1. 1 Limit of a complex function Lecture # 7 MTH 324

2. 2 Complex power function Principal square root function Inverse function Multiple-valued functions Previous Lecture’s Review

3. 3 Lecture’s Outline Concept of neighborhood Limit of a real valued function Limit of a complex function Real multivariable limit Limit of a complex function in terms of real valued function

4. 4 Concept of neighborhood in real

5. 5

6. 6 Deleted neighborhood

7. 7 Example: Solution:

8. 8 Concept of neighborhood in Complex

9. 9 Deleted neighborhood

10. 10 Example: Solution:

11. 11 Limit of a real valued function:

12. 12 Geometric meanings of real limit:

13. 13 Remark: Example:

14. 14

15. 15

16. 16 Limit of a complex valued function:

17. 17

18. 18 Geometric meanings of complex limit:

19. 19 Example: Solution:

20. 20

21. 21

22. 22 Criterion for the nonexistence of a limit

23. 23 Example: Solution:

24. 24

25. 25 Real and imaginary parts of limit Theorem

26. 26 Example: Solution:

27. 27 Properties of complex limit:

28. 28

29. 29

30. 30 Example: Solution:

31. 31 Comparison of Real valued functions with complex valued functions

32. 32 References A First Course in Complex Analysis with Applications by Dennis G. Zill and Patrick D. Shanahan. Complex variables and applications by James Brown and Ruel Churchill