TEAM PROJECT. Cauchy's Integral Theorem. (a) Main Aspects.
Chapter 14, Problem 14.2(choose chapter or problem)
TEAM PROJECT. Cauchy's Integral Theorem. (a) Main Aspects. Each of the problems in Examples 1-5 explains a basic fact in connection with Cauchy's theorem. Find five examples of your own, more complicated ones if possible. each illustrating one of those facts. (b) Partial fractions. Write f(::) in terms of partial fractions and integrate it counterclockwise over the unit circle, where (i) f(::) = _2 + 1- 4(ii)653z + If(::) = -=----:;:2 + 2::(c) Deformation of path. Review (c) and (d) of TeamProject 34, Sec. 14.\. in the light of the principle ofdeformation of path. Then consider another family ofpaths with common endpoints. say, ::(t) = r + ia(r - (2).o ~ ( ~ 1. and experiment with the integration of analyticand nonanalytic functions of your choice over these paths(e.g., ::. 1m::. ::2, Re .:2, 1m Z2, etc).
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