By David H. von Seggern
Because the book of the 1st version, Mathematica® has matured significantly and the computing energy of computing device desktops has elevated significantly. this permits the presentation of extra advanced curves and surfaces in addition to the effective computation of previously prohibitive graphical plots. Incorporating either one of those facets, CRC normal Curves and Surfaces with Mathematica®, moment version is a digital encyclopedia of curves and capabilities that depicts the vast majority of the normal mathematical services rendered utilizing Mathematica.
While the easy-to-use structure continues to be unchanged from the former variation, many chapters were reorganized and higher graphical representations of diverse curves and surfaces were produced.
An introductory bankruptcy describes the fundamental homes of curves and surfaces, contains convenient tables of 2-D and three-D curve and floor modifications, and gives a short knowing of the fundamental nature of mathematical features. To facilitate extra effective and extra thorough use of the fabric, the full gamut of curves and surfaces is split into 16 person chapters. The accompanying CD-ROM comprises Mathematica notebooks of code to build plots of all of the capabilities provided within the book.
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Extra info for CRC Standard Curves and Surfaces with Mathematica, Second Edition
0 2. 0 3.
32 y Z cða C bxÞ2 =x3 x3 yKb2 cx2 K2abcxKa2 c Z 0 1. 01 2. 01 3. 33 y Z cða C bxÞ3 =x3 x3 yKb3 cx3 K3ab2 cx2 K3a2 bcxKa3 c Z 0 1. 002 2. 002 3. 1 y Z c=ða2 C x2 Þ a2 y C x2 yKc Z 0 Special case: cZa3 gives Witch of Agnesi 1. 04 2. 04 3. 2 y Z cx=ða2 C x2 Þ a2 y C x2 yKcx Z 0 Serpentine 1. 3 2. 3 3. 3 y Z cx2 =ða2 C x2 Þ a2 y C x2 yKcx2 Z 0 1. 0 2. 0 3. 4 y Z cx3 =ða2 C x2 Þ a2 y C x2 yKcx3 Z 0 1. 0 2. 0 3. 5 y Z c=½xða2 C x2 Þ a2 C x3 yKc Z 0 1. 02 2. 02 3. 6 y Z c=½x2 ða2 C x2 Þ a2 x2 y C x4 yKc Z 0 1.
Note that this operation is not homomorphic like Cartesian translation because the curve is stretched in the angular direction while undergoing the radial translation. This operation can be performed on the radial coordinate of either cylindrical or spherical coordinate systems in three dimensions. 7 Weighting In a two-dimensional Cartesian system, let y 0 Z jxja y: This operation performs a weighting on the curve by the factor jxja, a symmetric operator. 0, the curve is compressed by a factor that decreases with x.
CRC Standard Curves and Surfaces with Mathematica, Second Edition by David H. von Seggern