calculus of variations
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Part 1a of the 2008 BC free response.
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Parts b and c of problem 1 (free response).
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Parts c&d of problem 1 in the 2008 AP Calculus BC free response.
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Part 1d of the 2008 AP Calculus BC exam (free response).
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We first apply our big idea--backward induction--to analyze quantity competition between firms when play is sequential, the Stackelberg model. We do this twice: first using intuition and then using calculus. We learn that this game has a first-mover advantage, and that it comes commitment and from information in the game rather than the timing per se. We notice that in some games having more information can hurt you if other players know y...more
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Behavioral Finance is a relatively recent revolution in finance that applies insights from all of the social sciences to finance. New decision-making models incorporate psychology and sociology, among other disciplines, to explain economic and financial phenomenon, such as erratic stock price variations. Psychological patterns such as overconfidence and perceived kinks in the value function seem to impact financial decision-making, but are...more
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Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists).
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2a of 2008 Calculus BC exam (free response).
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Parts 2b and 2c of the 2008 BC exam (free response).
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Part 2d of the 2008 Calculus BC exam free-response section.
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Using calculus and vectors to show that centripetal acceleration = v^2/r.
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Calculus-Derivative: Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line).
