chats are a group of broadcasts by Franklin D. Roosevelt (FDR) which allowed him to speak directly to the people.

Below you will find a list of the Fireside articles.

First Order ODEs are Differential Equations that only takes one derivative.

Typically, by the nature of how they are modeled, we usually state it in a equation between three things:

\begin{equation} t, y(t), y’(t) \end{equation}

as in—we only take one derivative.

Sometimes the solution may not be analytic, but is well-defined:

\begin{equation} y’ = e^{-x^{2}} \end{equation}

we know that, by the fundamental theorem of calculus, gives us:

\begin{equation} y(x) = \int_{0}^{x} e^{-s{2}} \dd{s} \end{equation}