# Analysis and Synthesis

We learn this in MATH213.

Analysis

Analysis: Given a forcing term $f(t)$ solve for $y(t)$.

Synthesis

Synthesis: Given a $y(t)$, or some conditions on $y(t)$, find a forcing term $f(t)$ such that $y(t)$ solves the differential equation.

The first part of the course of MATH213 was introducing us to analysis. In the second part, we focus on synthesis (which is generally more useful in engineering).