1 3 integral calculus n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
1.3 Integral Calculus PowerPoint Presentation
Download Presentation
1.3 Integral Calculus

Loading in 2 Seconds...

  share
play fullscreen
1 / 16
giles

1.3 Integral Calculus - PowerPoint PPT Presentation

163 Views
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. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - 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