## Levi-Civita Symbol and How to Write Cross Product with it

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.

Learn the arts of numbers, logical definitions, and constructed abstract structures, as well as their relationships to each other, which will help you better master physics.

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.

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

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

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

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.

Learn how to solve first order homogeneous differential equations using the separation of variables (SoV) method. With example for the decay law.

Learn "Variation of constants" - solution method. With its solution formula you can solve ordinary inhomogeneous differential equations of 1st order.

Learn how to solve linear differential equations (2nd order) using the exponential approach and how to use the characteristic equation (+ example).

Learn how to solve 2nd order (in)homogeneous linear differential equations using the exponential ansatz. The DEQ of the harmonic oscillator is solved.

Separation of variables (product approach) is suitable for converting partial differential equations (PDE's) into ordinary differential equations and then solving them with other methods.

Learn how to solve partial differential equations (PDE) with separation of variables (product ansatz). Here we make an example with the one-dimensional wave equation.

Learn how to solve 1st order inhomogeneous linear differential equations using the "variation of constants" (variation of parameters) method.

Here you will learn how to solve 1st order homogeneous linear differential equations using the "separation of variables" solving method.

Learn the Divergence Theorem in only 8 minutes, namely how it links a volume integral with a surface integral.