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bio website mathtm.blogspot.com
location University of California Los Angeles, CA
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visits member for 2 years, 2 months
seen Jul 16 at 15:11

I am a recent graduate in applied mathematics at UCLA and currently trying to break into the quantitative investment/trading industry while also continuing to pursue advanced graduate-level mathematics as both a hobby and career necessity.


May
9
comment Questions about surface integrals and an example problem
What do you mean? It's just notation for integrals; you're not literally multiplying anything by $dS$. $\int_{S}(x+y)\;dS$ just means integrate $(x+y)$ over $S$ with respect to the surface measure $dS$. To reduce matters to an ordinary iterated Riemann integral, you parameterize the surface and pull back $S$ to the parameter domain $D$, and along the way $dS$ becomes $|\phi_{u}\times\phi_{v}|\;du\;dv$. This can all be made rigorous, and indeed, if you looked in your calculus text book you would find a sketch of the proof.
May
9
comment Variation of parameters: $y''-y'-2y=4e^{-t}$
Your answer is fine. It depends on what you take to be $y_{1}$ and $y_{2}$; permuting them in the definition of $W$ will only change the sign, since $W$ is a determinant. But once you decide on your labeling, you must be consistant with the definitions for $v_{1}$ and $v_{2}$ (see the derivation of $v_{1}$ and $v_{2}$ in your text book).
May
9
comment Variation of parameters: $y''-y'-2y=4e^{-t}$
$W[e^{-t},e^{2t}](t)=2e^{-t}e^{2t}-(-e^{-t}e^{2t})=2e^{t}+e^{t}=3e^{t}$.
May
9
answered Variation of parameters: $y''-y'-2y=4e^{-t}$
May
9
answered Questions about surface integrals and an example problem
May
9
revised Riemann-Lebesgue lemma
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May
9
answered Riemann-Lebesgue lemma
May
9
awarded  Yearling
May
8
revised Let $f$ be a real-valued function on $[a,b]$ such that $f(x) = 0$ for all $x \neq c_1,…,c_n$. Prove that $f \in R[a,b]$ with $\int_a^b f = 0$
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May
8
revised Let $f$ be a real-valued function on $[a,b]$ such that $f(x) = 0$ for all $x \neq c_1,…,c_n$. Prove that $f \in R[a,b]$ with $\int_a^b f = 0$
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May
8
comment Let $f$ be a real-valued function on $[a,b]$ such that $f(x) = 0$ for all $x \neq c_1,…,c_n$. Prove that $f \in R[a,b]$ with $\int_a^b f = 0$
Once $\delta$ is small enough, the $c_{n}$ do lie in separate sub-intervals.
May
8
answered Let $f$ be a real-valued function on $[a,b]$ such that $f(x) = 0$ for all $x \neq c_1,…,c_n$. Prove that $f \in R[a,b]$ with $\int_a^b f = 0$
May
6
revised Find $[E(Y^2)]$. When $Y = 3 * X - 5$ and $X$ is distributed in range $[0, 5]$
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May
6
revised Find $[E(Y^2)]$. When $Y = 3 * X - 5$ and $X$ is distributed in range $[0, 5]$
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May
6
answered Find $[E(Y^2)]$. When $Y = 3 * X - 5$ and $X$ is distributed in range $[0, 5]$
May
6
answered Fourier transform and sufficient condition…
May
6
answered Consider the differential equation: $y'=\frac{x^2}{1-y^2}$
Apr
29
comment Left sided limit of an Riemann-Stieltjes integral
Yes, that's fine, since $\alpha$ is left continuous at $b$ and $|f|$ is bounded by the assumption $f\in\mathscr{R}(\alpha)$.
Apr
28
comment What is $\int e^{-\frac{(y-\mathbf{x}^T\mathbf{\theta})^2}{2}}d\mathbf{\theta}$?
It's the same thing. You're just taking one more step.
Apr
28
comment Need to find infimum S!!
^ essentially, yes. And using your calculator to plug in sample values is not an acceptable argument. It is sometimes helpful for giving you intuition and an idea of what the answer should be, but in this situation you need to apply some additional reasoning.