In the previous three chapters, we laid the groundwork required to model physical systems based on the conservation laws and presented a number of illustrations which provided the reader a ﬁrst glimpse of the scope and power of mathematical modeling. The reach of this discipline is, in fact, quite considerable, perhaps even unsurpassed, within the applied sciences and engineering. When properly applied, it illuminates the topic it addresses in a way that is only matched by direct experimentation. As with experimentation, modeling pokes and prods the subject, often revealing it in a new light or uncovering the unexpected. Most major discoveries have come about through the twin efforts of experiment and theory, of which modeling is a major weapon.