Understanding Differential Forms in the Physical Sciences

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Explore the concept of differential forms and their applications in the physical sciences with insights on operators such as gradient, curl, and divergence. Discover the advantages of utilizing differential forms over tensors and delve into curvilinear coordinates and integration methods. Uncover the fundamental theorems of calculus and the chain rule in differential calculus.

  • Differential Forms
  • Physical Sciences
  • Operators
  • Curvilinear Coordinates
  • Integration

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Presentation Transcript


  1. Differential Forms Part I - Derivatives Christopher Crawford UK SPS Lecture series 2024-03-20

  2. What are differential forms? Harley Flanders, "Differential Forms with Applications to the Physical Sciences"

  3. forms

  4. differential

  5. differential 1) chain rule

  6. differential 2): Fund. Theorem of Calculus

  7. differential forms + metric

  8. Main course: the Differential operator d Apply d to everything in sight!

  9. Differential operator: gradient

  10. Differential operator: curl

  11. Differential operator: divergence

  12. Curvilinear coordinates general formulas

  13. Pullback and integration

  14. Jacobian determinant

  15. Differential forms versus tensors

  16. Advantages of differential forms

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