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Mathematics

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.
Video
Level 3 (with higher mathematics)

Dirac's Delta Function

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 (with higher mathematics)

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