Recent content by smithg86

I can't seem to solve the equation explicitly for f (I think it's transcendental). Can I still use the Taylor series method?

What does \frac{R_1-R_2}{R_1+R_2} equal when \frac{R_1}{R_2}=1000? It's 999/1001. But I don't know how to apply that to find an approximate solution. How do you go about finding an approximate solution to that, or any other function?

Homework Statement question: approximate the function f if the ratio R_1 / R_2 is about 1000. given: the van der pauw equation for resistivity: \rho = ( pi * d / ln[2] ) * (R_1 + R_2})/2 * f(R_1 / R_2), where f is a function of the ratio R_1/R_2 only and satisfies the relation...

Homework Statement I'm not interested in the proof of this statement, just its geometric meaning (if it has one): Suppose T \in L(V) is self-adjoint, \lambda \in F, and \epsilon > 0. If there exists v \in V such that ||v|| = 1 and || Tv - \lambda v || < \epsilon, then T has an...

T(v) = a_{1} e^*_{1}(b_{1} e_{1}) + a_{2} e^*_{2}(b_{2} e_{2}) = a_{1} e^*_{1}(b_{1} e_{1}) + 0 + a_{2} e^*_{2}(b_{2} e_{2}) + 0 = a_{1} e^*_{1}(b_{1} e_{1}) + a_{1} e^{*}_{1}(b_{2} e_{2}) + a_{2} e^*_{2}(b_{2} e_{2}) + a_{2} e^{*}_{2}(b_{2} e_{2}) = a_{1} e^{*}_{1}(b_{1} e_{1} + b{2} e_{2})...

Thanks for your help so far. I came up with something to show that span(e^{*}_{1}, e^{*}_{2}) = \textbf{V}^* : \forall T \in \textbf{V}^*, T:\textbf{F}^2 \rightarrow \textbf{F}, define T(e_{1}) = a_{1}, T(e_{2}) = a_{2}, for some a_{1},a_{2} \in \textbf{F} . Since \forall v \in...

HallsofIvy, Thanks for clarifying what the a's were. CompuChip, I tried doing what you suggested: For some v in V, T(v) = T(a_{1} e_{1} + a_{2} e_{2}), since e_{1}, e_{2} span V. But don't I have to show that V* is spanned by e*_{1}, e*_{2} before I decompose T into a linear combination of...

[SOLVED] Linear Algebra - Dual Spaces Homework Statement (V and W are vector spaces. F is a field) "The space L(V,W) of linear maps from V to W is always a vector space. Take W = F. We then get the space V* := L(V,F) of F-linear maps V --> F. This is called the dual space of V." 1. Let V =...

Homework Statement This is regarding a Fabry-Perot Interferometer with identical mirrors: If you shine a beam of light on a 99% reflecting mirror, 1% goes through and the other 99% is reflected. But if a second mirror is placed behind the first one, where there is only 1% of the light...

Gokul, This problem arose during a lab. Let me explain: Two identical simple pendula hung from a support rod, about 4-5 inches apart from each other. If set in motion, the motion of pendula A did not affect the motion of pendula B, and vice versa. The length of the pendula strings is...

Homework Statement I need to figure out the normal frequencies (or eigenfrequencies) of a system of two simple pendula (call them A and B), connected with by a massless rigid rod at an arbitrary distance from the pivot point or the mass. That is, the pendula are not connected at their masses...

nvm Nevermind, I got it :)

This is what I did. Tell me if I’m wrong: Let: y(A,t) = Ae^(-gt) uncertainty of A = dt uncertainty of t = dt uncertainty of y = dt then: dy = {[dy1)^2 + [dy2]^2}^(1/2) such that: dy1 = y(A + dA, t) – y(A, t) dy2 = y(A, t + dt) – y(A,t) dy1 = dA e^(-gt) dy2 = Ae^(-g(t+dt))...

Homework Statement this is regarding propagation of error for a lab i did: we measured the amplitude of a damped harmonic oscillation over a time period, taking amplitude measurements every 1 second for 14 seconds. when graphed (by excel), the plot has the form of y = Ae^(-gt), where A is...

Homework Statement PROBLEM STATEMENT: Under these conditions, the motion of the mass when displaced from equilibrium by A is simply that of a damped oscillator, x = A cos(ω_0t) e^(−γt/2) where ω_0 = K/M, K =2k,and γ = b/M. Later we will discuss your measurement of this phenomenon. Now...