Recent content by sandylam966

need a good book on topology and metric spaces! I'm an undergrad taking a course on non-linear dynamical systems, just realising my pre-knowledge is slightly under the requirement since I have not taken any course on topology. I only know basic real analysis and some complex analysis. so any...

Yes that's a mistake, u is the radius So for D2 is (r cosθ, r sinθ, r^2), 0<θ<2pi, 0<r^2<2r(cosθ + sinθ) -1 correct?

Homework Statement Let F = <z,x,y>. The plane D1: z = 2x +2y-1 and the paraboloid D2: z = x^2 + y^2 intersect in a closed curve. Stoke's Theorem implies that the surface integrals of the of either surface is equal since they share a boundary (provided that the orientations match)...

hmm I don't think I get it. partial differentiating v wrt r and ρ, then take the cross product of the 2, I got ((-√3 r cosρ)/4, (-√3 r sinρ)/4, 3r/4) , pointing into the ring. is this not the correct normal?

oh I see thanks!

yes that's what I've used. using let θ=pi/3 I parameterise the surface in terms of ρ and r. did I make any mistake here?

Homework Statement find ∫E.dS, where E = (Ar^2, Br (sinθ),C cosρ), over the outside conical surface S, given by 1≤r≤2, θ=\pi/3 (this is an open surface, excluding the end faces).Homework Equations The Attempt at a Solution from the context I believe ρ is the plane polar angle on the x-y...

hi Quesadilla, yes that's what I'm trying to do, but i think i made some mistake in my working above.

thanks, LCKurtz. here's my working: the surface area A = the double integral of a(a^2-x^2)^-1/2 dxdy, over the circle x^2+y^2=a^2 on the x-y plane, so A = double integral of a(a^2-(r cos (u))^2)^-1/2 rdrdu, for 0<r<a, 0<u<2pi first we solve the dr part, so A = integral (wrt to u only now) of...

thanks, HallsofIvy. but i don't see why it isn't integrated over a circle, since x^2+y^2=a^2 is cylinder centred at origin, surely if the other cylinder goes through it, the cross section (on the x-y plane) must be a circle?

find the area of the cylinder x^2+z^2=a^2 that is inside the cylinder x^2+y^2=a^2. my attempt: parameterise x^2+z^2=a^2 as a vector r(x,y) = (x,y,(a^2-x^2)^1/2). using the formula given here : http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx, I found the surface area = the...

Homework Statement Given ∑^{∞}_{n=1} n An sin(\frac{n\pi x}{L}) = \frac{λL}{\pi c} σ(x-\frac{L}{2}) + A sin(\frac{\pi x}{2}), where L, λ, c, σ and A are known constants, find An. Homework Equations Fourier half-range sine expansion. The Attempt at a Solution I understand I...