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Alexander Fufaev

Videos about mathematics

Here you will find 11 free Mathematics video lectures.

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
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
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