<p>My question is: how much does multi depend on a solid AP Calc BC foundation?</p>
<p>During senior year, I slacked off a lot. I'm placed in multi because I managed to get a 5 on the BC test through memorization. I don't know ANY of the concepts behind Taylor series or that Lagrange stuff, only how to carry it out. I don't fully grasp what all the convergence-divergence deal was about either, but I did memorize the "kinds" of functions that belong in either category. For a lot of the more complex types of integration, I just ignored them and they turned out not be a big part of the test.</p>
<p>So basically, does multi review the theory behind all the basic stuff, if it builds off of that at all?</p>
<p>You won't have to deal with series, but you better make sure your integration is solid. Without a good foundation in integration (differentiation is pretty easy, relatively), the new forms of integration (multiple, line, Stokes', Greene's theorems) will be tough to grasp. But unless your going to the honors section, your professors will probably review requisite material.</p>
<p>Yeah you have to be very good at integration (and differentiation). A little error on one line can be hard to find when doing a triple integral or something like that. The thing i had to brush up on the most was u-substitutions, we used them a lot. Also, know that sin^2 + cos^2 = 1 haha</p>
<p>hmm, i'm taking it this coming semester, but coming from my friend who took it where I go to school, he said it was mostly IBP, and not as much u-substitution. maybe there's a lot of more implicit u-subs, or maybe the problems at my school just tend to IBP more</p>
<p>I didn't need any fancy integration techniques in multivariable calculus. </p>
<p>In multivariable calculus we learned how to integrate a function of several variables by reducing the problem to integrating a function in one variable. The new/interesting part is reducing the problem, not evaluating the final integral. That's what my professor thought and that's why he never had us integrate anything tricky or messy, only the standard integrals from calc 1 and 2.</p>
<p>I felt that MVC was a lot different from the other two calculus classes. IMHO, the integration is MVC was A LOT easier than in calc II. MVC is a weird class. I didn't use my past knowledge of calc much in the course except for basic substitution to solve the integrals. You need to know basic differentiation also, of course.</p>
<p>It can vary a bit. I thought knowing some basic linear algebra helped a lot - simple stuff: vectors, dot product, cross product, matrix multiplication. Nothing fancy, but you ought to know how to do them and be fairly fluent.</p>
<p>My calc-3, the professor did nearly <em>everything</em> in polar/cylindrical/spherical coordinates (after briefly introducing the cartesian version). Your class may be simpler in this regard, but it's likely worth knowing polar and spherical coordinates well and be able to write the change-of-variables readily.</p>
<p>Same with differentiation and integration. Nothing fancy, but you should be fairly fluent in the basics. This means ripping off stuff like chain rule, integration by parts, u-substitution, without skipping a beat.</p>
<p>It can also be helpful to know how to sketch 3D graphs, but I was downright awful at it and it's not that big a hinderance.</p>
<p>in multi, most of the integrals and derivatives that they ask you to do are polynomiel. It is assumed that you have mastered IPB and trig and u substitutions in single variable. They are not testing your ability to differentiate or integrate… they want you to understand the concepts behind the formulas. I did not find multi to be too difficult. you just need to see conceptually where the formulas come from. Most of them, despite looking complicated, are very intuitive on the simplest level.</p>
<p>Multi dealt largely with three-dimensional coordinate systems. Lots of integration was used in the course but not complex integration methods were required. If you want to be ready for the course, study 3D graphs… This course sucked for many people because they simply could not picture or visualize many of the graphs. Knowing Linear Algebra helped me with multi. All in all I thought it was the toughest of the calculus sequence.</p>
I don’t know how “hard” multivariable calculus would feel to you (that depends a lot on your personal inclination for math and the instructor who’s teaching your course), but HL Math does cover all of the calculus background you need for multivariable calc. Even better: you already have some intuition for 3-dimensional geometry from the vector calculus and matrix portions of HL Math.</p>
<p>The one thing that might be useful to review is how to change coordinates. Multivariable calculus often switches between coordinates to exploit the symmetries of your problem. You definitely need to know how to change coordinates, and recognizing when a change of coordinates might simplify an integral will make your life a whole lot easier. I don’t think HL Math emphasizes this a whole lot.</p>
<p>OP, I was in pretty much the exact same boat as you last year. Multivariable has very little to do with BC stuff. I memorized BC stuff, too; but my AB stuff were solid.</p>
<p>I did very well in multivariable. The biggest thing is you truly have to understand and visualize the concept in multivariable. You will be fine if you put the time and effort into it.</p>
<p>I am TAing this course right now and here are things you just need to know to succeed</p>
<p>1) How to integrate by parts and use u-substitution. If time permits, review on trig substitution to prepare for spherical and polar integration.
2) Know some trig identities and is comfortable with polar coordinates
3) Depending on the instructor, series can be a topic, but it wouldn’t be stressed so hard.
4) Know how to solve simultaneous equations for Lagrange Multipliers.
5) Know how to take basic derivaties - know your product rule, chain rule.
6) Review some calculus I theorems on absolute max/min on closed intervals. We had a quiz last week and everyone bombed it.</p>