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Alexander Fufaev

Mathematics videos

Here you will find 2 free mathematics videos. These are suitable for use in school and university.

Video
Level 3 (for advanced students)

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
Video
Level 3 (for advanced students)

Kronecker delta explained simply in 11 minutes!

In this video you will learn the Kronecker delta within 10 minutes and how you can use it to write down the scalar product in index notation.

Content of the video
  1. [00:00] Hello there!
  2. [00:42] Definition and Examples
  3. [01:52] Einstein's Summation convention
  4. [02:49] 4 Rules for Kronecker delta
  5. [06:38] Scalar product with Kronecker delta