Recent content by Caspian

Pretty much knows the triangle inequality. \left| a + b \right| \le \left| a \right| + \left| b \right| I was reading a source which asserted the following extension of the triangle inequality: \left| a + b \right|^p \le 2^p \left(\left| a \right|^p + \left| b \right|^p\right) This is...

Ok, ok... I get it. (1,2,3,4) is in the vector space spanned by (1,0,0,0)...(0,0,0,1), but these vectors aren't a basis for the subspace which is the line through (1,2,3,4) because these vectors span too much space. Ok, I guess this was a dumb question. Thanks for your help :).

My book made the following claim... but I don't understand why it's true: If v_1, v_2, v_3, v_4 is a basis for the vector space \mathbb{R}^4, and if W is a subspace, then there exists a W which has a basis which is not some subset of the v's. The book provided a proof by counterexample...

That was just what I was looking for -- not only the solution, but a tool to use in the future :). Thank you so much!

[solved] Sum of k x^k? I happened upon a thread in a math forum, where someone asserted that this is true: \sum_{k=0}^\infty (k+1) \left(\frac{5}{6}\right)^k = 36 I suppose this makes intuitive sense. But if it's true, it must have a general form. I.e., \sum_{k=0}^\infty (k+1) r^k = ...

I'm trying to design a digital circuit which will accept input from a touchscreen. Does anyone know if a touchscreen is manufactured which has input/output cables which are meant to be read by a digital logic circuit? (yes, it'll be a very complicated digital logic circuit). Even if I can...

Thanks everyone for the ideas :). I like the blogging idea... in the meantime, I'll try to make my simulations more "interesting".

I'm a college student pursuing a degree in physics, with an interest in computational physics. I got a website where I figured I'd make simulations and publish them so that those with an interest in physics could play around with them and learn a bit. Unfortunately, my simulations aren't quite...

Sorry, I left out intermediate steps in my original post... let me provide more detail. let f(x) = x^2. So, \dfrac{\partial f}{\partial x} = 2x Thus, \sigma_f = \sqrt{(2x)^2 \sigma_x^2}. .. Now, let g(x,y) = x \ctimes y. So, \dfrac{\partial g}{\partial x} = y and \dfrac{\partial g}{\partial...

Yeah, I messed up in my LaTeX, and forgot to put parenthesis, but I did square the function after taking the partial derivative. So, that's not where I've gone wrong here. There's got to be something else going on here... does the derivation behind the formula for error propagation assume that...

Ok, this isn't a homework question -- more out of curiosity. But it seems so trivial that I hate to post it under "General Physics" We all know the standard formula for error propagation: \sigma_f = \sqrt{\dfrac{\partial f}{\partial x}^2 \sigma_x^2 + \dfrac{\partial f}{\partial y}^2 \sigma_y^2...

Thanks for all your suggestions. I like denverdoc's suggestion since force and velocity can be broken into x and y components... so force of drag in the x direction won't effect the y direction. So, here's what I've got for the y direction: y = \frac{1}{2} (g - \frac{F_{drag}}{m}) t^2 + v_0 t y...

I need to compute the time of flight of a projectile which is subject to air resistance. Here's where I am so far in solving the problem: F_{drag} = -B v^2 a = \frac{\partial v}{\partial t} = \frac{-B v^2}{m} integrate and solve for v... v = \sqrt[3]{\dfrac{1}{3 \dfrac{B}{m} t + C}} I then...

Thanks, D H! I've modified the formulas I'm using and my system works great now. Thank you for your help!

I'm trying to make a program which makes use of Newton's law of universal gravitation to model planetary motion. I've set up a system very similar to the earth-sun system (i.e., masses and distances are similar to the actual earth-sun system). When I run the simulation, the "earth" orbits the...