Recent content by twizzy

Homework Statement If f(x) is a piecewise-continuous function in [-L,L], show that its indefinite integral F(x) = \int_{-L}^x f(s) ds has a full Fourier series that converges pointwise. Homework Equations Full Fourier series: f(x)=\frac{1}{2}A_0 + \sum_{n=1}^\infty A_n \cos (\frac{n \pi }{L}x)...

So then if \phi(x) were not a constant, would the question even make sense?

Since u(x,y)=f(x^2+\frac{1}{y}) and u(x,0)=\phi(x) , we have u(x,0)=f(x^2+\frac{1}{\epsilon})=\phi(x) where \epsilon\rightarrow 0. This would imply that \lim_{u\rightarrow \infty}f(u)=\phi(x). Then again, that can't be right because the limit as u\rightarrow \infty should not depend on x. I'm...

Homework Statement Solve the equation u_{x}+2xy^{2}u_{y}=0 with u(x,0)=\phi(x) Homework Equations Implicit function theorem \frac{dy}{dx}=-\frac{\partial u/\partial x}{\partial u/\partial y}The Attempt at a Solution -\frac{u_x}{u_y}=\frac{dy}{dx}=2xy^2 Separating variables...