## Convex functions, second derivatives and Hessian matrices

In single variable calculus, a twice differentiable function \(f:(a,b)\to\mathbb{R}\) is convex if and only if \(f^{\prime\prime}(x)\ge 0\) for all \(x\in(a,b)\...

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# Author: wj32

## Convex functions, second derivatives and Hessian matrices

## Differentiation done correctly: 5. Maxima and minima

## Differentiation done correctly: 4. Inverse and implicit functions

## Differentiation done correctly: 3. Partial derivatives

## Differentiation done correctly: 2. Higher derivatives

## Differentiation done correctly: 1. The derivative

## Some series convergence problems

## Every continuous open mapping of R into R is monotonic

## PAE patch updated for Windows 8

## Free product of free groups and group presentations

information when you need it

In single variable calculus, a twice differentiable function \(f:(a,b)\to\mathbb{R}\) is convex if and only if \(f^{\prime\prime}(x)\ge 0\) for all \(x\in(a,b)\...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima In this final post, we...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima Now we’re going ...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima While we saw that diff...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima Last time, we covered ...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima In multivariable calcu...

Here are some series convergence problems that I gathered quite a while ago. A few of them are a bit tricky.

I’m willing to bet that most students who have used Rudin’s Principles of Mathematical Analysis have encountered this problem: 15. Call a mapping of...

Note: An updated version for Windows 8.1 is available. This patch allows you to use more than 3/4GB of RAM on an x86 Windows system. Works on Vista, 7, 8, has b...

Here is Problem 9-4(b) from Introduction to Topological Manifolds by John M. Lee: Let \(S_1\) and \(S_2\) be disjoint sets, and let \(R_i\) be a subset of the f...