COMPLEX VARIBALES AND APPLICATIONS |
Common terms and phrases
analytic continuation analytic function angle arctan bounded branch cut C₁ Cauchy integral formula Cauchy-Goursat theorem Cauchy-Riemann conditions closed contour coefficients complex number complex variable conjugate harmonic functions continuous function corresponding cosh curve defined definition denote Dirichlet problem domain entire function essential singular point Exercise exists f(zo finite number flow fluid follows function f ƒ is analytic half plane harmonic function Hence inequality infinite integral formula integrand Laurent series limit line segment linear fractional transformation Maclaurin series maps neighborhood P(ro partial derivatives pole polygon positive number power series problem prove quadrant r₁ r₂ real axis real numbers region represents residue satisfy shown in Fig single-valued singular point sinh strip tends to infinity tion upper half vanishes vector velocity w₁ w₂ write written xo,yo z₁ ди მყ