finalmaterial

finalmaterial - ACM 95a/ACM 100a Final Information 2008...

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ACM 95a/ACM 100a Final Information 2008 Topics Introduction to complex numbers, polar form, Euler's formula, the complex exponential, trigonometric functions, deMoivre's formula, integer powers and roots, the complex logarithm, multiple-valuedness, periodicity, complex exponents, inverse trigonometric functions, Riemann surfaces, the point at infinity, the stereographic projection, branch points and branch cuts, branch point at infinity, regions of the complex plane, limits and continuity, the complex derivative, analyticity, the Cauchy-Riemann equations, complex integration, parameterization, contours, fundamental theorem for contour integration, equivalence between existence of antiderivatives, vanishing of closed contour integrals and independence of path, the Cauchy-Goursat theorem, extensions to self-intersecting contours and multiply-connected domains, deformation of contours, Cauchy integral formula, derivatives of analytic functions, generalized Cauchy integral formula, Morera's theorem, uniform convergence, Taylor series, uniqueness of analytic functions, power
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