
 Spring 2004 Math 185 (Complex Analysis) homepage (Site not responding. Last check: 20071013) 
  Differentiation, (contour) integration, Cauchy's theorem, Liouville's theorem, proof of the Fundamental theorem of algebra, Maximum modulus principle, Taylor and Laurent series, residues and introduction to conformal mappings. 
  Lecture 9: Defined the contour integral of a function f:C>C along a piecewise C^{1} curve gamma:[a,b]>C; i.e., gamma is continuous on [a,b], and there is a subdivision of [a,b] such that the derivative of gamma exists on each open subinterval (a_i, b_i), and the derivative is continuous on each closed subinterval [a_i,b_i]. 
  We moved on to the main theorem of the course: Cauchy's theorem, which states that the contour integral of a function f that is analytic on and inside a closed curve is zero. 
 math.berkeley.edu /~ayong/Spring2004_Math185.html (2447 words) 
