Email Definition and 191 Threads

Hi All, I remember reading somewhere ( unfortunately can't remember the precise place) about some email program/service that would forward to it , emails from an existing account. Say I have Address1@mail1.com as an existing address. This service, with account , say Address2@mail2.com...

We should note that the two functions intersect at $\displaystyle \begin{align*} x = -\frac{1}{2} \end{align*}$ and $\displaystyle \begin{align*} x = 1 \end{align*}$. (a) Using the method of washers, the inner radius is $\displaystyle \begin{align*} 3 - \left( x + 1 \right) = 2 - x...

(a) We should recall that for a small change in x, then $\displaystyle \begin{align*} \frac{\mathrm{d}y}{\mathrm{d}x} \approx \frac{\Delta\,y}{\Delta\,x} \end{align*}$, so $\displaystyle \begin{align*} \Delta\,y \approx \frac{\mathrm{d}y}{\mathrm{d}x}\,\Delta\,x \end{align*}$, so in this case...

This requires using Integration By Parts twice... $\displaystyle \begin{align*} I &= \int{\mathrm{e}^{-2\,x}\cos{ \left( 3\,x \right) } \,\mathrm{d}x} \\ I &= \frac{1}{3}\,\mathrm{e}^{-2\,x} \sin{(3\,x)} - \int{ -\frac{2}{3}\,\mathrm{e}^{-2\,x} \sin{(3\,x)}\,\mathrm{d}x } \\ I &=...

If we remember that the derivative is defined by $\displaystyle \begin{align*} \frac{\mathrm{d}y}{\mathrm{d}x} = \lim_{\Delta\,x \to 0} \frac{y\left( x + \Delta\,x \right) - y\left( x \right)}{\Delta \, x} \end{align*}$ then that means that as long as $\displaystyle \begin{align*} \Delta \,x...

(a) Differentiate both sides of the equation with respect to x: $\displaystyle \begin{align*} \frac{\mathrm{d}}{\mathrm{d}x} \left[ y^3 + y + x\,y^2 \right] &= \frac{\mathrm{d}}{\mathrm{d}x} \left[ 10 + 4\sin{(x)} \right] \\ 3\,y^2\,\frac{\mathrm{d}y}{\mathrm{d}x} +...

I am assuming that this line integral is along the straight line from $\displaystyle \begin{align*} (0,0,0) \end{align*}$ to $\displaystyle \begin{align*} \left( 5, \frac{1}{2}, \frac{\pi}{2} \right) \end{align*}$, which has equation $\displaystyle \begin{align*} \left( x, y, z \right) = t\left(...

I am sorry if this sounds very basic, but I am really troubled on what to title an email regarding a request to join a research group! Any ideas or guidelines?

Hi everyone, I'm planning to apply to a few terminal masters programs this fall, with the goal of doing a thesis option and applying to PhD programs after the masters. (I have various reasons for wanting to go this route instead of applying straight to a PhD). I know it's good to seek out and...

Hey all. I've recently accumulated upwards of 5 or 6 different email accounts that I need to check and I'm having a hard time keeping track of it all. I'm looking for a good program for windows that I can use to keep track of all my accounts instead of having to open and log into each one...

As the Heaviside function is a function of t - 4, that means all other terms must also be functions of t - 4. The sine function is, but the exponential isn't. However with a little manipulation, we get $\displaystyle \begin{align*} f\left( t\right) &= \mathrm{H}\,\left( t - 4 \right) \,\sin{...

Taking the Laplace Transform of both sides we have $\displaystyle \begin{align*} \mathcal{L}\,\left\{ y'' + 4\,y \right\} &= \mathcal{L}\,\left\{ \mathrm{H}\,\left( t - 7 \right) \right\} \\ s^2\,Y\left( s \right) - s\,y\left( 0 \right) - y'\left( 0 \right) + 4\,Y\left( s \right) &=...

As the denominator is a function of s + 3, it suggests a shift had to have been utilised. As such, we also need the numerator to be a function of s + 3... Let $\displaystyle \begin{align*} u = s + 3 \end{align*}$, then $\displaystyle \begin{align*} s = u-3 \end{align*}$ and thus...

It's not entirely obvious what to do with this question, as the denominator does not easily factorise. However, if we realize that $\displaystyle \begin{align*} s^4 + 40\,000 = \left( s^2 \right) ^2 + 200^2 \end{align*}$ it's possible to do a sneaky completion of the square... $\displaystyle...

Suppose one was working for a Professor. Then you mutually decide that it's not a good fit. The professor has been helpful in terms of suggestions for other people to work with and you found another professor who has given you some reading material earlier. How do I email the new professor if...

$\displaystyle \begin{align*} A\,A^T &= \left[\begin{matrix} 3 & 0 & -4 \\ 4 & 0 & \phantom{-}3 \\ 0 & 5 & \phantom{-}0 \end{matrix}\right]\left[ \begin{matrix} \phantom{-}3 & 4 & 0 \\ \phantom{-}0 & 0 & 5 \\ -4 & 3 & 0 \end{matrix}\right] \\ &= \left[ \begin{matrix} 3\cdot 3 + 0 \cdot 0 +...

A matrix is symmetric if it is equal to its own transpose, so to show $\displaystyle \begin{align*} C^T\,C \end{align*}$ is symmetric, we need to prove that $\displaystyle \begin{align*} \left( C^T\,C \right) ^T = C^T\,C \end{align*}$. $\displaystyle \begin{align*} \left( C^T\,C \right) ^T &=...

As there is a repeated root, the partial fraction decomposition we should use is: $\displaystyle \begin{align*} \frac{A}{x - 1} + \frac{B}{\left( x - 1 \right) ^2 } + \frac{C}{x - 2} &\equiv \frac{x^2}{\left( x - 1 \right) ^2\,\left( x - 2 \right) } \\ \frac{A\,\left( x - 1 \right) \left( x - 2...

We should note that we can write any complex number as $\displaystyle \begin{align*} z = r\,\mathrm{e}^{\mathrm{i}\,\theta} \end{align*}$ where $\displaystyle \begin{align*} r = \left| z \right| \end{align*}$ and $\displaystyle \begin{align*} \theta = \textrm{arg}\,\left( z \right) + 2\,\pi\,n ...

First let's write this number in its polar form. $\displaystyle \begin{align*} \left| z \right| &= \sqrt{\left( -2 \right) ^2 + 2^2} \\ &= \sqrt{4 + 4} \\ &= \sqrt{8} \\ &= 2\,\sqrt{2} \end{align*}$ and as the number is in Quadrant 2 $\displaystyle \begin{align*} \textrm{arg}\,\left( z...

$\displaystyle \begin{align*} z^3 + 1 &= 0 \\ z^3 &= -1 \\ z^3 &= \mathrm{e}^{ \left( 2\,n + 1 \right) \,\pi\,\mathrm{i} } \textrm{ where } n \in \mathbf{Z} \\ z &= \left[ \mathrm{e}^{\left( 2\,n + 1 \right) \, \pi \,\mathrm{i}} \right] ^{\frac{1}{3}} \\ &= \mathrm{e}^{ \frac{\left( 2\,n + 1...

To start with, we should find the points of intersection of the two functions, as these will be the terminals of our regions of integration. $\displaystyle \begin{align*} 2\,x^2 &= x + 1 \\ 2\,x^2 - x - 1 &= 0 \\ 2\,x^2 - 2\,x + x - 1 &= 0 \\ 2\,x\,\left( x - 1 \right) + 1 \,\left( x - 1...

Q5. Here is a graph of the region to be integrated and the line to be rotated around. First we should find the x intercept of the function $\displaystyle \begin{align*} y = 3 - 4\,\sqrt{x} \end{align*}$ as this will be the ending point of our region of integration. $\displaystyle...

Here is a sketch of the region to be rotated around the y axis. You first need to visualise this entire region being rotated around the y axis, to get a mental picture of what the solid looks like. Then you need to imagine that the solid is made up of very thin vertically-oriented hollow...

Here is a graph of the region to be rotated. Notice that it is being rotated around the same line that is the lower boundary. The volume will be exactly the same if everything is moved down by 4 units, with the advantage of being rotated around the x-axis. So using the rule for finding the...

Here is a sketch of the region to be rotated and the line to be rotated around. Notice that the volume will be exactly the same if we were to move everything up by 3 units, but with the advantage of rotating around the x axis. So we want to find the volume of the region under $\displaystyle...

Here is a sketch of the region to be rotated. To find a volume using cylindrical shells, you first need to picture what the region would like like when that area is rotated around the y axis. Then consider how it would look if that solid was made up of very thin cylinders. Each cylinder has...

Here is a sketch of the region R and the line to be rotated around. Clearly the x-intercept of $\displaystyle \begin{align*} y = 3 - 3\,\sqrt{x} \end{align*}$ is (1, 0) so the terminals of the integral will be $\displaystyle \begin{align*} 0 \leq x \leq 1 \end{align*}$. We should note that...

We should first find the $\displaystyle \begin{align*} x \end{align*}$ intercept of the function $\displaystyle \begin{align*} y = 2 - 5\,\sqrt{x} \end{align*}$, as this will be the end of our region of integration. $\displaystyle \begin{align*} 0 &= 2 - 5\,\sqrt{x} \\ 5\,\sqrt{x} &= 2 \\...

Hi, I want to write a program to email using gmail smtp. I got following code from internet. import javax.mail.*; import javax.mail.internet.InternetAddress; import javax.mail.internet.MimeMessage; import java.util.Properties; /** 10 * Created by anirudh on 28/10/14. 11 */ public class...

What is the $\displaystyle \begin{align*} \int{ \frac{54\,t - 12}{\left( t- 9 \right) \left( t^2 - 2 \right) } \,\mathrm{d}t } \end{align*}$ We should use Partial Fractions to simplify the integrand. The denominator can be factorised further as $\displaystyle \begin{align*} \int{ \frac{54\,t -...

I had a skype interview with a professor in Canada for M.Sc. admissions. This was 10 days ago on April 20. The interview went okay. He said he would talk to the graduate coordinator, check my application and get back to me by the end of April. Monday, May 2nd would be the first working day after...

What is the derivative (with respect to t) of $\displaystyle \begin{align*} y = 16\,\left[ \sinh{(7\,t)} \right] ^3 \cosh{(7\,t )} \end{align*}$? One way to do this is to apply the product rule. To do this, we need to know the derivative of each factor. $\displaystyle \begin{align*}...

What is the derivative (with respect to t) of $\displaystyle \begin{align*} 15\log{ \left| \sec{ \left( 9\,t \right) } + \tan{ \left( 9\,t \right) } \right| } \end{align*}$? $\displaystyle \begin{align*} y &= 15\log{ \left| \sec{ \left( 9\,t \right) } + \tan{ \left( 9\,t \right) } \right| } \\...

What is the indefinite integral (with respect to t) of $\displaystyle \begin{align*} 50\,t\cos{ \left( 5\,t^2 \right) } \end{align*}$? $\displaystyle \begin{align*} \int{ 50\,t\cos{\left( 5\,t^2 \right) } \,\mathrm{d}t } &= 5\int{ 10\,t\cos{ \left( 5\,t^2 \right) }\,\mathrm{d}t } \end{align*}$...

Since we have this relationship between x and y, as the two sides are equal, so are their derivatives. We just have to remember that as y is a function of x, any function of y is also a function of x, with the inner function "y" composed inside whatever is being told to do to the y. So to...

I noticed that almost every professor and departmental staff at any university only uses salutations (Dear xxx, etc.) in their first email post. In subsequent email posts in the same email thread, they do not continue to use salutations. Will it be considered rude if I, as a student, also use...

To perform implicit differentiation we must make use of the chain rule. Basically if you have a function composed in another function, its derivative is the product of the inner function's derivative and the outer function's derivative. All other rules (such as the sum rule, the product rule...

We write the system as an augmented matrix $\displaystyle \begin{align*} \left[ \begin{matrix} \phantom{-}1 & 4 & \phantom{-}1 & 0 & \phantom{-}5 \\ \phantom{-}1 & 6 & -1 & 4 & \phantom{-}7 \\ -1 & 2 & -9 & 2 & -9 \\ \phantom{-}0 & 1 & \phantom{-}2 & 0 & \phantom{-}4 \end{matrix} \right]...

We can write the system in an augmented matrix as $\displaystyle \begin{align*} A = \left[ \begin{matrix} 2 & -2 & -1 & \phantom{-}0 & \phantom{-}6 \\ 2 & \phantom{-}3 & \phantom{-}2 & -5 &-14 \\ 0 & \phantom{-}5 & \phantom{-}2 & \phantom{-}2 &\phantom{-}1 \\ 0 & \phantom{-}0 & \phantom{-}2 & -3...

To start with, since $\displaystyle \begin{align*} A = P\,L\,U \end{align*}$, that means in our system we have $\displaystyle \begin{align*} P\,L\,U\,\mathbf{x} = \mathbf{b} \end{align*}$. Normally to solve for $\displaystyle \begin{align*} \mathbf{x} \end{align*}$ we would use inverses, so we...

The closest Inverse Laplace Transform from my table is $\displaystyle \begin{align*} \mathcal{L}^{-1}\,\left\{ \frac{2\,a\,s\,\omega}{\left( s^2 + \omega ^2 - a^2 \right) ^2 + 4\,a^2\,\omega ^2 } \right\} = \sin{ \left( \omega \, t \right) } \sinh{ \left( a \, t \right) } \end{align*}$ so we...

Effie has correctly found that the eigenvalues of $\displaystyle \begin{align*} A = \left[ \begin{matrix} \phantom{-}3 & \phantom{-}2 \\ -3 & -4 \end{matrix} \right] \end{align*}$ are $\displaystyle \begin{align*} \lambda_1 = -3 \end{align*}$ and $\displaystyle \begin{align*} \lambda_2 = 2...

I'm not sure where you're getting the idea that z = 2, as this is not correct. I'm assuming this is to be done without pivoting... Set up your augmented matrix: $\displaystyle \begin{align*} \left[ \begin{matrix} 2 & \phantom{-}1 & -3 & -5 \\ 1 & -1 & \phantom{-}2 & 12 \\ 7 & -2 & \phantom{-}...

Hi All, I recently started a new job and I was assigned a personal email address by the company, but I am clueless on how it works: The email is of the form : username@companyname.com I was told I can "log on to it" through Gmail. Anyone know how this works? I mean, how can I...

Recently Google decided to flood me with softcore porn. Enough. I tried about a dozen other free email providers. All I want to do is import my contacts and send email. I couldn't get it done. It was the usual software nightmare. Anyone have a recommendation?

Is it ok to email a professor asking them to confirm your grades to this point e.g. you send them all your homework grades and midterm grade in case of error and ask them about your final exam score? Would this be nagging and or condescending. Wouldn't want to hurt my image just before final...

I've applied to a particular university for fall 2016 graduate admission. The deadline for my referees to submit the application is December 01. One of my referees is currently extremely busy and has asked me to request the graduate administrator to contact him regarding the reference letter...

I have been interviewing interns for our spring internship program and one of the candidates recently sent me an email basically reiterating what he considers his strengths, thanking me for the time to interview him, and letting me know that he appreciated the opportunity. Now, I know people...

First, because the series is positive term, we don't have to worry about absolute values. Now $\displaystyle \begin{align*} a_n = \frac{2n + 3}{4n^3 + n} \end{align*}$ and $\displaystyle \begin{align*} a_{n + 1} &= \frac{2\left( n + 1 \right) + 3}{4 \left( n + 1 \right) ^3 + n + 1} \\ &=...