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Course Mathematics for physics enthusiasts II

Advanced tools from mathematics for physicists.
A two-dimensional scalar function - 3D Plot
Level 3 (for advanced students)
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
  1. 1
    Video

    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
    Quests with solutions
  2. 2
    Lesson

    Differential equations (DEQ): Important basics + 4 solving methods

    Here you will learn the basics of differential equations (DGL), what types there are (ordinary, partial, linear, homogeneous) and 4 solving methods (separation of variables, variation of constants, exponential and separation ansatz).

    Video

    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
Practicing what you have learned...