Antiderivatives as Areas

Integral calculus is mainly concerned with the area below the graph of a function. Let’s investigate that. Geometry and Areas The most common areas used in integration are triangles, \(A = \frac{1}{2} bh\), and rectangles, \(A = bh\), where \(b\) is the base, the \(x\)-axis, and \(h\) is the height, the \(y\)-axis. def area(b, h, polygon="rectangle"): if polygon == "triangle": A = 1/2 * (b * h) else: A = b * h return A Distance as Area A vehicle travels at 50 mi/hr for 2 hr. …

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Antidifferentiation

Antidifferentiation is the process of, given a function \(f(x)\), finding another function \(F(x)\) whose derivative is the given function, \(\frac{d}{dx} F(x) = F^\prime(x) = f(x)\). Antidifferentiation and the antiderivative are part of a larger process called integration. Formally, the antiderivative of \(f(x)\) is the set of functions \(F(x) + C\) such that \[\frac{d}{dx}[F(x) + C] = f(x)\] where \(C\) is what’s called the constant of integration. This can be restated as follows: if two functions \(F(x)\) and \(G(x)\) have the same derivative \(f(x)\), then \(F(x)\) and \(G(x)\) differ by at most a constant \(F(x) = G(x) + C\). …

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Notes on Development Environments

After trying to figure out to make Vim, Python, Zsh, and Tmux play along for the second time in a couple of years, I came to the conclusion(s) that: spending hours on end reading docs for things that other tools offer at a much lower barrier to entry is not worth it. losing your temper over even the smallest of battles (e.g how to change colors in Tmux, or configuring setup files) is a waste of energy. …

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Economics Applications of Derivatives

Some interesting things you can do with derivatives in the context of economics are to: Find the price elasticity of a demand function. Find the maximum of a total-revenue function. Characterize demand in terms of elasticity. Retailers and manufacturers often need to know how a small change in price will affect the demand of a product. If a small increase in price produces no change in demand, then the price increase is a reasonable decision to make. …

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Beware of Code on the Internet

As I try to figure out how to ease back into Vim, Tmux, and other “esoteric” tools, I’m reminded again that you should never trust people’s suggestions on the Internet (especially their code). I suspect that the hundreds of blog posts on “how to configure x”, “how to setup y”, or “why everyone should be using z” contribute to the general attitude of mistrust that I have towards people trying to be helpful online. …

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