## First and Second Green's Identity

Proof of the two Green's identities (formulas) using the Gauss integral theorem, which are useful in the calculation of some electric potentials.

Proof of the two Green's identities (formulas) using the Gauss integral theorem, which are useful in the calculation of some electric potentials.

In this video you will learn what Fourier series / coefficients are and how to specify / calculate them for a function.

` $$ \varphi ~=~ \frac{ \class{red}{s} }{r} $$ `

Here you will learn what a Fourier series is, how it can be calculated, and the role of Fourier coefficients and basis functions.

Here you will learn about Levi-Civita symbol; how it is defined and how it can be used to write and prove scalar triple product and cross product.

In this video you will learn what the Dirac delta function is. We also derive its properties and make examples.

Here you will learn about the delta function and its properties, which you can use for example to describe an electric point charge.

` $$ \Gamma^{ \class{red}{c} }_{\;\class{blue}{a}\class{green}{b}} ~=~ \frac{1}{2} \, g^{\class{red}{c}s} \, \left( \partial_{\class{blue}{a}} \, g_{\class{green}{b}s} ~+~ \partial_{\class{green}{b}} \, g_{\class{blue}{a}s} - \partial_s \, g_{\class{blue}{a}\class{green}{b}} \right) $$ `

Here you practice calculating integrals in which a Dirac delta function occurs. You have to use the properties of the Dirac's delta.

In this physics video you will learn what Hermitian operators and matrices are and what important properties they have.