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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

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MAT 3730 Complex Variables

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  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

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