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Download CRC standard curves and surfaces with Mathematica by David H. von Seggern PDF

By David H. von Seggern

Since the ebook of this book’s bestselling predecessor, Mathematica® has matured significantly and the computing strength of computing device desktops has elevated vastly. The Mathematica® typesetting performance has additionally develop into sufficiently powerful that the ultimate reproduction for this version might be reworked at once 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 capabilities that depicts the vast majority of the normal mathematical features and geometrical figures in use this present day. the general structure of the ebook is essentially unchanged from the former variation, with functionality definitions and their illustrations offered 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 whole ebook in a suite of interactive CDF (Computable record layout) files

The publication provides a accomplished choice of approximately 1,000 illustrations of curves and surfaces frequently used or encountered in arithmetic, portraits layout, technological know-how, and engineering fields. One major swap with this version is that, rather than proposing various realizations for many services, this version offers just one curve linked to each one functionality.

The image 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 reveal. this allows readers to gauge what a cheap diversity of parameters can be whereas seeing the results of one specific number of parameters.

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Extra resources for CRC standard curves and surfaces with Mathematica

Sample text

Orthogonal surfaces require fewer operations to evaluate over a grid of the domain of x and y because the defining equation only needs to be evaluated once along the x direction and once along the y direction, with all other points evaluated by simple multiplication of the x and y factors appropriate to each point on the (x, y) plane. 6 Basic Curve and Surface Operations There are many simple operations that can be applied to curves and surfaces in order to change them. Knowledge of these operations enables one to adapt a given curve or surface to a particular need and to thus extend the curves and surfaces given in this reference work to a larger set of mathematical forms.

For surfaces, pure shear will only apply to two of the three coordinate directions, with the remaining one having no change. Pure shear is a special case of linear scaling under this circumstance. Matrix Method for Transformation The foregoing transformations can all be expressed in matrix form, which is often convenient for computer algorithms. This is especially true when several transformations are concatenated together, for the matrices can then be simply multiplied together to obtain a single transformation matrix.

This is convenient for polar coordinates, but the rotation can also be expressed in Cartesian coordinates as x′ = x cos(α) + y sin(α), y′ = −x sin(α) + y cos(α). In three dimensions, a surface can be rotated about any of the three axes by using these equations on the coordinate pairs (x, y), (y, z ), or (x, z ) depending on whether the rotation is about the z, x, or y axis, respectively. Linear Scaling The relations for linear scaling are x′ = ax, y′ = by, z′ = cz. These stretch the curve or surface by the factors a, b, and c along the respective axes.

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