Transcription of 3 Contour integrals and Cauchy’s Theorem
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3 Contour integrals and Cauchy’s Theorem
3 Contour integrals and cauchy s Line integrals of complex functionsOur goal here will be to discuss integration of complex functionsf(z) =u+iv, with particular regard to analytic functions. Of course, one way tothink of integration is as antidifferentiation. But there is also the definiteintegral. For a functionf(x) of a real variablex, we have the integral baf(x)dx. In casef(x) =u(x) +iv(x) is a complex -valued function ofa real variablex, the definite integral is the complex number obtained byintegrating the real and imaginary parts off(x) separately, baf(x)dx= bau(x)dx+i bav(x)dx.
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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