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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)

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
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Video
Level 3 (with higher mathematics)

Differential Equations explained simply in 47 minutes!

In this Lecture you will learn to classify and to solve arbitrary differential equations (ODE / PDE) in 42 minutes.

Content of the video
  1. [00:16] Why do I need differential equations?
  2. [00:47​] What is a differential equation?
  3. [03:41​] Different notations of a differential equation
  4. [05:19​] What should I do with a differential equation?
  5. [06:31​] How to identify a differential equation
  6. [07:28​] What are coupled differential equations?
  7. [08:53​] Classification: Which DEQ types are there?
  8. [16:05​] What are DEQ constraints?
  9. [18:24] Difference between boundary and initial conditions
  10. [20:55​] Solving method #1: Separation of variables
  11. [21:08​] Example: Radioactive Decay law
  12. [22:50​] Solving method #2: Variation of constants
  13. [25:59​] Example: RL Circuit
  14. [29:14​] Solving method #3: Exponential ansatz
  15. [34:50​] Example: Oscillating Spring
  16. [41:15​] Solving method #4: Product / Separation ansatz