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Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
The differential wave equation can be used to describe electromagnetic waves in a vacuum. In the one dimensional case, this takes the form $\frac{\partial^2\phi}{\partial x^2}-\frac{1}{c^2}\frac{\partial^2\phi}{\partial t^2} = 0$. A general function $f(x,t) = x \pm ct$ will propagate with speed c. To represent the properties of electromagnetic waves, however, the function $\phi(x,t) = \phi _0 sin(kx-\omega t)$ must be used. This gives the Electric and Magnetic field equations to be $E (z,t) = \hat{x} E _0 sin(kz-\omega t)$ and $B (z,t) = \hat{y} B _0 sin(kz-\omega t)$. Using this solution as well as Maxwell's equations the relation $\frac{E_0}{B_0} = c$ can be derived. In addition, the average rate of energy transfer can be found to be $\bar{S} = \frac{E_0 ^2}{2 c \mu _0} \hat{z}$ using the poynting vector of the fields.
Eric Minor
E6 Übungsblatt 12
E6 Übungsblatt 12
Experimentalphysik 6: Festkörperphysik
Jean Amadeus Elsner
N-gram Frequency Discounts
N-gram Frequency Discounts
A short note on the motivation for n-gram frequency discounts in the context of the Katz backoff algorithm.
Paul Glezen
Solutions to in-class problems
Solutions to in-class problems
Solutions to in-class problems
Kathryn Bragwell
E5 Übungsblatt 5
E5 Übungsblatt 5
Experimentalphysik 5: Kern- und Teilchenphysik
Jean Amadeus Elsner
Homework 1
Homework 1
Homework 1
Jennifer Iler
Señales y Sistemas
Señales y Sistemas
Señales y Sistemas
Raymar Ortega
Markowitz Portfolio Optimization Theory and Application
Markowitz Portfolio Optimization Theory and Application
Suppose you have a data matrix comprised of several stock options over a set period of time. How do you choose the optimal collection of stocks such that you maximize your returns for a given level of risk? What Markowitz found was an elegant equation. What we realized rather quickly is there does not exist a closed form solution to this problem. Instead we use the tried and tested linear approximation. By transforming this problem into Matrix multiplication, we are able to quickly and (with desired accuracy) approximate the optimal solution, using only linear algebra.
ymxu

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