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    01141 Complex Analysis

    Here you will find a short dictionary prepared by Bodil Branner 2006 {Translation from English to Danish}. The dicionary is also available as a pdf-file.

    A | B | C | D |  E | F | G | H |  I | J | K | L |  M | N | O | P |  Q | R | S | T |  U | V | W | X |  Y | Z

    A

    Absolute value = absolut værdi, 8

    Absolute convergence = absolut konvergens, 237

    Accumulation point = akkumulations-punkt, 43

    Analytic continuation = analytisk fortsættelse, 292

    Analytic function = analytisk funktion, 70

    Antiderivative = stamfunktion, 173

    Arc = kurve uden selvgennemskæringer, 150

    Argument = argument, 17

    Arctic circle = (nordlig) polarcirkel, 45

    B

    Bijective = bijektiv

    Bilinear transformation = bilineær transformation, 389

    Binomial formula = binomial formel, 6, 250

    Boundary = rand, 42

    Bounded set = begrænset mængde, 42

    Branch = gren, 122, 132

    Branch of argument = gren af argument, 18

    Branch of logarithm = gren af logaritme, 119

    Branch, principal = hovedgren, 18, 119

    Branch cut = forgreningssnit, 18, 119

    Branch point = forgreningspunkt, 122

    C

    Cauchy criterion = Cauchy kriterium, 262

    Cauchy estimates = Cauchy vurderinger, 214, 215

    Cauchy product = Cauchy produkt, 247

    Cauchy sequence = Cauchy følge, 262

    Cauchy series = Cauchy række, 263

    Cauchy's integral formula = Cauchy's integralformel, 204, 210, 211

    Cauchy's integral theorem = Cauchy's integralsætning, 187, 194

    Cauchy-Riemann equations = Cauchy-Riemann ligningerne, 73

    Chain rule = kæderegel, 69

    Chordal distance = kordeafstand, 49

    Circle of convergence = konvergenscirkel, 253

    Closed contour = lukket kontur, lukket kurve, 157

    Closed disk (set) = afsluttet cirkelskive (mængde), 42

    Compact = kompakt, 42

    Comparison test = sammenligningskriterium, 236

    Complex conjugate = kompleks konjugeret, 10

    Complex number = komplekst tal, 3

    Complex plane = kompleks plan, 8

    Complex plane, extended = udvidet kompleks plan, 288

    Conformal = konform, 378

    Conjugate = konjugeret, 10

    Connected set = sammenhængende mængde, 40, 44

    Contour = kontur, kurve, 154

    Contour, integral along = kurveintegral, 162, 167

    Contour, length of = længde af kurve, 159

    Convergence = konvergens, 58

    Convergence, Cauchy criterion for = Cauchy kriteriet for konvergens, 262

    Convergence, absolute = absolut konvergens, 237

    Convergence, pointwise = punktvis konvergens, 238

    Convergence, uniform = uniform eller ligelig konvergens, 238

    Cross-ratio = dobbeltforhold, 397

    Curve = kurve, 149

    D

    De Moivre's formula = De Moivre's formel, 29

    Deformation invariance theorem = deformations-sætningen, 186

    Deformation of contours = deformation af konturer (eller kurver), 182

    Denominator = nævner

    Derivative = afledet, 67

    Differentiability = differentiabilitet, 67

    Differential equation = differentialligning, 67

    Differential equation, power series = potensrækker og differentialligning, 258

    Distance = afstand, 9

    Directed smooth arc = orienteret glat kurve uden selvgennemskæringer, 152

    Dirichlet problem = Dirichlet problem, 222

    Dirichlet problem for unit disk = Dirichlet problem for enheds cirkelskiven, 224

    Disk = cirkelskive

    Domain = område, domæne, 40

    Domain of analyticity = analyticitetsområde

    Domain of conformality = område hvor funktionen er konform, 378

    Domain of definition = definitionsmængde, 53

    E

    Entire function = hel function, 70

    Equipotential = ækvipotential, 81

    Essential singularity = væsentlig singularitet, 279, 282

    Essential singularity at infinity = væsentlig singularitet i uendelig, 288

    Euler's equation = Euler's ligning, 27

    Exponential function = eksponential funktion, 27, 111

    Extended complex plane = udvidet kompleks plan, 48, 288

    F

    Fibonacci sequence = Fibonacci følge, 268

    Fixed point = fikspunkt, 92

    Focus, focal point = brændpunkt

    Fractals = fraktaler, 93

    Fundamental region = fundamentalmængde (eller område), 112

    Fundamental theorem of algebra = algebraens fundamentalsætning, 101, 216, 362

    Fundamental theorem of calculus = integralregningens fundamentalsætning, 161

    G

    Generalized Cauchy integral formula = generaliseret Cauchy integralformel, 210, 211

    Generalized circle = generaliseret cirkel, 388

    Geometric series = kvotientrække, 236

    Great circle = storcirkel, 50

    Green's theorem = Green's sætning, 192

    H

    Harmonic conjugate = harmonisk konjugeret, 80

    Harmonic function = harmonisk funktion, 79, 221

    Holomorphic function = holomorf funktion, 70

    Hyperbolic functions = hyperbolske funktioner, 114

    I

    Image = billede, 53

    Imaginary axis = imaginær akse, 8

    Improper integrals = uegentlige integraler, 337

    Independence of path = uafhængighed af vejen, 173

    Infinity (point at) = uendelig (punkt i), 288

    Initial point = begyndelsespunkt, 173

    Integral = integral, 162

    Integral, bounds for = grænser for integral, 169

    Integral, contour = kurveintegral, 167

    Integration by parts = partiel (eller delvis) integration, 179

    Interior point = indre punkt, 39

    Inverse trigonometric functions = inverse trigonometriske funktioner, 134

    Inversion = inversion, 55, 387

    Isolated singularity = isoleret singularitet, 277

    Isotherms = isotermer, 81, 419

    J

    Jacobian = Jacobiant, 78

    Jordan curve theorem = Jordan's kurvesætning, 158

    Joukowski, 57, 438

    Julia set = Julia mængde, 92

    K

    L

    L'H\opital's rule = L'H\opital's regel, 72, 261

    Laplace's equation = Laplace's ligning, 79, 221, 369

    Laurent series = Laurent række, 269

    Leibniz's formula = Leibniz's formel, 248

    Level curve = niveau kurve, 81

    Limit = grænse, 58

    Linear transformation = lineær transformation, 57, 385

    Liouville's theorem = Liouville's sætning, 215, 226

    Logarithm = logaritme, 118

    Loop = løkke, 157

    M

    Maclaurin form = Maclaurin form, 103

    Maclaurin series = Maclaurin række, 242,

    Magnification = skalering, 57, 385

    Mandelbrot set = Mandelbrot mængden, 93

    Mapping = afbildning, 53

    Maximum modulus principle = maksimum modulus princip, 217

    Maximum principle = maksimum princip, 222

    Mean-value property = middelværdi egenskab, 226

    Meromorphic = meromorf, 355

    Minimum modulus principle = minimum modulus princip, 220

    Minimum principle = minimum princip, 222

    Möbius transformation = Möbius transformation, 389, 396, A-19

    Modulus = modulus, 8

    Multiple-valued = flertydig, 118

    M-test = Weierstrass majorant kriterium, 263

    N

    Neighborhood = omegn, 39

    Numerator = tæller

    O

    One-to-one function = en-til-en eller en-entydig funktion, 111

    Open disk (set) = åben cirkelskive (mængde), 39

    Open mapping property = åben afbildningsegenskab, 363

    Orbit = bane, 91

    Order relation = ordnings relation, 7

    P

    Parametrization = parametrisering, 149, 154

    Partial fraction decomposition = dekomponering i stambrøker, 105

    Partial fractions = stambrøker, 105

    Partial sum = afsnit, 235

    Picard's theorem = Picard's sætning, 282

    Piecewise smooth curve = stykkevis glat kurve, 157

    Pointwise convergence = punktvis konvergens, 238

    Polar form = polær form, 18

    Pole = pol, 104, 279

    Pole of order m (or multiplicity) = pol af orden m (eller multiplicitet), 104, 279

    Polygonal path = polygonal sti (eller vej), 39

    Polynomial = polynomium, 61

    Polynomials = polynomier, 99

    Potential = potential, 200

    Power series = potensrække, 252

    Primitive m'th root of unity = primitiv m'te enhedsrod, 34

    Principal branch = hovedgren, 119

    Principal value of argument = hoverværdi af argument, 18

    Principal value of logarithm = hovedværdi af logaritme, 119

    Principal value of integral = hovedværdi af integral, 319

    Pure imaginary number = rent imaginært tal, 4

    Q

    Quadratic formula = løsningsformel til rødder i kvadratisk polynomium, 36

    R

    Radius of convergence = konvergensradius, 253

    Range = værdimængde, 53

    Ratio test = kvotientkriterium, 237

    Rational function = rational funktion, 62, 99

    Real axis = reel akse, 8

    Regular = regulær, 70

    Removable discontinuity = hævelig diskontinuitet, 62

    Removable singularity = hævelig singularitet, 279

    Residue = residuum eller residue, 109, 308

    Residue theorem = residue sætning, 312

    Resistance = modstand, 139

    Riemann hypothesis = Riemann hypotesen, 268

    Riemann mapping theorem = Riemann's afbildningssætning, 380

    Riemann sphere = Riemann-kuglen, 45

    Riemann sum = Riemann sum, 162

    Riemann zeta function = Riemann's zeta funktion, 268

    Roots of unity = enhedsrødder, 34

    Rotation = rotation, 57, 384

    S

    Schwarz-Christoffel transformations = Schwarz-Christoffel transformationer, 407

    Sequence = følge, 235

    Series = uendelig række, række, 235

    Simple pole = simpel pol, pol af orden 1, 280

    Simple zero = simpelt nulpunkt, nulpunkt af orden 1, 278

    Simply connected domain = enkeltsammenhængende område, 184, 193

    Single-valued = entydig (ikke at forveksle med one-to-one = en-entydig), 118

    Singular part = singulær del, 107

    Singularity = singularitet, 278, 279

    Singularity, essential = væsentlig singularitet, 279

    Singularity, pole = pol, 279

    Singularity, removable = hævelig, 279

    Slit plane = opskåret plan

    Smooth arc = glat (eller regulær) kurve uden selvgennemskæring, 150

    Smooth closed curves = glatte (eller regulære) lukkede kurver uden selvgennemskæring, 150

    Streographic projection = stereografisk prjektion, 44

    Strip = strimmel

    T

    Taylor form = Taylor form, 103

    Taylor series = Taylor række, 242

    Terminal point = endepunkt, 173

    Translation = translation, parallelforskydning, 57, 384

    Triangle inequality = trekantsulighed

    Trigonometric functions = trigonometriske funktioner, 113, 114

    Tropic of Cancer = (Krebsens) vendekreds, 45

    U

    Uniform convergence = uniform eller ligelig konvergens, 238, 239

    V

    W

    Washer = pakning, 125

    Wedge = kile, 126

    Weierstrass M-test = Weierstrass majorant kriterium, 263

    X

    Y

    Z

    Zero of order m = nulpunkt af orden m, 277



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    Sidst ændret: 20.08.2010 kl 15:41:17
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