Graph, Wall, Tome: Difference between revisions
→The Wall
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Eric talked about some of the important equations on the wall. There are 2 different recorded versions of the conversation if you want to listen to it. | Eric talked about some of the important equations on the wall. There are 2 different recorded versions of the conversation if you want to listen to it. | ||
=== Expansion === | |||
Einstein's mass-energy equation: | |||
: $$E = mc^2$$ | |||
'''Maxwell's equations (2):''' | |||
: $$\nabla \times \mathbf{B} = \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t}$$ | |||
: $$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}}{\partial t}$$ | |||
: $$\nabla \cdot \mathbf{B} = 0$$ | |||
: $$\nabla \cdot \mathbf{E} = 0$$ | |||
Stokes' theorem: | |||
: $$\int_M d\omega = \int_{\partial M}\omega$$ | |||
The boundary of a boundary is zero: | |||
: $$\partial\partial = 0$$ | |||
Heisenberg's indeterminacy relation: | |||
: $$\Delta x \Delta p \geq \frac{\hbar}{2}$$ | |||
Euler's formula for Zeta-function: | |||
: $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$ | |||
'''Klein-Goarden equation (4):'''' | |||
: $$\frac{1}{c^2} \frac{\partial^2}{\partial t^2} \psi - \nabla^2 \psi + \frac{m^2 c^2}{\hbar^2} \psi = 0$$ | |||
Kepler's 2nd law: | |||
: $$\frac{d\theta}{dt} \propto \frac{1}{r^2}$$ | |||
Newton's force-acceleration equation: | |||
: $$\mathbf{F} = m\mathbf{a}$$ | |||
Keplers 3rd law: | |||
: $$T^2 \propto a^3$$ | |||
Newtons gravitational law: | |||
: $$F = \frac{G m_1 m_2}{r^2}$$ | |||
''''Einstein's General Relativity equation (1):'''' | |||
: $$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$ | |||
Schrodinger's equation: | |||
: $$i \hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2)}{2 m} \nabla^2 \psi + V \psi$$ | |||
'''Dirac equation (3)''': | |||
: $$(i \not{D} - m)\psi = 0$$ | |||
Atiyah-Singer theorem: | |||
: $$dim\, ker \not{D}_E - dim \, coker \not{D}_E = \int_M \hat{A}(M) \cdot ch(E)$$ | |||
'''Yang-Mills equations (2):'''' | |||
: $$d^*_A F_A \propto J$$ | |||
Defining relation of supersymmetry: | |||
: $$\{Q,Q\} = P$$ | |||
== The Tome == | == The Tome == | ||