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.
Mathematical proof
Level 3 (with higher mathematics)

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 (for physics pros)

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 (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