Christopher A. Wong
Reputation
12,623
Top tag
Next privilege 15,000 Rep.
Protect questions
 Jan 22 comment Evaluate complex integral using deformation theorem Hint: You can evaluate the circle integral (integral about $\gamma$) directly by parametrizing the circle. Jan 21 comment Prove that $W = \{u = (x, y): y = 5x\}$ is a subspace of $\mathbb R^2$. Interpret $W$ geometrically. What's the dimension of $W$? @user306944, every vector space is a linearly dependent set. Jan 21 comment Prove that $W = \{u = (x, y): y = 5x\}$ is a subspace of $\mathbb R^2$. Interpret $W$ geometrically. What's the dimension of $W$? This looks fine. Depending on who is teaching your course, they may be a little bit pedantic about showing explicitly that $0 \in W$. Also, be explicit about determining the dimension of a subspace. For example, you could write down a basis for $W$, and count the number of basis vectors. Because often it is not obvious what the dimension of a space is without doing some computations. Jan 17 answered How to find “unique” eigenvalues when computed numerically? Dec 31 awarded Yearling Dec 10 comment How to compute this integral If I use the word "residue" does that put you in the right direction? Dec 9 comment No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy Your proof does not fail; you observed that $1/f$ is analytic and $|1/f|$ obtains a strict max at $z = 0$, which is impossible. Dec 9 comment No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy You seem to be missing some words. "contradiction the fact the $f$ isn't". The only thing I can point out is that you don't need to discuss anything about $f$ obtaining a max; all that matters is $1/f$. Dec 1 comment How do I do a finite expansion of $\int e^{x^2} \, dx$? We typically say "expressed in terms of elementary functions" instead of "finite expression" because otherwise you could just say that $\mathrm{erf}(x)$ (times some constant) is a finite expression for the antiderivative. Dec 1 comment Euler differential equations Do you know the "Method of Undetermined Coefficients"? It can be applied to determine the solution to the inhomogeneous problem. Nov 23 reviewed Approve $P = \{x \in \Bbb R^n \mid x \cdot v = 0\}$ is a subspace of $\Bbb R^n$ Nov 19 comment Finding hilbert space basis Note that the method you've proposed will produce an orthonormal basis, whereas in the question you didn't specify that requirement. However, the work you've done will give you an answer. In the last three equations for $x_1, x_2, x_3$ that you wrote, you can substitute the 1st and 2nd equations into the 3rd into order to solve for $x_1$ (not a unique solution), from which you can obtain $x_2, x_3$. Nov 18 reviewed Close Reduction formula for $\int_0^{\pi/2}\cos^m\theta\sin^n\theta\,d\theta$ Nov 12 comment Undefined partial derivative with respect to complex conjugate independent of Cauch-Riemann equations? No. The C-R equations literally say $\partial f/\partial \bar{z} = 0$, which is not satisfied if you cannot even compute the derivative. Nov 10 comment Does an equation of this type have complex solutions? @Arthur, completing the square is equivalent to using the quadratic formula, since that is how the quadratic formula is derived. Nov 6 comment Frechet Derivatives of a nonlinear integral operator Based on what you've said, it seems clear to me that that term cannot be controlled in the usual topology of $C[0,1]$. Nov 4 comment Integral of $\int_0^\infty \frac{\sin^4(u)}{u^{k}}du$ where $k\in(1,3)$ It's convergent because the integrand is bounded in a neighborhood of $0$ and decays like $x^{-k}$ for large $x$. Nov 4 comment How can I prove this proposition of linear algebra? Try performing the row-pivoted LU by hand on a 3x3 matrix, perhaps, to see what the entries of L look like. Nov 3 reviewed Approve How can I prove this proposition of linear algebra? Nov 3 answered How can I prove this proposition of linear algebra?