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Today we reviewed polar integration and differentiation. To find the area within a polar curve. one sums up the area of the sectors, using the equation A = 1/2 * integral(f(theta)^2, theta1, theta2). Surface area is similar to the parametric method, but with the height function multiplied by sin(theta) or cos(theta).
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Review of basic integration techniques, as well as a review of the AB Calculus curriculum.
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Review of differential equations, namely how to solve them for a general solution, and then use a known point to find the particular solution.
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Review of Infinite Series - how to test for convergence, and how to solve for the sum of a geometric series (a / (1 - r)).
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Review of Talyor Series, polynomials, MacLaurian Series, polynomials, and power series. These can be used to approximate functions, or to represent trancendental functions. Very useful and cool.
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Review of techniques such as trig subadubdub and integration by parts (also partial fractions) - these techniques can almost always be used to solve tricky problems.
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Review of how to apply integration to solving problems - volume of an area rotated about an axis, surface area, arc length, that sort of thing.
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Simple review of polar functions - how to integrate, differentiate. We then did a little game to solidify our understanding.
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A challenging test on all things polar that I almost ran out of time on (I had to skip a problem).
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Explanation of solution to the free response questions on the take home test.
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Walked around the school completing a helpful review sheet that teaches one what to think about when they hear certain phrasing.
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The Actual AP Test for BC Calculus! It went surprisingly well, and I felt like I had aced it.
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We have split into groups and are researching "Family Feud" so that we can replicate with Calculus concepts.
