<p>You must be 100% comfortable with calculus, differential and integral. You don’t have to have every theorem memorized but you must be perfectly at ease with the algebra involved.</p>
<p>After (or during) the regular calc-based physics sequence that all STEM majors take you start the classical mechanics/mathematical methods sequence taught by Kilcup that I mentioned before. It builds up any area of your math skills that are lacking, as I believe you can start the sequence with only the second calc class under your belt. Taylor series, complex numbers, simple linear algebra, multivariable calc, etc., you’ll cover it all alongside the physics. You have both a dense math tome and a dense physics tome that will be your girlfriends for that year. It’ll make a man out of you! Homework assignments are drawn from both books.</p>
<p>Thing is, math classes teach you “proper math,” but in physics you often have to use little “cheats” like the fact that the sin(x) and tan(x) are both approximately equal to x for small values of x, lots of little tricks like that to make otherwise intractable problems solvable. Other math tricks like dimensional analysis for guessing the correct formula for a problem or looking at limits are helpful too. The classical mechanics sequence is almost entirely symbolic, meaning you don’t have a lot of questions like “a mass of 1.7 kg slides along a ramp at angle 32.1 degrees with a frictional coefficient of 0.2 and length 1.2 meters, at what time (in seconds) does the block come to the end of the ramp?” Rather it will be “a mass m slides along a ramp at angle theta with a frictional coefficient of mu and length L, at what time t does the block come to the end of the ramp?” The point of working symbolically like that is:</p>
<p>1) it’s actually easier, PROVIDED YOUR ALGEBRA IS STRONG
2) if you solve the numerical problem numerically, you only have <em>one</em> solution to <em>one</em> problem. But if I solve it symbolically, so I get something like t=m*cos(theta)/sqrt(mu) then I can see what happens to t if I let theta go to pi/2, or mu approaches 0, or whatever, so under certain limits it ought to “reduce” to a formula that I already know, like the time for an object to fall a height L is sqrt(2L/g), so if I get a formula that reduces to t=sqrt(2L/g) when I let theta go to pi/2 (which would mean it’s inclined vertically, so it just falls straight down), then I probably have the right formula. This is a key skill in physics.</p>
<p>I don’t find it necessary to have taken diffy qs before starting this class (it is a requirement eventually). I found it helpful to have taken linear algebra first simply because it meant matrices weren’t brand new to me, but matrices form a very small part of the classical mechanics sequence. Either vector analysis or linear algebra must be taken, but you don’t have to take both. However, if you want to go to grad school, take them both.</p>
<p>My advice is to take no more than three classes a semester. Four tops. Your engineering classes, whatever concentration you choose, will keep you busy. If you have the ability, try to CLEP out of AP out of as many deadweight GECs as you can.</p>