<p>I got accepted into this Summer Program, right before College. Among many things that happen, I have to take one class while I'm there. I've taken AP Calculus BC as well as a GCE A-Level Mathematics exam and I'm pretty confident on my Calculus skills after prolonged exposure to Mu Alpha Theta. I've checked with the university and I know I'll get Calculus I and II credit assuming I get a decent score (I'm extremely confident I will have gotten at the very least a 4 in BC Calculus). </p>
<p>The problems comes from the fact that this school makes Calc III and Diff. Eqs special by making them different for those in the institute of technology (calling them IT Calc III and IT Diff Eq. respectively). Supposedly, they have an emphasis on the use of computer technology (Mathematica and the like). However, these classes aren't offered over the summer, and they highly recommend I just take Calc II (also the fact that the scores haven't arrived yet make them weary of putting me in a higher class).</p>
<p>So, my question is, should I just take Calc II and take the IT Calc III and/or IT Diff. Eq in the fall, or just take Calc III or Diff. Eqs now, with no IT component? How hard is it to pick up Mathematica, Maple, or Matlab?</p>
<p>I go to a school that offers Mathematica math courses for all the engineering math classes (calculus/diff eq. series), and I hear that they are much easier than the equivalent pencil & paper courses. This may not be true at your school.</p>
<p>I think you should take the old-fashioned courses. You’ll learn more math that way, which will pay off in later classes, especially if you are in physics or will be taking a lot of physics-ish classes in whatever engineering department you’ll be in. Calc III and diff. eq. are fundamental for those subjects.</p>
<p>Calc III will be a test. If you really understood calculus I, then it won’t be too bad. If you thought limits were unimportant, a waste of time or knew the derivative only as “slope” or never realized that the S on the integral sign stood for “sum”, then you may find Calc III kind of tricky.</p>
<p>I think they are too, since it’s my understanding that anything involving calculators becomes easier. However, the school really pushes this, and I’ve heard from multiple sources that learning Matlab/Mathematica/Maple can be difficult, so I just wanted to hear CC’s thoughts. The school said that they didn’t want me “struggling with advanced problems” if I didn’t know the basics of Mathematica and matlab that I would learn in these classes.</p>
<p>Calc III wasn’t all that hard. I self-studied for the topic test at Mu Alpha Theta State Convention. It felt like single-variable, with just an extra variable. xD. The only part that messes up is the boundaries on the integrals. All the single-variable concepts come in, but slightly different. Tangent line becomes tangent plane, area under curve becomes volume under curve. The only ‘new’ things are vectors and their functions (int. of F . dr and the likes).</p>
<p>A couple of remarks . . . (below I will nitpick some stuff)</p>
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<p>Eh, I think it is way more profitable to think about the derivative as being local information about a function.</p>
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<p>I think the best interpretation of the integral is that it is the continuous analogue of the sigma (sum). How do you think about finding the mass of an object given its shape and a volume density distribution? Area under the hypervolume?</p>
<p>My stupid little lecture above was to say that slightly more sophisticated interpretations of calculus will pay off in later classes (esp. physics and probability). Since it sounds like you are already familiar with a lot of the stuff in calculus III, that’ll help you get past the mechanics of the material and understand a little bit about what is going on in calculus. This intuition is worth way more than being able to memorize all of the anti-derivatives for all the functions or whatever and will make your future courses way easier.</p>
<p>Local information of a function? Hmm… never thought about it that way.</p>
<p>As far as integral, yeah, that’s usually how I start teaching people who want to know how to integrate. Start out with the need to find areas of non-linear things, the idea of the Riemann Sum, then taking it to the limit. </p>
<p>However, my question remains: How hard is it to pick up Matlab or any of those programs?</p>
<p>It depends on how much experience you have with programming. Matlab, Mathematica, or Maple are all way easier than learning something like C though (and are much more pleasant to use!).</p>
<p>At my university we are required to take Calc 1 and 2 with the usage of Matlab or Maple, as well as taking DiffEq with Maple. These classes are not easier than classes taught without these computer programs as you need to learn both ways of doing the problems: by hand and by code. Generally, in these classes, calculators and computers were not allowed on exams or quizzes. So, it’s not like you had a differential equation that you were tested on and you just typed it in the computer and wrote down the answer the computer spat out. You had to show your work. But this is just my school, it could be different at yours (I don’t think so though).</p>
<p>I use Matlab quite often and it’s rather easy to learn. Most of the time the “hard part” is actually finding the function you want to do something. It can do A LOT of stuff, it’s just a matter of finding the function.</p>