Math 246A, Notes 3: Cauchy's Theorem and Its Consequences
by Terence Tao · UCLA (What's new)
Graduate lecture notes from Terence Tao's UCLA 246A course. Establishes Cauchy's theorem via Goursat and homotopy arguments, then derives the integral formula, Liouville's theorem, the argument principle, and the residue theorem, with exercises throughout. The rigorous counterweight to the computational courses: Tao states and proves Cauchy's theorem at full generality (winding numbers, homotopy invariance) rather than only for star domains, and shows explicitly how the residue theorem falls out.
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