Math 411: Honours Complex Variables - University of Alberta
Math 411: Honours Complex Variables - University of Alberta
Math 411: Honours Complex Variables - University of Alberta
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
120 INDEX<br />
holomorphic nth roots, 71<br />
Holomorphic Inverses, 113<br />
Holomorphic Logarithms, 71<br />
holomorphic logarithms, 71<br />
Holomorphic Roots, 71<br />
holomorphic roots, 71<br />
homologous to zero, 68<br />
homotopic to zero, 117<br />
Hurwitz’s Theorem, 91<br />
Identity Theorem, 46<br />
imaginary part, 6<br />
imaginary unit, 6<br />
initial point, 22<br />
integrable, 22<br />
Integration <strong>of</strong> Power Series, 21<br />
interior, 66<br />
isolated singularity, 52<br />
Jordan’s Lemma:, 80<br />
Laurent Coefficients, 61<br />
Laurent Decomposition, 59<br />
Laurent decomposition, 61<br />
Laurent series, 61<br />
length, 23<br />
line integral, 23<br />
Liouville’s Theorem, 40<br />
Local Uniform Convergence, 42<br />
locally constant, 24<br />
Locally Constant vs. Connectivity, 25<br />
locally uniformly, 42<br />
Maximum Modulus Principle, 48<br />
MaximumModulusPrincipleforBounded<br />
Domains, 49<br />
Mean Value Equation, 36<br />
mean value property, 101<br />
meromorphic function, 88<br />
Meromorphic Functions Form a Field, 89<br />
Monodromy Theorem, 105<br />
Montel’s Theorem, 109<br />
Morera condition, 39<br />
Open Mapping Theorem, 48<br />
order, 54<br />
ordered, 6<br />
orthogonal, 112<br />
path, 22<br />
path homotopic, 117<br />
piecewise smooth, 22<br />
point <strong>of</strong> expansion, 14<br />
Poisson kernel, 98<br />
Poisson’s Integral Formula, 98<br />
pole, 53<br />
power series, 14<br />
Power Series for Holomorphic Functions,<br />
45<br />
principal argument, 31<br />
principal branch <strong>of</strong> the logarithm, 31<br />
principal part, 61<br />
Radius <strong>of</strong> Convergence, 16<br />
radius <strong>of</strong> convergence, 16<br />
Rational Functions, 78<br />
Rational Trigonometric Polynomials, 75<br />
real part, 6<br />
region, 26<br />
removable, 52<br />
residue, 72<br />
Residue Theorem, 73<br />
reversed curve, 25<br />
Riemann Mapping Theorem, 114<br />
Riemann sphere, 88<br />
Riemann’s Removability Condition, 52<br />
Rouché’s Theorem, 92<br />
Runge’s Approximation Theorem, 118<br />
Schwarz’s Lemma, 49<br />
secondary part, 61<br />
simple pole, 54<br />
simply connected, 68<br />
Simply Connected Domains, 116<br />
sine, 15<br />
sliced plane, 31<br />
star shaped, 30