2 Complex Functions and the Cauchy-Riemann Equations

ask that the usual di erence quotient exists. De nition A function f(z) is complex di erentiable at cif lim z!c f(z) f(c) z c exists. In this case, the limit is denoted by f0(c). Making the change of variable z= c+h, f(z) is complex di erentiable at cif and only if the limit lim h!0 h = = 1:

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2 Complex Functions and the Cauchy-Riemann …

2 Complex Functions and the Cauchy-Riemann Equations 2.1 Complex functions In one-variable calculus, we study functions f(x) of a real variable x.

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Calculus III: Practice Final Name: Circle one: Section 6 Section 7 . Read the problems carefully. Show your work unless asked otherwise. Partial credit will be given for incomplete work. ... tan x = sec 2 x (5) d dx cot x = csc 2 x (6) d dx sec x = sec x tan x (7) d dx csc x = csc x cot x (8) d dx ex = ex (9) d dx ln jx j = 1 x (10) d dx arcsin ...

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3 Contour integrals and Cauchy’s Theorem

3 Contour integrals and Cauchy’s Theorem 3.1 Line integrals of complex functions Our goal here will be to discuss integration of complex functions f(z) = u+ iv, with particular regard to analytic functions. Of course, one way to think of integration is as antidi erentiation. But there is also the de nite integral.

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HTML ENCODING IN .NET 3 Framework Methods System.Security.SecurityElement.Escape This method is more relative to XML elements than it is for HTML elements.