<p>I am going to be a freshman engineer at Cornell next year - probably going to major in either Applied & Engineering Physics w/ a focus on ECE (minor and then some) or straight ECE. </p>
<p>My question: I took a class last year that covered most of the topics in the Calc III course I'd need to take this upcoming semester (5 on Calc BC got me out of Calc I/II, and I'm very comfortable with those concepts) and I've already bought the textbook and obtained a copy of the course syllabus used in Cornell's Calc III course. Originally my intention was to use the book to review the concepts we covered in my class last year and to teach myself the concepts that weren't covered. I am relatively comfortable with the concepts I've covered.</p>
<p>Would I be ill-advised as an AEP or ECE major to do this and then take a placement exam to test out of Calc III? This would put me right into 200-level math (either Differential Equations or Linear algebra) and effectively put me a full 2 semesters ahead in both math and science courses. I guess I am kind of asking just how important 3D calculus is for someone in AEP or ECE...the course would be a lot of review but it could also help pound the topics and concepts into my head and would make sure I've learned them adequately, but testing out of it would allow me to avoid half a semester of mundane review and could also help me save my parents some $$$ by helping me graduate a semester or two early.</p>
<p>If you can test out, I would do so. They won't let you get out of it unless you know the concept.</p>
<p>I'm a MechE and I never use Calc 3 stuff in undergrad classes. I've had to use it in some of the grad classes I've taken but even then it doesn't get too intense.</p>
<p>If you can test out of it an earn an A--go for it. If not, it might be better to take it and earn the A just so you have a buffer from the inevitable Engineering ownage.</p>
<p>Multivariable calculus (especially vector calculus) is rarely used in ECE, except for electromagnetics classes. AEP would use a little more than ECE, but in either case I highly recommend skipping Calc III if you've already taken it. Most people forget the tricky concepts anyway, so they'll probably have a quick review when you get to it.</p>
<p>Don't test out. First of all, I don't think that testing out of multi will allow you to graduate early - there's too many other engineering requirements that just don't depend on that. You could certainly take multi-variable concurrently with classes that may require if it you have a relatively good grasp of the material anyway.</p>
<p>Maybe it's just because I did so much coursework that required multi-variable, but I would honestly say that you should have those concepts down flat. Make sure that calc is as familiar to you as basic arithmetic. </p>
<p>The other thing is that college classes, esp. the real ones (i.e. not freshman-level) move very, very fast. You should get used to college first and develop some excellent study habits (and get used to the fact that you'll do a year's worth of high school work in a semester, but only have class 2 days a week, for 1/4th the classtime that you would get in high school) before taking anything too advanced.</p>
<p>I think the reinforcement can be valuable. Particularly as it pertains to mutiple integration and vector calculus (div, grad, curl), if that's what it covers. A solid mastery of this material is, IMO, very helpful for certain upper-level science and engineering science courses, particularly E&M.</p>
<p>If you do take it, plan to work hard. The people with backgrounds in the material didn't do any better in the course than the people without such backgrounds, when I took it. I think the first group may have taken it too lightly, or thought they knew more than they actually did. The level of this course will likely be very high. But this is exactly what you need for upper level E&M.</p>
<p>I only took E&M in the Physics department. It could be that, in the versions of these courses given by the EE department, the mathematical level is "watered down" somewhat, to the level that some posters have described above. In which case further reinforcement on multivariable might have less utility. But the level of these courses in AEP will be just as high as in the Physics department.</p>
<p>And, thinking about it now, it's not just E&M, it's quantum mechanics, statistical mechanics, dynamics, probability,- lots of subject areas draw on this material as a foundation..</p>