MTH 324 Lecture 7 Limit of a complex

MTH 324 Lecture # 7 Limit of a complex function 1

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

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 3

Concept of neighborhood in real 4

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Deleted neighborhood 6

Example: Solution: 7

Concept of neighborhood in Complex 8

Deleted neighborhood 9

Example: Solution: 10

Limit of a real valued function: 11

Geometric meanings of real limit: 12

Remark: Example: 13

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Limit of a complex valued function: 16

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Geometric meanings of complex limit: 18

Example: Solution: 19

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Criterion for the nonexistence of a limit 22

Example: Solution: 23

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Real and imaginary parts of limit Theorem 25

Example: Solution: 26

Properties of complex limit: 27

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Example: Solution: 30

Comparison of Real valued functions with complex valued functions 31

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 32