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Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

Course Mathematics for physics enthusiasts II

Advanced tools from mathematics for physicists.
  1. 1
    Orthonormale Basisvektoren - kartesisches Koordinatensystem

    Here you learn everything about Kronecker-Delta! Including 4 calculation rules with Einstein's summation convention, typical mistakes and more.

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    Video
    Kronecker delta

    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
    Differentialgleichungen - Klassifizierung

    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).

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    Video
    Differential equations

    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
    Related Illustrations
Details about the course
  • Copyright: ©2021
  • License: CC BY 4.0This lesson may be used with indication of the copyright!
  • This content was added by FufaeV on .
  • This content was updated by FufaeV on .