Yohance Defns Flashcards
(46 cards)
Defn of a subset U being open
Defn of neighbourhood
Defn of Function being continious
Defn of subset being compact
Details of mobius transformation
Defn of function being analytic (power series)
Defn of CR eqns in both real form and imaginary form
Defn of partial derivative wrt to z and z*
Defn of a function u(x,y) being harmonic
defn of v being harmonic conjugate to u
Defn of a curve being closed
Suppose f is continious and gamma is a smoth curve, define the intergral of f.
also define the parametiztion f = P +iQ
Define L(z)
statement about polynomials factorisaiton and zeros, with order of zeros
Defn of isolated singularity
Defn of Laurent Expansion. When is z_0 a removable singularity? defn of pole of order m?
defn of essential singularity?
If z_0 is an isolated singularity, defn the principle part
Define the residue of f at z_0
Define the principle part of z_0 if;
i) singularity is removable
ii) singularity is a pole
iii) in the case of an essential singularity
Defn of entire. Defn of meromophic
Statement about continuity of f(z) where f(z) is described as a power series
Maclaurin Taylor expansion of f(z)
Requirment of conformality of a function f(z)
if f’(z) = 0 for all z in complex plane then …
