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CRC Standard Curves and Surfaces with Mathematica

计算循环冗余校验码标准曲线与表面及数学

ISBN：9781482250213，出版年：2017，中图分类号：O18 被引 62次

Introduction Concept of a Curve Concept of a Surface Coordinate Systems Qualitative Properties of Curves and Surfaces Classification of Curves and Surfaces Basic Curve and Surface Operations Method of Presentation References Algebraic Functions Plotting Information for This Chapter Functions with xn/m Functions with xn and (a + bx)m Functions with (a2 + x 2) and xm Functions with (a2 x2) and xm Functions with (a3 + x3) and xm Functions with (a3 x3) and xm Functions with (a4 + x4) and xm Functions with (a4 x4) and xm Functions with a + bx and xm Functions with a2 x2 and xm Functions with x2 a2 and xm Functions with a2 + x2 and xm Miscellaneous Functions Functions Expressible in Polar Coordinates Functions Expressed Parametrically Transcendental Functions Plotting Information for This Chapter Functions with sinn (2 ax) and cosm(2 bx)(n,m integers) Functions with 1 +/- sinn (2 ax) and 1 +/-} cosm (2 bx) Functions with c sinn (ax) + d cosm (bx) Functions of More Complicated Arguments Inverse Trigonometric Functions Logarithmic Functions Exponential Functions Hyperbolic Functions Inverse Hyperbolic Functions Trigonometric Combined with Exponential Functions Trigonometric Functions Combined with Powers of x Logarithmic Functions Combined with Powers of x Exponential Functions Combined with Powers of x Hyperbolic Functions Combined with Powers of x Combined Trigonometric Functions, Exponential Functions, and Powers of x Miscellaneous Functions Functions Expressible in Polar Coordinates Functions Expressible Parametrically Polynomial Sets Plotting Information for This Chapter Orthogonal Polynomials Nonorthogonal Polynomials References Special Functions in Mathematical Physics Plotting Information for This Chapter Exponential and Related Integrals Sine and Cosine Integrals Gamma and Related Functions Error Functions Fresnel Integrals Legendre Functions Bessel Functions Modified Bessel Functions Kelvin Functions Spherical Bessel Functions Modified Spherical Bessel Functions Airy Functions Riemann Functions Parabolic Cylinder Functions Elliptic Integrals Jacobi Elliptic Functions References Green's Functions and Harmonic Functions Plotting Information for This Chapter Green's Function for the Poisson Equation Green's Function for the Wave Equation Green's Function for the Diffusion Equation Green's Function for the Helmholtz Equation Miscellaneous Green's Functions Harmonic Functions: Solutions to Laplace's Equation References Special Functions in Probability and Statistics Plotting Information for This Chapter Discrete Probability Densities Continuous Probability Densities Sampling Distributions Laplace Transforms Plotting Information for This Chapter Elementary Functions Algebraic Functions Exponential Functions Trigonometric Functions References Nondifferentiable and Discontinuous Functions Plotting Information for This Chapter Functions with a Finite Number of Discontinuities Functions with an Infinite Number of Discontinuities Functions with a Finite Number of Discontinuities in First Derivative Functions with an Infinite Number of Discontinuities in First Derivative Random Processes Plotting Information for This Chapter Elementary Random Processes General Linear Processes Integrated Processes Fractal Processes Poisson Processes References Polygons Plotting Information for This Chapter Polygons with Equal Sides Irregular Triangles Irregular Quadrilaterals Polyiamonds Polyominoes Polyhexes Miscellaneous Polygons Three-Dimensional Curves Plotting Information for This Chapter Helical Curves Sine Waves in Three Dimensions Miscellaneous 3-D Curves Knots Links References Algebraic Surfaces Plotting Information for This Chapter Functions with ax + by Functions with x2/a2 +/- y2/b2 Functions with x2/a2 + y2/b2 +/-c2)1/2 Functions with x3/a3 +/- y3/b3 Functions with x4/a4 +/- y4/b4 Miscellaneous Functions Miscellaneous Functions Expressed Parametrically Transcendental Surfaces Plotting Information for This Chapter Trigonometric Functions Logarithmic Functions Exponential Functions Trigonometric and Exponential Functions Combined Surface Spherical Harmonics Complex Variable Surfaces Plotting Information for This Chapter Algebraic Functions Transcendental Functions Minimal Surfaces Plotting Information for This Chapter Elementary Minimal Surfaces Complex Minimal Surfaces References Regular and Semi-Regular Solids with Edges Plotting Information for This Chapter Platonic Solids Archimedean Solids Duals of Platonic Solids Stellated (Star) Polyhedra References Irregular and Miscellaneous Solids Plotting Information for This Chapter Irregular Polyhedra Miscellaneous Closed Surfaces with Edges Index

Addition theorem Complex-valued function Inverse trigonometric functions Special functions Jacobi elliptic functions Trigonometric functions Even and odd functions Generalized function Mathematical analysis Mathematics

Electromagnetic Fields -- Restrictions and Approximation

电磁场

Wiley Boris Z Katsenelenbaum

ISBN：9783527403882，出版年：2008，中图分类号：O4 被引 21次

1 Introduction. 1.1 Introduction. 1.2 Subject and Method of Investigation. 1.3 Realizability, Approximability, Amplitude Approximability. 1.4 Outline of the Book. 2 Nonapproximability of Patterns. 2.1 Nonapproximability and Zero Lines of the Real Wave Field. 2.2 Examples of Specific Lines. aAA ProhibitedaAA Antenna Shapes. 2.3 Amplitude Nonapproximability. 2.4 Probabilistic Description of Body Shape by the Likeness Principle. 2.5 Body Shape Reconstruction by its Scattered Patterns. 2.6 Properties of Specific Lines. 3 Nonapproximability of Near Fields. 3.1 Approximability Condition for Near Fields. 3.2 Construction of a Field by its Zero Line. Case of the Circle Arc. 3.3 Analytical Extension of the Eigenoscillation Field outside the Boundary of the Domain. 4 The Norm of the Current. 4.1 The Minimal Current Norm at a Given Accuracy of Approximation. 4.2 Generalized Functions of Double Orthogonality. Nonapproximability and Existence of Nonradiating Currents. 4.3 Optimal Current Synthesis. The General Case. 4.4 Domain of Specific Line Influence. 5 Electromagnetic Field. The Maxwell Equations. 5.1 Trivial Generalizations. 5.2 Properties of Specific Surfaces. 6 Long Narrow Beam of Electromagnetic Waves. 6.1 Two--dimensional Fourier Transformation. 6.2 Transmission of Field by Wave Beam: Possibilities and Restrictions. 6.3 Shape of Antenna and Rectenna. Bibliography for Chapters 1aAA"6. Appendix: Antenna Synthesis by Amplitude Radiation Pattern and Modified Phase Problem (by N. N. Voitovich). A.1 Synthesis of Antennas by Amplitude Radiation Pattern. A.1.1 Introduction. A.1.2 Problem formulation for the curvilinear antenna. A.1.3 Reducing to the LagrangeaAA"Euler equation. A.1.4 Case of linear antenna. Main properties of solutions. A.2 Modified Phase Problem. Continuous Case. A.2.1 Modified phase problem and related mathematical and physical problems. A.2.2 Analytical solutions to the LagrangeaAA"Euler equation for linear antenna. Theoretical results. A.2.3 Solution branching. A.2.4 Numerical example. Problem with symmetrical data. A.2.5 Problems with nonsymmetrical data. A.3 Modified Phase Problem. Discrete Case. A.3.1 Problem formulation for linear antenna array. LagrangeaAA"Euler equations. A.3.2 Theoretical results. A.3.3 Numerical results. Bibliography for Appendix. Index.

Radiation pattern Antenna array Euler equations Maxwell's equations Electromagnetic field Phase problem Amplitude Generalized function Mathematical analysis Geometry Mathematics