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