Recent content by bjohnson2001

I don't think it goes anywhere though, I get: 8cos(t)-4sin(t)cos(t) when it comes time to bring the original variable back in I get a mess of cos(arcsin(y/2)) but maybe I am missing something

Homework Statement Evaluate. \int(4-y)\sqrt{4-y^{2}}dy I have the solution using CAS software here: 2y\sqrt{4-y^{2}}+8sin^{-1}\frac{y}{2}+\frac{1}{3}(4-y^{2})^{3/2} but I need to do this by hand. I have researched the usual trig methods but am having some difficulty. Can...

Thanks, I will give this a shot

I'm with you, but I am unfamiliar with the technique. How is this accomplished?

OK I just heard about the following hint that came from the prof: set z = ε e^{it} Maybe this is an alternate way to compute the residue method? I cannot find this in my textbooks

Homework Statement Let \Gamma be the square whose sides have length 5, are parallel to the real and imaginary axis, and the center of the square is i. Compute the integral of the following function over \Gamma in the counter-clockwise direction. You must use two different methods to solve...

Homework Statement Draw the phase portrait and classify the origin of the system: xdot = [1 2; 2 1]x Homework Equations characteristic equation: det(A-lambda*I) = 0 The Attempt at a Solution First find the eigenvalues and eigenvectors: det(A-lambda*I) =...

Homework Statement Find the equilibrium points and their stability in the system xdot = xy - 2y - x + 2 ydot = xy + x Homework Equations Jacobian matrix = g'(x) The Attempt at a Solution first find the points that a critical point would satisfy...

I did and it satisfies all conditions of a subspace, I can conclude that it must be a subspace. Making the connection that x1=x2 and x3=0 was something I noticed for my example sets but didn't think to generalize for all x. This makes the proof much more complete. Thank you again for your help!

OK that sounds good, so its alright that the expression of the set is not linear? Usually I read proofs dealing with linear combinations of vectors where we can assume a number of things. I am not sure that the same properties are inherited when we square the difference of two vectors. Or is it...

Thats right, x4, x5 and x6 are all free variables and can be any value since they aren't constrained by the set. I think that's OK, if we were in R3 and only placed limits on x and y I would imagine that z could have any value like an infinite plane. I'm not sure if that should sound normal...

Oh good call, x is definitely a vector. So we know that x is a vector in R6 so linear combinations of x inherit the same properties of the original vector space. Since the subspace expression is not linear, does that mean the properties are not inherited and we have to go back and reprove all...

Homework Statement x belongs to the vector space R^6. Is (x1-x2)^4 + x3^6 = 0 a subspace? Homework Equations Since we already know x is a vector space we only need to check: 1. The existence of the zero vector 2. Closure under vector addition 3. Closure under scalar addition The Attempt...