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Basic Integration
Today we talked about some basic integration and AB topics before we went away for Spring Break. I have to remember to first make sure integration problems cannot be easily solved with AB methods before breaking out the BC toolbox. There's a weird kind of u-substitution, in which extra x's are replaced with their u equivalents, which lets you solve integration problems more easily than using parts. Also, don't forget about dividing certain fractions before integrating. -
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Calculus AP Review
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Differential Equations
Probably my worst unit, maybe tied with conics/polar/parametrics. I have the most trouble with logistic DifEQs, especially integrating and graphing them. I should remember that the fastest rate of change occurs at half the carrying capacity, and to find what that rate of change is, I plug this population into the dP/dt equations as P to get the rate of change. I also need to review Newton's Law of Cooling, since it's weird. The rate of cooling is proportional to the difference of temps. -
Series Convergence
Today we graded homework from over the break and talked about series convergence, which was my favorite unit this year. I need to remember that for the ratio and root tests, we are looking for the result to be less than one in order to be convergent. For the LC test, it doesn't matter what number we get, as long as it isn't zero or infinity. If you can easily integrate something and the other tests won't work, use the integral test. But really, try to avoid using the integral test. -
Infinite Series
Today we talked about infinite series, which are the reason I took calculus in the first place (and also to avoid making the guidance department mad at me). There's this one series type that we didn't talk about much during this unit that keeps coming up in our practice problems. It looks like (k^(3/2)+3k)/(9k+3) or something along those lines. I've determined that the LC test is the way to go. In the comic, problem number 2 on her test is what I was talking about, only alternating. -
Taylor Series
Today we talked about Taylor polynomials and series. I need to review the use of the LaGrange error bound, which is for non-alternating series. I should remember that when we are estimating for sine and cosine, I should use 1 as the max value because that is the max value for both of those. I also need to review common power series. I remember sine, cosine, arctan, e^x, and 1/1-x well, but have trouble with ln(x) and ln(x+1). Also, it's worth noting that 1/1-x and 1/1+x are geometric. -
Advanced Integration
We graded homework today, and I did much better than I'd done on the last couple weeks of homework (it helped that I had a math party all-day Sunday). I'm doing pretty well with convergence of series and can usually get Taylor polynomial questions, but I have trouble with DifEQs still, especially logistic ones. We talked about advanced integration, and while I can do parts and partial fractions well, I have a lot of trouble with trig-based problems, especially knowing when to use identities. -
More Advanced Integration and Applications
Today we reviewed more applications of integration and advanced techniques. Fortunately, trig sub will not be on the test, though I'm very worried about having to integrate secant cubed of x and I may have a panic attack if I see it. I need to review volume and surface area of revolution as I got confused about how to account for revolutions around lines other than x=0 or y=0. Also, I asked Mark if you could revolve functions around curved lines. We decided they would destort. -
Review for Polar Exam
Today we reviewed for our Polar Test, which everyone else will take tomorrow and I will take on Monday. I'd forgotten some important things like the simplified arc length formula, but since I remembered the parametric one, in a pinch I would still be able to solve the problem. I also need to remember that when you find the tangent lines at the poles you solve for r=0 and then you get dy/dx at that. I also need to practice my graphing. -
More Polar Review
I missed today's Polar Test for Law Day, so this is a continued review of the topic. I need to work on converting polar equations to linear ones. First, you look to see if the polar function is obviously a linear function that you know (like a line or a circle). If not, then find ways to substitute x and y using x = rcostheta and y = rsintheta or x^2 + y^2. I should also review converting polar coordinates to rectangular ones and vice versa. Also, watch out for hungry lemniscates. -
AP Practice Problems
Today Mr. Hyman had mysteriously vanished, so we did some AP practice problems. The multiple choice problems seemed to take a lot more time than usual to do, although that may have been because I had to show all my work as opposed to randomly skipping steps like I usually do. Sometimes the wording of the questions is extremely confusing, and I mixed up the mean value theorem for derivatives with the mean value theorem for integrals. Don't use velocity function to find average velocity! -
Polar Test of Doom
So today I took the Polar Test while simultaneously listening to a lecture on genetics. The material wasn't scary but there was a lot of problems to do and I didn't have much time to check them. I apparently need to work more on converting between polar and rectangular coordinates, since I'm having trouble still. Also, I forgot how to do tangent and did adjacent over opposite, but fortunately I fixed that right before time was up. (I searched 'scary lemniscate' and found this.) -
The Final Countdown!
Today we went for a randomwalk (as in the math term) around the school area and discussed calculus things. I also reviewed all of the units and realized that none of our practice APs ever involved any conic sections, which is a relief because I'm terrible at those. The final things I need to remember are to put the +C's on indefinite integrals, finding average velocity does not involve using the velocity function, and to make sure problems are asking for relative extrema, and not absolute. -
The Judgment Day is Upon Us!
Today we had the AP exam. The multiple choice seemed much easier than the practice multiple choice we did, and it took much less time. Only a couple of the questions actually seemed to involve BC material--most were just AB stuff. The free response questions were a little bit weird. Sometimes they used terms we didn't use in class, like linear approximation, but I finished everything and got to check some of it. I think I did alright.
