Recent content by tourjete

Homework Statement This integral is actually part of a question I had on an exam about analytic continuation. The integral is \int_0^1 dx \frac{x^n}{\sqrt{x^3+5}} . The first part of the question is "what is its domain of validity for absolute convergence of the integral?" It then goes...

Homework Statement In the circuit below, the capacitors labeled C1 and C2 both have capacitance C. They are connected through a switch and a resistor of resistance R. Capacitor C1 is initially charged with a potential V1(0) at time t = 0, while capacitor C2 is uncharged at time t=0. At...

okay, so it's impossible to know the signs of the charges without knowing whether \frac{dB}{dt} is increasing or decreasing? (Thanks for the help, by the way, it was very useful)

I'm assuming I'm supposed to use Kirchoff's Law's then? I did V_1 + V_2 -A \frac{dB}{dt} = 0, where V_1 and V_2 are the voltages across each capacitor. I also know that two capacitors in series have \frac{1}{C_{eq}} = \frac{V_1+V_2}{Q} = \frac{1}{C_1} + \frac{1}{C_2}. Solvin Kirchoff's Law...

Homework Statement Grad student here, reviewing for my quals. It's been awhile since E&M and I think I need a refresher since this problem has me stumped. A planar circuit surrounds a solenoid and consists of two capacitors of capacitances C_1 and C_2 joined together by normal wires. The...

Homework Statement Let va be a dual vector field. Show that the quantity ∂[a vb] transforms as a type (0, 2) tensor under coordinate transformations. Homework Equations wu' = (dxu / dxu') wu The Attempt at a Solution My main problem is that I don't know what the brackets mean...

I'm in Minkowski flat space-time so the metric tensor is \begin{array}{ccc} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array} and the tensor is \begin{array}{ccc} 2 & 0 & 1 & -1 \\ -1 & 0 & 3 & 2 \\ -1 & 1 & 0 & 0 \\ -2 & 1 & 1 & -2 \end{array} I'm afraid I'm still...

Homework Statement Xuv is a 4x4 tensor and Vu is a vector. Vu = (-1, 2, 0, -2) (i.e. it is a 1x4 vector). Find the quantities Vu Vu and Vu Xuv Homework Equations Given above The Attempt at a Solution I'm having trouble finding Vu. Initially I thought that it should be the...

Homework Statement Our universe is observed to be flat, with density parameters Ωm,0 = 0.3 in non-relativistic matter and Ω\Lambda,0 = 0.7 in dark energy at the present time. Neglect the contribution from relativistic matter. At what redshift did the expansion of the universe start to...

so I have: xn+1/(n+1) = bt + C then I plug in the initial condition x=x0 at t = 0 C = x0n+1/(n+1) I just need to solve this for x now, correct?

Thanks! I solved the ODE by integrating both sides and got xn+1/(n+1) = bt. I don't see where the constant comes into play here.

Homework Statement A particle of mass m's velocity varies according to bx-n Find the position as a function of time, setting x = x0 at t=0 Homework Equations v(x) = bx-n possibly relevant: f(x) = -b2mnx-2n-1 The Attempt at a Solution The first part of the question asked me to...

Sorry to drag up an old thread, but I'm working on the same problem and understand everything except where the x^4 - 2pi^2 * x^2 came from. Any help would be appreciated.

Homework Statement Consider the vector space C[a,b] of all continuous complex-valued functions f(x), x\in [a,b]. Define a norm ||f|| = max{|f(x)|, x\in [a,b]] a) show that this is a norm b) Show that this norm does not satisfy the parallelogram law, thereby showing that its not an...

Homework Statement Suppose that A', B' and C' are at rest in frame S', which moves with respect to S at speed v in the +x direction. Let B' be located exactly midway between A' and C'. At t'=0, a light flash occurs at B' and expands outward as a spherical wave. 1. According to an observer...