Calculus IV - Vector Calculus - Line Integrals, Surface Integrals, Vector Fields, Green's Theorem, Divergence Theorem, Stokes Theorem

Calculus IV - Vector Calculus - Line Integrals, Surface Integrals, Vector Fields, Green's Theorem, Divergence Theorem, Stokes Theorem

DrTreforBazett via YouTube Direct link

Finding the scalar potential function for a conservative vector field // Vector Calculus

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16 of 39

Finding the scalar potential function for a conservative vector field // Vector Calculus

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Calculus IV - Vector Calculus - Line Integrals, Surface Integrals, Vector Fields, Green's Theorem, Divergence Theorem, Stokes Theorem

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  1. 1 What is VECTOR CALCULUS?? **Full Course Introduction**
  2. 2 Curves, Parameterizations, and the Arclength Parameterization
  3. 3 What is a LINE INTEGRAL? // Big Idea, Derivation & Formula
  4. 4 Line Integrals: Full Example
  5. 5 Line Integrals in 3D // Formula & Three Applications
  6. 6 Intro to VECTOR FIELDS // Sketching by hand & with computers
  7. 7 The Gradient Vector Field
  8. 8 Line Integrals of Vector Fields // Big Idea, Definition & Formula
  9. 9 Example: Computing the Line Integral of a Vector Field (i.e. Work Done)
  10. 10 Line Integrals with respect to x or y // Vector Calculus
  11. 11 Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus
  12. 12 Flux Integrals // Big Idea, Formula & Examples // Vector Calculus
  13. 13 Conservative Vector Fields // Vector Calculus
  14. 14 The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus
  15. 15 How to Test if a Vector Field is Conservative // Vector Calculus
  16. 16 Finding the scalar potential function for a conservative vector field // Vector Calculus
  17. 17 Curl or Circulation Density of a Vector Field // Vector Calculus
  18. 18 Curl, Circulation, and Green's Theorem // Vector Calculus
  19. 19 Divergence, Flux, and Green's Theorem // Vector Calculus
  20. 20 Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus
  21. 21 Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus
  22. 22 The Surface Area formula for Parametric Surfaces // Vector Calculus
  23. 23 Why is the surface area of a Sphere 4pi times radius squared???
  24. 24 Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus
  25. 25 Computing the Surface Area of a surface parametrically // Example 2 // Vector Calculus
  26. 26 Surface Area for Implicit & Explicit Surfaces // Vector Calculus
  27. 27 Computing the Surface Area of an Implicitly Defined Surface
  28. 28 Surface Integrals // Formulas & Applications // Vector Calculus
  29. 29 Orientable vs Non-Orientable Surfaces and the Mobius Strip
  30. 30 Flux of a Vector Field Across a Surface // Vector Calculus
  31. 31 Computing the Flux Across a Surface // Vector Calculus
  32. 32 The CURL of a 3D vector field // Vector Calculus
  33. 33 Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus
  34. 34 Stokes' Theorem Example // Verifying both Sides // Vector Calculus
  35. 35 The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus
  36. 36 Divergence Theorem example: Flux across unit cube // Vector Calculus
  37. 37 Divergence Theorem for regions bounded by two surfaces // Vector Calculus
  38. 38 Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus
  39. 39 A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)

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