Complex Variables with Physical Applications |
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Page 67
... interior points of R , and R. Thus , if zo is a regular point of f ,, it maps into an interior point w 。 of R , and , hence , there is a neighborhood of zo that maps into an open set that contains wo and is contained within R. Any ...
... interior points of R , and R. Thus , if zo is a regular point of f ,, it maps into an interior point w 。 of R , and , hence , there is a neighborhood of zo that maps into an open set that contains wo and is contained within R. Any ...
Page 69
... interior . Similarly , for the branch f2 . A simple closed curve г , which contains the branch point z = 0 in its interior , maps onto a simple arc I under f ,, which is a semicircle extending from one boundary of R to the other ...
... interior . Similarly , for the branch f2 . A simple closed curve г , which contains the branch point z = 0 in its interior , maps onto a simple arc I under f ,, which is a semicircle extending from one boundary of R to the other ...
Page 124
... interior form a hole , D ' is multiply connected . But the complement of D ' with respect to the ( finite ) z - plane is the connected set consisting of C and its interior ; that is , D ' appears to be a simply connected domain . On the ...
... interior form a hole , D ' is multiply connected . But the complement of D ' with respect to the ( finite ) z - plane is the connected set consisting of C and its interior ; that is , D ' appears to be a simply connected domain . On the ...
Contents
COMPLEX NUMBERS | 1 |
15 | 24 |
FUNCTIONS OF A COMPLEX VARIABLE | 33 |
Copyright | |
13 other sections not shown
Common terms and phrases
absolutely convergent analytic continuation analytic element analytic function b₁ b₂ boundary bounded branch point C₁ C₂ Cauchy-Riemann equations centered closed curve complex number complex potential cosh D₁ D₂ defined derivative direct analytic continuation disc f₁ f₂ f₂(z function f(z fundamental regions harmonic harmonic conjugate Hence infinity inside integral interior isolated singularity k₁ k₂ lim f(z limit point maps neighborhood nth root P₂ pole polygon positive integer positive number positively-sensed Prob PROBLEM Prove radius real number removable singularity Riemann surface satisfying sequence Show shown in Fig simple polygon sin² single-valued singularity sinh Solution streamlines subset T₁ T₂ theorem transformation upper half upper half-plane vanishes vector w₁ w₂ x-axis z-plane z₁ z₂ zero Σπί ди ду