Students often contact me with concerns before the course begins:
These are justified concerns.
Yes, we do use calculus occasionally.
Yes, the course is fast-paced, and it will be difficult to catch up with some aspects of math (such as trigonometry) during the semester. You need your focus to master the problem-solving that physics challenges you to do.
Yes, it often does help to have had physics in high school before. But it is no guarantee for success, nor do you need to worry about failure if you did not have physics before. There is really no clear correlation.
And no – even with physics in high school I guarantee you that you will be challenged.
If you are concerned whether you are prepared enough before the course, below are some things you can do to put yourself into a good position before the semester. They are arranged in order of decreasing significance, with the last one still being pretty significant. You may also refer to appendix B in your text book to see examples of what mathematically lies ahead of you.
1. Review trigonometry and geometry!
Mastering these is more important for your comfort in this class than remembering some calculus. Most of the semester, we will spend representing all sorts of physical phenomena using vectors. Those little arrow symbols combine in triangles and polygons on the paper. Once you have drawn them, you will use the drawings to calculate unknown lengths, angles, etc. which means: there is geometry and trigonometry everywhere. Often we need to draw from every trick in the math book to solve the problem.
Your review should include:
b. Similar angles in intersecting lines, in particular parallels
d. Vocabulary: orthogonal, opposite, adjacent, hypotenuse
e. The trigonometric functions sine, cosine, tangent and their geometric interpretation (soh-cah-toa)
f. The trigonometric functions and their inverse functions
g. The trigonometric functions and their arguments (radians?, degrees?)
h. The trigonometric functions and their graphs (important for oscillations)
2. Know your algebra!
Throughout all of problem solving, we will be confronted with situations in which we do need algebra. Be sure to keep up with these points:
b. Know how to solve quadratic equations (quadratic formula!)
c. Review logarithms and expressions containing powers
d. Big one: be able to solve a system of equations for multiple variables. In this semster, we will usually have two or three equations and two or three variables. Mathematics has equipped you with several tools to deal with a system of equations, the simplest one being repeated substitution.
3. Review a few rules for integration and differentiation!
We will use differentiation and integration in some well-defined places, and use mostly very simple examples. The lecture and the text book will introduce these places in a way similar to what you may have seen in your calculus course. However, after the introduction, you will sometimes be confronted just to “do” a derivative or integral of some function, and for that it is useful to remember a few simple rules.
I recommend your review focuses on the following:
a. Interpretation of a derivative in a graph (slope of a line in a point)
b. Interpretation of an integral in a graph (area under the line, summation)
e. Rules for integration of powers, exponentials and trig functions
4. Enjoy reading a few physics-related texts other than the text book– and that one is really up to you. You may wonder about the rules governing the motion of satellites, or why your tires spin on snow (easier the more you push the gas), or why your bike does not tip over when it is moving. Why is this penny speeding up on its way down the wishing well? Why do the Australians not hang upside down, and how does this go together with our image of “gravity constant and down”? Why is there a gap between the top of the steam vent and the white cloud, and why is it rising? Where will this birthday balloon land if the wind from the west is increasing in speed and turning SW with height above the ground? Look around and wonder about things that you are taking for granted every day, and bring those thoughts to class …
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