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chessapig.github.io | ||
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divisbyzero.com
Below you will find some of the applets that I wrote. Some of them have an associated blog post. Enjoy Calculus and Real Analysis A continuous, nowhere differentiable function: the Blancmange function (blog post) Epsilon-delta definition of limit of a function (blog post) The limit of a sequence(blog post) Cantor set (blog post) Using a... |
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stephenmalina.com
Selected Exercises # 5.A # 12. Define $ T \in \mathcal L(\mathcal P_4(\mathbf{R})) $ by $$ (Tp)(x) = xp'(x) $$ for all $ x \in \mathbf{R} $. Find all eigenvalues and eigenvectors of $ T $. Observe that, if $ p = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 $, then $$ x p'(x) = a_1 x + 2 a_2 x^2 + 3 a_3 x^3 + 4 a_4 x^4. |
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mathwithbaddrawings.com
This generalizes, of course, to the Theorem of How You Learn Stokes' Theorem. |
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bldavies.com
Let \(A\) be the \(n\times n\) matrix with \({ij}^\text{th}\) entry \(A_{ij}=\min\{i,j\}\). From a previous post, we know \(A\) has a tridiagonal inverse \(A^{-1}\) with \({ij}^\text{th}\) entry1 $$\left[A^{-1}\right]_{ij}=\begin{cases} 2 & \text{if}\ i=j |
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