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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
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
Formula

Christoffel Symbols (without Torsion)

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