1 / 42

Integrals for Measuring Flow

VC.05. Integrals for Measuring Flow. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve.

dympna
Download Presentation

Integrals for Measuring Flow

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. VC.05 Integrals for Measuring Flow

  2. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve

  3. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve

  4. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve

  5. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve

  6. Example 1: Measuring the Flow of a Vector Field ALONG a Closed Curve

  7. The Line Integral: Formalizing What We Just Did

  8. The Line Integral: Formalizing What We Just Did

  9. Other Ways Of Writing The Line Integral

  10. Put it All Together: Measuring the Flow of a Vector Field ALONG a Curve These integrals are usually called line integrals or path integrals.

  11. Put it All Together: Measuring the Flow of a Vector Field ALONG a Curve

  12. Example 2: Measuring the Flow of a Vector Field Along Another Closed Curve

  13. Example 2: Measuring the Flow of a Vector Field Along Another Closed Curve  Counterclockwise

  14. Example 3: Measuring the Flow of a Vector Field ACROSS a Closed Curve

  15. Example 3: Measuring the Flow of a Vector Field ACROSS a Closed Curve

  16. Example 3: Measuring the Flow of a Vector Field ACROSS a Closed Curve

  17. Example 3: Measuring the Flow of a Vector Field ACROSS a Closed Curve

  18. Example 3: Measuring the Flow of a Vector Field ACROSS a Closed Curve

  19. Put it All Together: Measuring the Flow of a Vector Field ACROSS a Curve

  20. Put it All Together: Measuring the Flow of a Vector Field ALONG a Curve

  21. Example 4: Measuring the Flow of a Vector Field Across Another Closed Curve

  22. Example 4: Measuring the Flow of a Vector Field Across Another Closed Curve  Counterclockwise

  23. Example 5: The Flow of a Gradient Field Along a Closed Curve

  24. Example 5: The Flow of a Gradient Field Along a Closed Curve

  25. Example 5: The Flow of a Gradient Field Along a Closed Curve

  26. Summary: The Flow of a Gradient Field Along a Closed Curve

  27. Example 6: Is the Flow of ANY Vector Field Along a Closed Curve Zero?  Counterclockwise

  28. Example 7: How Do We Know When We Have a Gradient Field?

  29. The Gradient Test

  30. Example 7: How Do We Know When We Have a Gradient Field?

  31. Example 8: The Flow of a Vector Field Along an Open Curve

  32. Example 8: The Flow of a Vector Field Along an Open Curve

  33. Example 8: The Flow of a Vector Field Along an Open Curve

  34. Example 9: The Flow of a Gradient Field Along an Open Curve (Path Independence)

  35. Example 9: The Flow of a Gradient Field Along an Open Curve (Path Independence)

  36. Example 9: The Flow of a Gradient Field Along an Open Curve (Path Independence)

  37. Example 9: The Flow of a Gradient Field Along an Open Curve (Path Independence)

  38. Path Independence: The Flow of a Gradient Field Along an Open Curve

  39. Example 9: The Flow of a Gradient Field Along an Open Curve

  40. Example 9: The Flow of a Gradient Field Along an Open Curve

  41. Example 9: The Flow of a Gradient Field Along an Open Curve

  42. Example 10: Are All Vector Fields Path Independent? (Ex 8 Revisited)

More Related