1 / 32

MAT 3730 Complex Variables

MAT 3730 Complex Variables. Section 1.6 Planar Sets. http://myhome.spu.edu/lauw. Preview. For real variables, theorems are typically stated for functions defined on intervals (open, closed) We will introduce the corresponding concepts in the complex plane

xander-powers
Download Presentation

MAT 3730 Complex Variables

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. MAT 3730Complex Variables Section 1.6 Planar Sets http://myhome.spu.edu/lauw

  2. Preview • For real variables, theorems are typically stated for functions defined on intervals (open, closed) • We will introduce the corresponding concepts in the complex plane • Mostly the same as defined in R2 (MAT 3238?)

  3. Definition 1 Open Disk/ (Circular) Neighborhood

  4. Example 1

  5. Definition 2 Interior Points

  6. Example 2

  7. Definition 3 Open Sets

  8. Example 3

  9. Example 4

  10. Example 5

  11. Definition 4 Connected Open Sets

  12. Example 6

  13. Example 7

  14. Definition 5 Domain

  15. Domain • Many results in real and complex analysis are true only in domains. Below is an example in calculus (real analysis). We will take a look at why the connectedness is important.

  16. Idea Theorem

  17. Definition 6 Boundary Points

  18. Observations

  19. Definition 7 Boundary

  20. Example 8

  21. Example 8

  22. Definition 8 Closed Sets

  23. Example 9

  24. Example 10

  25. Example 10

  26. Definition 9 Region

  27. Definition 9 Region T or F: If D is a domain, then it is a region.

  28. Definition 9 Region T or F: If D is a domain, then it is a region. T or F: If D is a region, then it is a domain.

  29. Definition 10 Bounded Sets

  30. Question Can you name a unbounded set?

  31. Definitions Dependency nhood Interior Points Boundary Points Bounded Set Open Set Closed Set Connected Set Domain Region

  32. Next Class • Read Section 2.1 • Review Onto Functions

More Related