Recent content by lumpyduster

Homework Statement So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!) I am asked to solve this differential equation: y''+y'-2y=0 Homework Equations I know for a second order differential equation I can solve for the roots first. If...

Okay I think I have almost got it, but in your last example, how do we know that -ln(x) isn't y(x)? Does that make sense? How can you tell if you have f(x) or y(x)? I don't know what a closed form function is.

So in your example - are y'', y' functions or differentials in the form dy2/dx and dy/dx? I guess I do not know if the y's in this: ay'' + by' + cy = 0 are just y's or a function... if it's a function, and it's in terms of x and you have ay'' + by' + cy = f(x), then why can't you subtract f(x)...

Homework Statement I am currently in quantum chemistry, and in class one day my professor spent some time talking about Maxwell's equations. I am looking at my notes, trying to piece together Maxwell's equations, differential equations, and the principle of superposition, since this is not in...

I just don't know how to get these bounds though... Can I say that since 0≤x≤1 and since x=rcosθ and r=1, that arccos(0)≤θ≤arccos1? Thank you for your help!

Yeah I probably sound like a total noob here, but I've never done an integral where my lower bound was greater than my upper bound... Will try and report back if necessary :)

So I will integrate from π/2 to 3π/2? I guess I'm confused how to take into account that x≥0 when switching to polar coordinates. I just know I want to go from x=0 to x=1 on the Cartesian coordinate system. Would 0 to π also work?

Not sure at all about the lower bound... Should it be 3π/2? I was going to also say 0 to π, but if my upper bound is correct then that would be wrong.

Homework Statement Let F = <x, z, xz> evaluate ∫∫F⋅dS for the following region: x2+y2≤z≤1 and x≥0 Homework Equations Gauss Theorem ∫∫∫(∇⋅F)dV = ∫∫F⋅dS The Attempt at a Solution This is the graph of the entire function: Thank you Wolfram Alpha. But my surface is just the half of this...

Homework Statement Verify Stokes' theorem for the given surface S and boundary dS and vector fields F S = x2+y2+z2, z≥0 dS= x2+y2=1 F = <y,z,x> Homework Equations Stokes' theorem: ∫∫(∇×F)dS = ∫F⋅ds The Attempt at a Solution 1. Curl of F: ∇×F = <-1,-1,-1> 2. After getting the curl, I just...

Homework Statement Verfify Stokes' theorem for the given surface S and boundary ∂S, and vector fields F. S = [(x,y,z): x2+y2+z2=1, z≥0 ∂S = [(x,y): x2+y2=1 F=<x,y,z> I did this problem and checked the answer - I chose the wrong integral bounds and I am wondering why they are wrong. Homework...

Ohh okay I see, I did that at first but it was such a pain. It's weird that my textbook gave me such a long, tedious problem. Thank you everyone!

Wasn't sure of the best way to do this, but here you go :) Oops I copied my work down incorrectly - ∫∫(2xy-2x)dxdy. I actually did integrate this function. But I'm confused about what you're trying to say about my bounds. If I integrated from -2 to 1 in the x direction and -3 to 5 in the y...

Thanks. Sorry I should have been more clear when posting this. I'm not really interested in the fact what I did was wrong in the end if technically it should have worked and I just dropped a negative or something somewhere along the way. If you think what I did was wrong because my bounds were...

Homework Statement Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (-2,1), (-2,-3), (1,-1), (1,5) and back to (-2,1), in that order. Use Green's Theorem to evaluate the integral ∫(2xy)dx+(xy2)dy. Homework Equations Green's Theorem: ∫Pdx+Qdy...