Recent content by Smazmbazm

How would one work out the total mass for the top 3.2 meters of the ocean? Thanks in advance!

The way the problems progress suggest that you would use your answer for (e) to calculate the pressure at the bottom for (f). Something like 101325 + (1*916.7*9.80665) + ( whatever the answer from (e) for height was * 1000 * 9.80665) which would result in the pressure. That's why I'm unsure...

Homework Statement Consider two otherwise identical columns of water: one fresh, the other with an initial salinity of 35 pus. Both are initially isothermal at 4°C and each column is 100m deep. There is no horizontal mixing. Both columns are then cooled slowly under calm conditions until ice...

Ok great, thanks for the response. By that logic, wouldn't it imply that you can't move the (1-x^2) to the right side either? So you just take the double derivative of the eigenvector then multiply by (1-x^2) minus the first derivative of the eigenvector multiplied by x then solve for lambda...

Homework Statement Let B be the linear operator (1-x^{2}) \frac{d^2}{dx^2}-x\frac{d}{dx} Show that T_{4}(x) = 8x^{4} - 8x^{2} + 1 is an eigenvector of B, and find the corresponding eigenvalue. Attempt Righto, I find these rather difficult so a step by step solution would be nice but...

Thank you, good sir. That makes sense and seems slightly more intuitive than the method we were taught. This is a great explanation and it should hopefully help me for my examination tomorrow =/

Homework Statement Consider the vector field given by F(x, y, z) = yz \hat{i} + xz \hat{j} + (xy + 3z^{2})\hat{k} a. Calculate ∇xF and show that F is a conservative field. Done, result = <0,0,0> which implies the vector field is conservative. b. The way we were taught this is to set...

Great, thanks for that. Makes sense

Homework Statement Let H be the set of all vectors of the form (a-3b, b-a, a, b) where a and b are arbitrary real scalars. Show that H is a subspace of ℝ^4 and find a basis for it. Right, I've shown it's a proper subspace, just need help with finding a basis. Is {a-3b, b} a suitable...

Is that because it's a conservative field and calculations are therefore path independent?

Yea ok, I figured that out. So the path I got, following http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx was r(t) = <t, t+1,3-t> and after evaluating the whole expression I got an answer of 5. Dunno if that's right because we aren't given answers to our questions for some...

Sure. But I don't understand what dl is in this question. How does one determine dl and also what are the limits of integration..? What I find confusing is distinguishing between what dl, ds, and dr all mean in various contexts. Such as ∫_{C}F.ds ∫^{B}_{A}F.dl and ∫_{C}F.dr...

Here is the whole question http://imgur.com/KGI28pJ http://imgur.com/KGI28pJ

Homework Statement Given a vector field F(x,y,z) = (yz + 3x^{2})\hat{i} + xz\hat{j} + xy\hat{k} Calculate the line integral ∫_{A}^{B}F\bullet dl where A = (0,1,3) and B = (1,2,2) Homework Equations Right, first of all, what is dl ? I've gone over all my course notes and...

Can someone please confirm that this is incorrect / correct so that I know that I'm on the right track or not. Thanks