1 / 16

1.3 Integral Calculus

1.3 Integral Calculus. 1.3.1 Line, Surface, Volume Integrals. a) line integral:. Example 1.6. For a given boundary line there many different surfaces, on which the surface integral depends. It is independent only if. If the surface is closed:. b) surface integral:. 2. 2. 2.

arin
Download Presentation

1.3 Integral Calculus

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. 1.3 Integral Calculus 1.3.1 Line, Surface, Volume Integrals

  2. a) line integral:

  3. Example 1.6

  4. For a given boundary line there many different surfaces, on which the surface integral depends. It is independent only if If the surface is closed: b) surface integral:

  5. 2 2 2 Example 1.7

  6. volume integral:

  7. Example 1.8

  8. 1.3.3 Fundamental Theorem for Gradients The line integral does not depend on the path P.

  9. Example 1.9 along I-II and III

  10. 1.3.4 Fundamental Theorem for Divergences (also Gauss’s or Green’s theorem) The surface S encloses the volume V.

  11. dz dy dx

  12. Example 1.10 Check the divergence theorem for

  13. 1.3.5 Fundamental Theorem for Curls (also Stokes’ theorem) The path P is the boundary of the surface S. The integral does not depend on S.

  14. dz dy

  15. You must do it in a consistent way!

  16. Example 1.11 Check Stokes’ Theorem for

More Related