<p>I've been reviewing some stuff from Calc BC and will be taking Math 53 this fall. What topics do I need to know really well? I have gone over derivatives and integration (and the applications of both) in the Stewart textbook. What about parametric & polar functions, series, and/or differential equations? Anything else I should study heavily before going into 53? Thanks a lot.</p>
<p>be confident with differentiation/integration… u-sub/by parts/trig substitutions all that</p>
<p>i don’t know about the other professors but sethian spent like 2 weeks reviewing parametric/polar functions</p>
<p>Series and differential equations are, I think, largely irrelevant for 53. However, comfort with calculus when dealing with polar and parametric functions is advisable, especially for sake of maturity to handle similar things in 53. For instance, you will compute integrals, instead of across intervals, across regions, and ultimately the computation can be easier when the desired functions are written in polar form. Where parametric equations come in: you compute integrals along paths, of things like conservative vector fields, and so you need to parametrize the curve to get somewhere. What parameter one chooses to parametrize in terms of can be important. Overall, good familiarity and maturity with techniques of integration and differential calculus is important, but not so much on the applications of differential calculus. One of the few points of application will be, however, optimization problems for functions in multiple variables. The ideas and flavor of things will be similar to the single variable case, so familiarity with that one is advisable. Other than that, one just generalizes a lot of things to multiple variables, i.e. functions on either the plane or 3-space, so you need more foundational, conceptual knowledge of the basics of calculus – what a limit really is, what derivatives and integrals are, etc.</p>
<p>Okay thanks, I appreciate the help from both of you. I will go over polar & parametric stuff in the next week but have been focusing on derivatives and integrals mostly. Even though I knew series and differential equations somewhat at the end of Calc BC (junior year), I don’t remember them any more and will leave them until I prepare for 54 I guess. </p>
<p>Oh one thing! Do we need to know hyperbolic trig functions? I never learned any of that in BC and thus did not go over it in my review (like sinh cosh etc). Thanks again</p>
<p>The funny thing is that hyperbolic trig functions are very stupidly simple things, even though I didn’t realize this before I knew what they were, and would want to throw up when I saw sinh and all. </p>
<p>Don’t worry about them, and I highly doubt you’ll need to know anything about them for 53, unless someone just brings them up for kicks, in which case you can look up the definition.</p>
<p>I would advise looking at anything you look at for the conceptual understanding, not to remember formulas. Math 53 is about taking the ideas of calculus to higher dimensions, working with parametrizations of things in higher-dimensional space, and it should just be a natural transition.</p>
<p>Just make sure you read and grasp the last 2 sections of the Math 53 textbook a month before the final.</p>
<p>wow, this thread is crazily helpful! thanks for y’alls posts.</p>
<p>@J-dawg:</p>
<p>Dude, nobody truly grasps that last 2 sections.<br>
not even the GSIs.
lol.</p>
<p>bump, and are the recommended materials for Math 53 required? In general, do we need recommended stuff for any class? Thanks</p>
<p>all you need is the textbook - the solutions manual is very handy though, i recommend it.</p>
<p>lol YaoMing, that is true.</p>
<p>Nah, you just need the Stewart textbook.</p>
<p>You can get it off DC++ for free.</p>