1 Limit of a complex function Lecture # 7 MTH 324

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

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 Concept of neighborhood in real

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6 Deleted neighborhood

7 Example: Solution:

8 Concept of neighborhood in Complex

9 Deleted neighborhood

10 Example: Solution:

11 Limit of a real valued function:

12 Geometric meanings of real limit:

13 Remark: Example:

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16 Limit of a complex valued function:

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18 Geometric meanings of complex limit:

19 Example: Solution:

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22 Criterion for the nonexistence of a limit

23 Example: Solution:

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25 Real and imaginary parts of limit Theorem

26 Example: Solution:

27 Properties of complex limit:

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30 Example: Solution:

31 Comparison of Real valued functions with complex valued functions

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