<p>I revieced a 5 on the AP Calculus BC exam, and I have the option to go straight to Multivariable Calculus the fall of my Freshman year. Would it be a good idea to go straight to Multivariable Calculus Freshman year? If you did the same something, how was it for you. Were you able to handle the work load? How did Multivariable Calculus feel compared to previous Calculus courses? </p>
<p>Thanks </p>
<p>Oh, and I want to major in Aerospace Engineering </p>
<p>That’s really kind of a difficult question to answer as it depends highly on you. There is a very wide range in the level of preparation of people who pass the AP exams. Maybe the best thing to do is see if you can find some old calculus exams at the schools that interest you and see how easily you can work through them. It’s okay to be a little bit rusty, but you shouldn’t be clueless on anything on those exams.</p>
<p>You are probably safe skipping Calculus I, as that class is relatively easy so long as you come out of it understanding that derivatives are rates of change and integrals are effectively sums of infinitesimally small parts. Calculus II, on the other hand, is kind of a crap shoot. Do you really understand Taylor expansions? Those become quite important later on for aerospace engineers, and if you don’t have a reasonable understanding of what they are and what they represent, you may struggle a bit in certain later classes.</p>
<p>Hey boneh3ad, my son was selected for the same, direct placement into honors calc III. He’ll be studying ME. Since I took Calculus just before Brook Taylor’s work in 1712 
And it was sort of Calculus for Poets, what are the foundational skills from I and II that would be most applicable to ME? Thanks!</p>
<p>Well that is probably a bit more of an opinion question, but I will give it a shot. I’d call the following maybe the most important topics to know for mechanical and aerospace engineers. You can likely find other people who can think of things that I forget here or that have a different set of important concepts than I have based on their own experience.</p>
<p>[ul]
[li]Understanding that derivatives are not simply the slope of a line and that integrals are not simply the area under a curve. I know that the way my high school AP Calculus teacher taught the course, these two “applications” were heavily emphasized to the point that I was a bit pigeonholed into that train of thought and it took a little bit of unlearning to reprogram myself for engineering/physics applications where I had to recognize, for example, that all rates of change could be expressed as derivatives, thus the importance of differential equations.</p>[/li]
<p>[li]Being able to actually compute derivatives and integrals is important when it comes to trying to analytically get a feel for what various physical processes actually mean later on. A lot of students seem to be convinced that when they get farther along in their coursework, they will just use a computer to solve everything and don’t have to be bothered with computing by hand anymore, but if you are adept at manipulating the equations by hand first, you can come up with much better models and get a much better feel for things before dumping it into a numerical solver. Otherwise, there’s the saying “garbage in, garbage out.”</p>[/li]
<p>[li]I haven’t personally used series in generally very often, though in some branches of the field they are important. I remember in Calculus II doing convergence tests and just having no idea when I would ever need to know it, but things like radius of convergence due come up in areas like numerical analysis.</p>[/li]
<p>[li]I will address Taylor series separately because I think they are important enough to warrant their own bullet point. Taylor series will be used extensively in later courses. They are used to linearize equations and develop new models that simplify complex physics, they are used to build many numerical solution methods, and just in general, it seems like if you are stuck on what the next step in deriving an equation in a later class, more often than any other solution, the next step seems to be to Taylor expand and drop the higher-order terms.</p>[/li]
<p>[li]Exponential growth pops up literally everywhere and I believe that is generally covered in one of the two calculus classes. Exponential growth is life… literally.[/li][/ul]</p>
<p>I feel like most of the rest of the topics can be easily understood if you have a grasp of these ones, especially the first. If you understand, truly, when and how to apply derivatives and integrals, then other concepts like arc length and surfaces of revolution are much easier to understand and can be reasoned out fairly easily even if you don’t remember all the details.</p>
<p>Anyone else, feel free to add onto this list if I forgot anything. I am sure I probably have.</p>
<p>I will print this sage advice and pass it on. Thanks boneh3ad!</p>
<p>I did not do well in MV calc my first semester. My content preparation from AP was fine, but I didn’t understand how to study independently at the university level. Would have been fine if I had made more of an effort.</p>
<p>So it’s doable as long as I work hard, and know my stuff. </p>
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<p>That’s pretty much 90% of college and 50% of life in general :-)</p>
<p>Tangible action item - hunt down past finals from your prospective school.</p>
<p>Ok, thanks. </p>
<p>D had the same option at Purdue, she is a ChemE. She took her last Calc class her junior year so we were concerned. She chose to take the credits and take Multivariable Calc. At the beginning of the course she said “she needed to get her math brain back”. In the end she ended up with a B. Her second semester she took linear algebra and got an A. She also got credit for several other AP courses. The biggest advantage is that it allows her to take 14-16 hrs a semester rather than 17-18. She can also play in the orchestra. I’m just giving you an example of our experience. Good luck with your decision.</p>
<p>Thank you </p>
<p>Your other posts indicate University of Minnesota.</p>
<p>Try these old final exams for calculus 2 to check your knowledge:
<a href=“Home - Math 1272: Calculus II - Research Guides at University of Minnesota Minneapolis”>Home - Math 1272: Calculus II - Research Guides at University of Minnesota Minneapolis;
<a href=“https://diversity.umn.edu/multicultural/practiceexams”>https://diversity.umn.edu/multicultural/practiceexams</a></p>
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<p>Yes, this is important to know about the transition from high school to college. Even if you were learning college level material in high school (e.g. a well taught calculus course in high school), the high school course environment includes much more hand-holding and progress monitoring so that students won’t fall too far behind. The college course environment requires much more student self-motivation than the high school course environment, which is why you may see students trying to cram an entire course the week before the final, or trying to do a multi-week term project in the last week.</p>
<p>Success in college should not be too difficult if you:</p>
<ul>
<li>Attend class.</li>
<li>Do the readings.</li>
<li>Do the assignments.</li>
<li>Start projects early.</li>
<li>Ask the instructors (faculty and TAs) for help if needed (and not just the day before the test).</li>
</ul>
<p>As my professor stated: Multivariable is just everything you’ve done before, just that now you have to do them in 3 dimensions. There is less homework (practice on your own if you can), the problems can be a little trickier than previous Calculus courses. The course really depends on the student and professor! Some that aren’t the best at math get an easy A out of it while those that are really good have gotten a first non-A! <–Those are mixed opinions I got before entering my freshman year.
In my opinion, it was an easy A.</p>
<p>In my opinion, Cal 2 is much harder than multivariable calculus AKA cal 3 (although cylindrical/spherical coordinates was a bit tough for me; I managed in the end though). Cal 3 is just Cal 1 in three dimensions. 50% of my cal 3 class skipped every single class before the midterm (it was basically review: vectors and whatnot) and most of them still managed to make an A.</p>
<p>Going into Cal 2 is probably going to be just as tough if not tougher than going into Cal 3. I think it also depends on where you take your class though. I took all my cal courses at a large public university. If you are attending a liberal arts college or more rigorous college with a smaller teacher/student ratio, it might be more challenging. I highly doubt that this would make a difference in the relative difficulty levels between cal 2 and cal 3 though.</p>
<p>This is assuming he knows his stuff. The challenge with high school students skipping to college classes is the disconnect between memory and comprehension. In high school, the definition of a derivative was pretty much memorized. “Rate of change” I remember saying. In college, Calculus profs assumed you understood what derivatives meant. The class took a quiz and the question had to do with velocity. For the life of me I couldn’t figure out the answer, and after talking to the prof, I had to realize acceleration was the derivative of velocity and using the acceleration equation or function, I could determine the appropriate data for velocity. </p>
<p>If the op simply memorized what a term was and doesn’t understand the context, skipping may not be a wise idea. Although I will say that first half of Multivariable was not difficult. Double derivatives, intergrals, vectors etc… Essentially a refresher course on Calc I II and physics. Polar, Cylindrical and Spherical coordinates were funky for me as well, although it wasn’t the math. It was the set up needed before you could actually solve the problem. However to set up the problem, it is assumed you understand the problem. If op simply has a superficial understanding of derivatives and intergrals, even if they manage to do well in Calc III, they can have a large problem in physics. </p>
<p>I agree with boneh3ad’s analysis in post #3, as usual its spot on; except for one thing. Sequence/series and testing for convergence/divergence comes up later in Differential Equations and to be quite honest is the entire point of the course.</p>
<p>When you get done multivariable calculus the next course in line is Differential Equations AKA calculus IV. DiffEq will start off explaining to you the importance of the course(if the professor is worth his pay), what a differential equation is and what you’re going to be learning in the class. What you’ll be doing in the course is finding some function f(x) which satisfies the differential equation, its basically like being given the equation 6=5x+7 and being asked what x satisfies it.</p>
<p>After the introduction to the course you’ll be learning how to identify and solve various forms of differential equations like 1st order linear homogeneous equations, 1st order linear nonhomogeneous equations, 1st order non linear homogenous equations, 1st order nonlinear nonhomogenous equations, special cases of the previously mentioned differential equations and then you move onto higher and higher order differential equations and their special cases; all of which will have EXACT ANSWERS.</p>
<p>Next, you’ll learn how to approximate answers for differential equations with exact answers, basically you’ll be using sequences/series and tests of convergence to find the answers of all the stuff you learned earlier in the course to reveal to the you that it is possible to approximate answers using sequences/series and tests of convergence. </p>
<p>Lastly, you’ll be learning the entire point of the course, Laplace transformations, which is approximating differential equations for which we literally cannot find an exact answer to.</p>
<p>Now depending on what field you’ll be going into you may or may not have to use differential equations and therefore sequences/series and tests of convergence aren’t that important. </p>
<p>Differential Equations isn’t that scary of a course until you get into the approximations and is when I did poorly because I never grasped how to identify/manipulate various series,how to use their tests of convergence, and more importantly how to approximate functions using taylor/maclaurin series because the professor never emphesized why it was important along with it being a hard subject to begin with (which takes a very very special person to have a strong command of) and I just thought screw it, i’ll never use it again which ended up haunting me in DiffEq</p>
<p>PS: despite the name of the course being “differential” equation you use more integration than differentiation. So, make sure your integration techniques are up to snuff</p>
<p>Series are certainly important, but I can still honestly say that in all the differential equations I have used since learning the basics back during my sophomore year of college, I have not once that I can remember been required to perform a convergence test in order to solve a differential equation.</p>
<p>More often than not, equations fall into the broader categories (e.g. Sturm-Liouville problems) where a lot of the heavy lifting has been done previously and it is relatively “easy” to solve analytically without having to do any kind of convergence tests. If you get a bit deeper into math later in your career you can eventually learn about perturbation theory which lets you overcome some of the weaknesses inherent in the earlier techniques when there are singularities, but again, there generally isn’t much need to do a convergence test.</p>
<p>For much more complicated problems where you don’t need (or have no hope of getting) an analytical solution, then you “simply” need to know finite differences, Fourier series, and/or polynomial interpolation to get a good answer. Understanding some of those techniques definitely require the use of series and convergence tests, but you don’t generally have to perform one every time you go to solve a problem.</p>
<p>So I guess my point is that yes, those topics are important for a nontrivial number of students, but are not going to have the same impact on an engineer’s everyday life throughout school (and potentially later) as the ones I mentioned.</p>
<p>For what it’s worth, I was pretty pitiful when it came to convergence of series. I think they would probably be a lot easier to go back to now, knowing what I know. It’s amazing how many topics are like that now that I think about it (circuits, control theory…).</p>
<p>Multivariable Calculus is not that bad with the exception of the proofs.
I took the course in my sophomore year of high school.</p>
<p>“Do you really understand Taylor expansions? Those become quite important later on for aerospace engineers, and if you don’t have a reasonable understanding of what they are and what they represent, you may struggle a bit in certain later classes.”</p>
<p>@boneh3ad Does that apply equally to mechanical as well as to aerospace?</p>