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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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A function f(z)=u(x,y)+iv(x,y) is differentiable and analytic, there must be particular connection between u(x,y) and v(x,y)
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Chapter 20 Complex variables
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not , of ncombinatio the
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1
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is of conjugatecomplex and
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Chapter 20 Complex variables
dimension. two in equation
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Chapter 20 Complex variables
20.3 Power series in a complex variable
0at only converges 0 )!(lim ! (2)
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
20.5 Multivalued functions and branch cuts
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x
C
r
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2/1
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origin the enclose 2
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Chapter 20 Complex variables
Branch point: z remains unchanged while z traverse a closed contour C about some point. But a function f(z) changes after one complete circuit.
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20restrict
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y
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Chapter 20 Complex variables
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2211
2211
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i
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Chapter 20 Complex variables
20.6 Singularities and zeros of complex function
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in points allat analytic is )( integer, positive a is
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number complex zero-non finite, a is and analytic is )(
)]()[(lim
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Chapter 20 Complex variables
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1}sinh
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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Chapter 20 Complex variables
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