Here you will find 11 free Mathematics video lectures.

Video
Level 2 (without higher mathematics)

## Difference Between Partial and Total Derivative

Here you will learn by example what the difference is between the partial derivative and the total derivative.

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)

## How to Solve Linear 2nd Order Differential Equation with Characteristic Polynomial ( + Example)

Learn how to solve 2nd order (in)homogeneous linear differential equations using the exponential ansatz. The DEQ of the harmonic oscillator is solved.

Content of the video
1. [00:00] What is exponential ansatz good for?
2. [00:45] Derivation of the method
3. [03:09] Example: Undamped harmonic oscillator
Video
Level 3 (with higher mathematics)

## How to Solve Partial Differential Equations with Separation of Variables

Learn how to solve partial differential equations (PDE) with separation of variables (product ansatz). Here we make an example with the one-dimensional wave equation.

Content of the video
1. [00:00] What is Separation of Variables good for?
2. [00:23] Example: Separate 1d wave equation
Video
Level 3 (with higher mathematics)

## How to Solve 1st Order Homogeneous Differential Equations (with Separation of Variables)

Here you will learn how to solve 1st order homogeneous linear differential equations using the "separation of variables" solving method.

Content of the video
1. [00:00] What is Separation of Variables good for?
2. [00:39] Derivation of the method
3. [02:25] Example: Decay law
Video
Level 3 (with higher mathematics)

## How to Solve 1st Order Inhomogeneous Differential Equations (with Variation of Constants)

Learn how to solve 1st order inhomogeneous linear differential equations using the "variation of constants" (variation of parameters) method.

Content of the video
1. [00:00] What is Variation of Parameters good for?
2. [00:45] Derivation of the method
3. [03:09] Example: RL circuit
Video
Level 3 (with higher mathematics)

## Divergence Theorem: The Simplest Explanation Every Physicist Should Know

Learn the Divergence Theorem in only 8 minutes, namely how it links a volume integral with a surface integral.

Content of the video
1. [00:00] Equation
2. [00:05] Surface integral in the Divergence Theorem
3. [04:21] Volume integral in the Divergence Theorem
4. [07:09] Summary
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