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MY FAVORITE THEOREM
MY FAVORITE THEOREM
A requirement for our Math330 class.
princess sy
Solutions to in-class problems
Solutions to in-class problems
Solutions to in-class problems
Kathryn Bragwell
ARML Lecture:  Intermediate Proofs
ARML Lecture: Intermediate Proofs
A lecture on intermediate proofs that I taught at ARML.
Justin Stevens
CTQs
CTQs
Math homework for Accelerated Math students in Howard County, Critical Thinking Questions.
a Wilson-tétel megfordítása
a Wilson-tétel megfordítása
A Wilson-tétel megfordításának bizonyítása.
Tamás Waldhauser
Meagher.WritAsst1.Final.tex
Meagher.WritAsst1.Final.tex
A Statistics paper on Correlation and Linear Relationships.
Jake Meagher
standaard hw
standaard hw
hoi
Joris van der Hijden
HW1: Linear System Theory (ECE532)
HW1: Linear System Theory (ECE532)
HW1: Linear System Theory (ECE532)
thanh nguyentang
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

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