Course
preparation
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
c. Sums of angles in
triangles
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:
a. Be
able to resolve an
algebraic equation for one particular variable
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)
c. Rules for derivation of
powers, exponentials and trig functions
d. Multiplication rule,
quotient rule, chain rule and relatives of them
e. Rules
for integration of powers, exponentials and trig functions
f. The
difference between an antiderivative and a definite integral
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 …