Introduction
In physics, we use math bit differently from the way we use it in math class
We use math extensively in physics, but in math classes the focus is on abstract symbols and their relationships. In physics, we are often using the math to express relationships among physical measurements. This results in a number of features common to the use of math in physics classes that differ from what you may have seen in your math classes.
- We often use more symbols in physics than are used in math.
In math, it is traditional to use a fairly strict code: x, y, z for variables; a, b, c for constants. In physics we lots and lots of symbol names.
- We have many kinds of constants and variables and the line between them is somewhat fuzzy.
We have universal constants without dimensions (p, 2, e), universal constants with dimensions (e, c, h), constants that are parameters of a problem (m, R, g), and constants that are initial conditions for a specific "run" of a physical system (x0, v0.) We may choose to vary the constants. (What is the limiting case of our solution if the mass becomes large?) We have independent and dependent variables and may switch which one is (x in the mass on a spring vs. x in the oscillations of a string).
- We may use the same symbol to mean different things.
In the previous item, we used "e" to refer to both the number 2.718... and the charge on the electron. Think of all the different meanings we have for "k" (spring constant, Boltzmann constant, wave number...) or "p" (momentum, pressure, ...). We distinguish by the context, just as we tell the difference in English between "there", "their", and "they're".
- Symbols in physics stand for "things" -- elements of a physical model -- rather than just for numbers or sets of numbers.
The symbol "L" might stand for a length -- equally well represented as 1 inch or 2.54 cm. There is not a unique number associated with L. The value it takes depends upon our choice of units -- but we see it a standing for a unique length, which can be represented by a variety of different numbers.
- Equations in physics represent relationships rather than just as a way to calculate something.
(This is true in more advanced math as well.)
- In physics we often use extra information brought from the physics to interpret our equations.
This ties together a number of the earlier items. It's why we use so many different symbols, its the way we use the fact that a symbol stands for a physical "thing", and it has to do with the way we interpret relationships from equations. Here is an example of how we use extra information to interpret equations in physics.
The critical idea is to build up a rich interpretation of the symbols we use in math -- not just thinking of them as symbols, but blending together the mathematical and physical properties of the object.
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