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Vector Calculus For Physics: A Complete Self-Study Course

Curriculum

  • 4 Sections
  • 14 Lessons
  • Lifetime
Expand all sectionsCollapse all sections
  • Part 0: Course Introduction
    2
    • 1.1
      Course Introduction
    • 1.2
      Additional Resources
  • Part 1: Physics With Calculus
    1
    • 2.1
      Download Part 1 Here!
  • Part 2: Vector Calculus
    8
    • 3.1
      Scalar & Vector Fields
    • 3.2
      Multivariable Calculus & Partial Derivatives
    • 3.3
      Double & Triple Integrals
    • 3.4
      Gradient, Divergence, Curl & Laplacian
    • 3.5
      Parametric Curves & Surfaces
    • 3.6
      Line Integrals & Surface Integrals
    • 3.7
      Stokes’ Theorem & The Divergence Theorem
    • 3.8
      The Helmholtz Decomposition Theorem
  • Part 3: Calculus of Variations
    3
    • 5.1
      Functionals & Variations
    • 5.2
      The Euler-Lagrange Equation & Beltrami Identity
    • 5.3
      Examples of Variational Calculus

Additional Resources

This page will contain links to various free online resources, such as online calculators, articles, research papers or even Youtube videos.

I’m planning on building a helpful resource database here that you’ll be able to use to explore additional learning materials and tools.

Resources will be added here once I find something you may benefit from!

Online calculators

Doing calculations by hand is a great way to learn various mathematical skills and personally, I believe you should do pretty much all calculations by hand at the beginning.

However, if you already know how to perform various calculations, doing them over and over again can become repetitious and using calculators instead can save you a lot of time.

Below, I’ve included some useful online calculators that you can use for free:

  • Cross product calculator – Calculating cross products by hand can sometimes be annoying as you have to remember where all the minus signs go and so on. You can use this calculator to easily find the cross product of two vectors.
  • Curl calculator – Similarly to cross products, the curl of a vector field is often annoying to calculate, so you can use this online calculator to do that (in Cartesian coordinates).
  • WolframAlpha integral calculator – This can help you calculate some integrals that may be time-consuming to do by hand.

Other stuff

This Youtube playlist on vector calculus by Dr. Trefor Bazett covers some topics that are not covered in detail in this course. It’s also a nice way to get another perspective on the main topics that this course is about.

Course Introduction
Prev
Download Part 1 Here!
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