<p>I forgot to add this in my other thread.</p>
<p>I'm taking Diff. Eq. and Vector Analysis this fall. I've already started brushing up on DE-related stuff. What should I review for Vector Analysis? Thanks.</p>
<p>Multivariable Calculus. In some ways, Vector Analysis is just an expansion of that glass.</p>
<p>Yeah, vector analysis is sort of just a harder-core calc III.</p>
<p>I see. So what key areas should I review from Cal III?</p>
<p>Multiple integrals, coordinate transformations and the vector operations you learned in multi variable.(The gradient, divergence and rotation if you did them)</p>
<p>Yep. We did the gradient, divergence, the curl. I think we did rotation, too.</p>
<p>I suggest that when you take these math courses, you understand that they have real world applications and are not just theoretical constructs. I find too many of my students while able to manipulate divergence, curls etc have absolutely no understanding of what they really mean and how they are used.</p>
<p>Thanks, Doc. I’ll make sure to look at the applications.</p>
<p>Yeah, the fact that you didn’t recognize that curl and rotation are one in the same tells me that you probably didn’t have a ton of instruction into the physical meaning of the concepts, only the concepts themselves. If you learn these things as you are taking them, it will just make it easier to apply them later down the road if you already have some idea of their physical meaning. Tensors and tensor notation are also something you should pay attention to, as they rear their head in a lot of different fields quite a bit farther down the road.</p>
<p>Well, I finished Cal III Spring 2008 so I’m certainly a bit rusty. I vaguely remember curl on a sphere…?</p>
<p>I have my calculus book, of course, so I’ll take a look at that stuff shortly with increased awareness in the applications.</p>
<p>“I suggest that when you take these math courses, you understand that they have real world applications and are not just theoretical constructs. I find too many of my students while able to manipulate divergence, curls etc have absolutely no understanding of what they really mean and how they are used.”
- Really?</p>
<p>I find it’s much more of a problem that students in the “service” math courses don’t understand or appreciate the theory and instead become obsessed with applications and utility to the point of willful ignorance. I’d say go into the course with an open mind, and look for applications - actually look, don’t just complain if you don’t see any off hand - and if there are no applications then, well, learn it anyway. You’re paying good money for it, after all.</p>
<p>Actually, I prefer theory. I don’t have the disposition to be a math major, although I’m a math minor due to convenience, but I certainly enjoy and appreciate the theory behind mathematics. To me, if you know the theory a bit, the jump to application should be a natural one.</p>