Mathematical methods Lecture 8 of 34

October 4, 2012 by Multimedia Publications and Printing Services

Lecturer: K.S. Narain , ICTP

lecture 8

Cauchy-Rieman condition and  Binomial  expansion and Integration,

Introducing branch cut

  • We proved the necessary conditions for Cauchy-Rieman by continuity of partial derivative.
  •  Binomial  expansion was explained and we gave some examples of those
  •  given in page 16 equation 4.1.2. Also talk about Taylor expansion.
  • We give an example of any function which satisfies Laplace equation which called Harmonic function and in particular we give example in 2 dimensions.
  • The definition of integration with respect to z is given.
  • Section 9 Conformal transformation is not given but we follow the
  • rest of the chapter.
  • We give an example of having anaytic function at some point which
  •  must be differentiable at that point as well as the other point.
  • We introduce branch cut by applying Cauchy theorem.
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