# Browse Classroom Capsules and Notes

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Displaying 61 - 70 of 1212

Here is a technique for proving the fundamental theorems of analysis that provides a unified way to pass from local properties to global properties on the real line, just as ordinary induction...

A typical first course on linear algebra is usually restricted to vector spaces over the real numbers and the usual positive-definite inner product.  Hence, the proof that $\dim(\mathcal{S... Hölder’s inequality is here applied to the Cobb-Douglas production function to provide simple estimates to total production. Mathematical elegance is illustrated by rewriting the product and quotient rules of basic calculus in strikingly parallel forms. Applications are given for which these forms suggest meaning.... The author provides a somewhat recreational application of limit interchange and L'Hopital's rule. The goal is to hint at the importance of limit/sum interchange in Analysis without,... Using a simple trigonometric limit, the author provides an intuitive geometric proof of the Singular Value Decomposition of an arbitrary matrix. Motivated by the observation that the derivatives of \(e^x$ are all positive and the derivatives of $e^{-x}$ alternate sign, the author asks what kinds of sign patterns" are possible...

The author provides a simple context and some history in which actuarial computations take place.

In a classic pouring problem, given two unmarked jugs with capacities $m$ and $n$ pints, where $m$ and $n$ are relatively prime integers, and an...

Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to...