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Month: February 2013

Mathematics

Fréchet derivative of the (matrix) exponential function

Posted on February 28, 2013 by wj32 / 2 Comments

$$ D\exp(x)u = \int_0^1 e^{sx}ue^{(1-s)x}\,ds. $$ This intriguing formula expresses the derivative of the exponential map on a Banach algebra as an integral. In...

Mathematics

Convex functions, second derivatives and Hessian matrices

Posted on February 26, 2013 by wj32 / 1 Comment

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)\...

Mathematics

Differentiation done correctly: 5. Maxima and minima

Posted on February 25, 2013 by wj32 / 2 Comments

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

Mathematics

Differentiation done correctly: 4. Inverse and implicit functions

Posted on February 24, 2013 by wj32 / 0 Comment

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

Mathematics

Differentiation done correctly: 3. Partial derivatives

Posted on February 23, 2013 by wj32 / 0 Comment

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

Mathematics

Differentiation done correctly: 2. Higher derivatives

Posted on February 22, 2013 by wj32 / 0 Comment

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

Mathematics

Differentiation done correctly: 1. The derivative

Posted on February 21, 2013 by wj32 / 1 Comment

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

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