junriee

The definition given is as such:

Given the linear PDE L[u] = f, if f ≡ 0 on some region (that is, f is the zero-function on some region), we say that the PDE is homogeneous on that region. Otherwise, the PDE is nonhomogeneous.

However, it also says the following in an example:

The PDE u_x + 5u = x^2y is nonhomogeneous (on the x-y plane).

Would it be correct to more specifically say that the PDE is non-homogenous on the x-y plane but homogenous on the x=0 axis and y=0 axis? or does region specifically preclude a 1-D region??

http://www.d.umn.edu/~jgallian/advice.html In this link it says "I will ask them "What does |a| = 6 mean?" They will reply incorrectly that a^6 = e. Well, of course, if you do not know the definitions and theorems you won't be able to use them."

What does |a| = 6 mean then if not that?

There's a Prof at my uni who I'm on semi friendly terms with. So today I dropped by his office and asked to come in for a bit for some space to work, which I sometimes do with other professors who don't mind at all. So maybe I was a bit presumptuous because it was very awkward and I felt like I overstepped my bounds a bit.

I wanted to send him an email just so say sorry:

"I just felt like I was being a bit intrusive earlier. So, I just wanted to say sorry if I was overstepping, which was totally not my intention. That's about it; no response required."

Something like that.

Should I send it or is that weird?

for {a,b ∈ R, b=2a}

is this relation, symmetric, reflexive or antisymmetric?

If x=rcos(theta) and y=rsin(theta) and z =f(x,y) find the partial derivative with respect to theta and then find the partial derivative of that with respect to r.

http://i.imgur.com/5xMHKVO.jpg

Assume that you have a pile of n matches and split them into two smaller piles repeatedly until you have n piles of one match. At each step of subdividing, you multiply the number of matches in the formed smaller piles. At the end of the process you add all the numbers you obtained. Show that no matter how you split the piles, then the sum of the products is n(n − 1)/2.

looks something like this: http://i.imgur.com/q1wZ9La.png

I think you're supposed to use strong induction to prove it.

1. Find the point normal equation of the line through the point (3,-7) with normal vector n=[6,1]
2. Given the component equation 4(x+2) - (y-5) = 0 of a line, determine a normal vector to the line and a point on the line.

Find lim (x,y)->(0,0) of (x^2 * y)/(x^4 + y^2) if it exists.

I tried two paths, x=0 and y=x^2, and the first one led to 0 and the second led to 0.5, so I said it did not exist but apparently it does and I'm not sure how to prove it exists and what I previously did wrong.

Mass m_1 moves with speed v in a circular path of radius R on a frictionless horizontal table. It is attached to a string that passes through a frictionless hole in the centre of the table. A second mass m_2 is attached to the other end of the string. Derive an expression for R in terms on m_1, m_2, v and g.

Here's a diagram of what this would look like: http://i.imgur.com/zbni3pk.jpg

I'm pretty sure I should approach this from an angularmomentum perspective but I'm not sure how to find an expression for the angular momentum of m_2. Any help would be appreciated. Thank you!!

I'm working through a worksheet on Simple Harmonic Motion and Oscillations and I'm not sure about this question. I tried using energy to solve the question but I got the wrong answer of 2.54 so I must have done something wrong. The correct answer is 4.4.

A raft of mass 400kg is floating in a pond. When a 100 kg man climbs on board, the raft sinks 8cm deeper into the water to a new equilibrium position. If the man jumps off, how many vertical vibrations does the empty raft make in 5s?