copper.hat
Reputation
90,131
377/400 score
 43m comment Multistep Method: Gear's Formula Interpolation When you compute $q'(t_{n+1})$ you should have a formula that involves $h, y_{n+1}, y_n, y_{n-1}$. Equate this to $f(t_{n+1},y_{n+1})$ to get the formula above. 11h comment Multistep Method: Gear's Formula Interpolation Something like $q(t) = y_{n-1} {(t-t_{n})(t-t_{n+1}) \over (t_{n-1}-t_{n})(t_{n-1}-t_{n+1}) } + \cdots$. 17h comment Multistep Method: Gear's Formula Interpolation You need a quadratic polynomial that passes through the three points $(t_i, y_i)$ with $i=n-1,n,n+2$. 17h comment Multistep Method: Gear's Formula Interpolation The instructions given above are fairly explicit. Write a formula for the polynomial $q$ given the data points $(t_i,y_i)$. Compute $q'(t_{n+1})$. Remember that there is a constant step size, so $t_{i+1}-t_i = h$. 20h comment How do I link dimension of a normed vector space with closedness? $W$ is closed regardless of dimension because translation and $x \mapsto \|x\|$ are continuous and $[0,r]$ is closed. 20h comment How do I link dimension of a normed vector space with closedness? What is $W$? ${}{}{}$ 21h comment Uniform unboundedness of linear operators @MatthewKvalheim: I have had my intuition thwarted so many times that I would say you need to split your time between looking and trying to prove! 21h comment Uniform unboundedness of linear operators @DanielFischer: Almost certainly! 21h comment Uniform unboundedness of linear operators @DanielFischer: That's funny, I am usually the slowest! 22h comment If a subset of metric space $(X,d)$ like $S$ is closed and bounded, does it imply that $X$ is totally bounded? @BrianM.Scott: I often feel that the discrete metric is cheating :-). 23h comment If the integral of $|f_n|$ converges to zero, so does the integral of $f_ng$ for integrable $g$ What does the $0$ on $C_{cpt}^0$ mean? 23h comment If the integral of $|f_n|$ converges to zero, so does the integral of $f_ng$ for integrable $g$ For (b), note that the compactly supported continuous functions are dense in $L^1$. 1d comment Normal modes energy terms This would probably get better answers on the Physics SE. 1d comment How to combine inequalities Draw a picture. 1d comment Initial value problem $y'=e^{-y^{2}}-1.$ If there is a solution defined on the real line and $f$ is locally Lipschitz, then the solution is unique. 1d comment How to identify an orthogonal(orthonormal matrix)? Vectors are orthogonal if their inner product is zero. 1d comment How to identify an orthogonal(orthonormal matrix)? Well, you could notice that the columns (or rows) are orthogonal and that the columns have unit length. This is equivalent to computing the product... 1d comment How to identify an orthogonal(orthonormal matrix)? Note that $A^n = \begin{bmatrix} 1 & n \\ 0 & 1 \end{bmatrix}$. Also note that $P^T Q^{2005} P = P^T A^{2005} P$. 1d comment Isometric embedding of $\ell ^ 1$ in $\ell ^\infty$ in finite dimensions What do you mean by embedded? 1d comment Initial value problem $y'=e^{-y^{2}}-1.$ Glad to be able to help!