By David H. von Seggern

Since the ebook of this book’s bestselling predecessor, Mathematica® has matured significantly and the computing energy of machine desktops has elevated drastically. The Mathematica® typesetting performance has additionally develop into sufficiently strong that the ultimate reproduction for this variation may be remodeled without delay from Mathematica R notebooks to LaTex input.

Incorporating those facets, CRC normal Curves and Surfaces with Mathematica®, 3rd Edition is a digital encyclopedia of curves and services that depicts the vast majority of the normal mathematical services and geometrical figures in use this present day. the final structure of the publication is essentially unchanged from the former version, with functionality definitions and their illustrations awarded heavily together.

New to the 3rd Edition:

  • A new bankruptcy on Laplace transforms
  • New curves and surfaces in virtually each chapter
  • Several chapters which have been reorganized
  • Better graphical representations for curves and surfaces throughout
  • A CD-ROM, together with the total publication in a suite of interactive CDF (Computable record layout) files

The publication provides a entire number of approximately 1,000 illustrations of curves and surfaces usually used or encountered in arithmetic, snap shots layout, technological know-how, and engineering fields. One major switch with this variation is that, rather than featuring quite a number realizations for many capabilities, this version offers just one curve linked to every one functionality.

The photograph output of the manage functionality is proven precisely as rendered in Mathematica, with the precise parameters of the curve’s equation proven as a part of the photo demonstrate. this allows readers to gauge what an inexpensive variety of parameters could be whereas seeing the results of one specific selection of parameters.

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Extra resources for CRC standard curves and surfaces with Mathematica

Example text

Most of the integral forms have commonly used names (for example, “Bessel functions”). Other curves or surfaces in this reference work are expressed not by single equations, but rather by some set of mathematical rules. The method of presentation will vary in these cases, always with the objective of providing the reader with a means of easily constructing the curve or surface by machine computation. Plots Readers of previous editions will notice that, in this edition, only one realization of an equation is given.

This operation can be performed on the radial coordinate of either cylindrical or spherical coordinate systems in three dimensions. Weighting In a two-dimensional Cartesian system, let y′ = |x|a y. a This operation performs a weighting on the curve by the factor |x| , a symmetric operator. If a > 0, the curve is stretched in the y direction by a factor that increases with x ; but if a < 0, the curve is compressed by a factor that decreases with x. Similar treatments can be performed on surfaces in three dimensions.

Only a few of the most common operations are presented here. Of these, two (translation and rotation) are homomorphic operations, which means that the form of the curve is preserved, with merely its position or orientation in space being changed. Translation If one or more of the coordinates (x, y, z ) of a point is changed according to x′ = x + a, y′ = y + b, z′ = z + c, the curve or surface undergoes a translation of amount (a, b, c) along the (x, y, z ) axes, respectively. 2 Rotation In polar coordinates, if the angle θ is changed by a positive amount α thus θ′ = θ + α, 16 CRC Standard Curves and Surfaces with Mathematica R the curve undergoes a counter-clockwise rotation of α degrees.

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