# Mathematics

Mathematical proof
Level 3 (up to Physics B.Sc.)

## 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.

Video
Level 4 (up to Physics M.Sc.)

## Fourier Series. An Intuitive Explanation.

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

Content of the video
1. 00:00 Why Fourier series?
2. 01:08 The concept of Fourier series
3. 03:05 Fourier coefficients
4. 06:15 Fourier basis
5. 09:38 Example: Sawtooth function
Formula

## Angle Definition (Arc Length, Radius)

Lesson
Level 3 (up to Physics B.Sc.)

## Fourier Series (+ Coefficients) and How to Intuitively Understand it

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

Lesson
Level 3 (up to Physics B.Sc.)

## 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.

Video
Level 3 (up to Physics B.Sc.)

## Diracsche Delta-Funktion

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

Content of the video
1. What is the delta function good for?
2. 02:09 Delta function graphically
3. 02:21 Integral of the delta function at the origin
4. 03:08 Shifted delta function
5. 03:41 Integral of the shifted delta function
6. 04:33 Delta function is symmetric (even)
7. 05:44 Delta function with a factor
8. 06:38 Examples
9. 07:52 Three-dimensional delta function
Lesson
Level 3 (up to Physics B.Sc.)

## Dirac's Delta Function and its Most Important Properties

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

Formula

## Christoffel Symbols (without Torsion)

Exercise with solution
Level 3 (up to Physics B.Sc.)

## Simplify 6 Integrals with the Delta Function

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

Video
Level 3 (up to Physics B.Sc.)

## Hermitian Operators Simply Explained

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

Content of the video
1. 00:00 Motivation: Real mean values
2. 01:16 What are Hermitian operators?
3. 02:16 What is a self-adjoint operator?
4. 02:56 Notation of a Hermitian operator
5. 03:20 Eigenvalues are real
6. 04:27 Eigenvectors are orthogonal
7. 05:56 Eigenvectors form a basis
8. 06:37 What is a Hermite matrix?
9. 07:19 Examples for (non) Hermitian matrices