von Seggern, David H. 　著

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INTRODUCTIONConcept of a Curve Concept of a Surface Coordinate SystemsQualitative Properties of Curves and SurfacesClassification of Curves and SurfacesBasic Curve and Surface OperationsMethod of PresentationReferencesALGEBRAIC CURVESFunctions with xn/m Functions with xn and (a+bx)mFunctions with a2+x2 and xmFunctions with a2-x2 and xmFunctions with a3+x3 and xmFunctions with a3- x3 and xmFunctions with a4+x4 and xmFunctions with a4- x4 and xmFunctions with (a+bx)1/2 and xmFunctions with (a2-x2) 1/2 and xmFunctions with (x2- a2) 1/2 and xmFunctions with (a2C x2) 1/2 and xmMiscellaneous Functions Functions Expressible in Polar Coordinates Functions Expressed ParametricallyTRANSCENDENTAL FUNCTIONSFunctions with sinn(ax) and cosm(bx) (n, m integers)Functions with 1±a sinn(cx) and 1±b cosm(cx)Functions with a sinn(cx)+b cosm(cx)Functions of More Complicated Arguments Inverse Trigonometric Functions Logarithmic FunctionsExponential Functions Hyperbolic FunctionsInverse Hyperbolic FunctionsTrigonometric and Exponential Functions Combined Trigonometric Functions Combined with Powers of xLogarithmic Functions Combined with Powers of xExponential Functions Combined with Powers of x Hyperbolic Functions Combined with Powers of x Combinations of Trigonometric Functions, Exponential Functions, and Powers of x Miscellaneous Functions Functions Expressible in Polar Coordinates Functions Expressed ParametricallyPOLYNOMIAL SETSOrthogonal PolynomialsNonorthogonal PolynomialsReferencesSPECIAL FUNCTIONS IN MATHEMATICAL PHYSICSExponential and Related IntegralsSine and Cosine IntegralsGamma and Related FunctionsError Functions Fresnel IntegralsLegendre Functions Bessel FunctionsModified Bessel Functions Kelvin Functions Spherical Bessel Functions Modified Spherical Bessel FunctionsAiry FunctionsRiemann FunctionsParabolic Cylinder Functions Elliptic Integrals Jacobi Elliptic Functions ReferencesGREEN'S FUNCTIONS AND HARMONIC FUNCTIONSGreen's Function for the Poisson EquationGreen's Function for the Wave EquationGreen's Function for the Diffusion EquationGreen's Function for the Helmholtz EquationMiscellaneous Green's FunctionsHarmonic Functions-Solutions to Laplace's EquationReferences SPECIAL FUNCTIONS IN PROBABILITY AND STATISTICSDiscrete Probability DensitiesContinuous Probability Densities Sampling DistributionsNONDIFFERENTIALBE AND DISCONTINUOUS FUNCTIONSFunctions with a Finite Number of Discontinuities Functions with an Infinite Number of Discontinuities Functions with a Finite Number of Discontinuities in First DerivativeFunctions with an Infinite Number of Discontinuities in First DerivativeRANDOM PROCESSESElementary Random Processes General Linear ProcessesIntegrated ProcessesFractal ProcessesPoisson ProcessesReferencesPOLYGONSRegular PolygonsStar PolygonsIrregular TrianglesIrregular QuadrilateralsPolyiamondsPolyominoesPolyhexesMiscellaneous PolygonsTHREE-DIMENSIONAL CURVESHelical CurvesSine Waves in Three DimensionsMiscellaneous 3-D CurvesKnotsLinksReferencesALGEBRAIC SURFACESFunctions with ax+byFunctions with x2/a2±y2/b2Functions with (x2/ a2+y2/ b2±c2)1/2Functions with x3/a3±y3/b3Functions with x4/a4±y4/b4Miscellaneous Functions Miscellaneous Functions Expressed Parametrically TRANSCENDENTAL SURFACESTrigonometric FunctionsLogarithmic FunctionsExponential Functions Trigonometric and Exponential Functions Combined Surface Spherical HarmonicsCOMPLEX VARIABLE SURFACESAlgebraic FunctionsTranscendental FunctionsMINIMAL SURFACESElementary Minimal SurfacesComplex Minimal SurfacesReferencesREGULAR AND SEMI-REGULAR SOLIDS WITH EDGESPlatonic Solids Archimedean Solids Duals of Platonic SolidsStellated (Star) PolyhedraReferencesIRREGULAR AND MISCELLANEOUS SOLIDSIrregular PolyhedraMiscellaneous Closed Surfaces with EdgesINDEX