Throughout this course, we attempted to communicate the core content of the course via the Equations of the Week.
Understanding how to apply these equations is difficult, mainly because when speaking the the Math language—a language written in equations and spoken in jargon—there is a lot of information embedded in the context of the equations.
The Math language is a dragon: Replete with power and peril. As with any language, its power resides in the practically infinite number of concepts it can communicate. Equations are simply a relationships between parameters.
The Math language is a dragon: Replete with power and peril. As with any language, its power resides in the practically infinite number of concepts it can communicate.The main peril of the Math language lies in its added complexity of compactness. That is, equations are typically written in the shortest “sentences”possible. The job of the receiver of mathematics information is to bring to mind all of the unarticulated concepts embedded in the elliptic statements characteristic of mathematics. For the mathematical novice, this is impossible to do without critically asking questions and digging deeper, until you are certain you understand the concepts associated with the situation; then you can begin to read the mathematical expression, and eventually you can put it to work for you—you can use it to understand new concepts about the world.
Equations are simply a relationships between parameters.In this course we used equations in two ways. The first way is to view an equation as a relationship between some known and unknown parameters; when you use an equation to determine a particular value of a parameter (or set of parameters) based on some information that you either know or have observed, we say you are solving the equation. The second way that we use equations is to view them as a balance; by varying the quantities on one side or the other, we can see which way the balance will “tip” for a given set of parameters. That is, we can determine how a physical system will react to a specific state of the world. Knowing when to employ each of these views is paramount; though they are related, using the wrong method will lead to unfounded conclusions and misunderstandings. Herein I aim to elucidate that context for our equations of the week and present a full view of the course content along the way. Before taking a close look at the concepts presented each week, I begin by discussing a few ideas about the way scientists and engineers use equations. In other words, I start with a discussion about a few of the finer points of talking in the Math language.