CRC Standard Curves and Surfaces with Mathematica, Second by David H. von Seggern

By David H. von Seggern

Because the ebook of the 1st variation, Mathematica® has matured significantly and the computing strength of computing device pcs has elevated vastly. this permits the presentation of extra complicated curves and surfaces in addition to the effective computation of previously prohibitive graphical plots. Incorporating either one of those facets, CRC common Curves and Surfaces with Mathematica®, moment version is a digital encyclopedia of curves and features that depicts the vast majority of the traditional mathematical capabilities rendered utilizing Mathematica.

While the easy-to-use structure is still unchanged from the former variation, many chapters were reorganized and higher graphical representations of various curves and surfaces were produced.
An introductory bankruptcy describes the elemental homes of curves and surfaces, contains convenient tables of 2-D and three-D curve and floor changes, and offers a brief knowing of the elemental nature of mathematical features. To facilitate extra effective and extra thorough use of the cloth, the entire 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 features offered within the book.

New to the second one Edition

  • Chapters on minimum surfaces and Green's features that contain Poisson, wave, diffusion, and Helmholtz equations
  • Knots and hyperlinks within the 3D curves bankruptcy
  • Archimedean solids, duals of Platonic solids, and stellated varieties within the general polyhedra chapter
  • Additional curves and surfaces in virtually each chapter
  • Expanded index for speedy entry to curves or surfaces of curiosity and to discover definitions of universal mathematical terms
  • Upgraded Mathematica notebooks with extra uniform formatting, extra whole documentation on specific curves and surfaces, an evidence of the plotting algorithms, and extra particular designations of variable parameters to simply modify curve or floor plots
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    Example text

    Stewart. 1978. Catastrophe Theory and Its Applications, New York: Pitman. 3. M. Abramowitz, ed. 1974. Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, New York: Dover. 4. B. Mandelbrot. 1983. H. Freeman. © 2007 by Taylor & Francis Group, LLC 2 Algebraic Curves The curves in this chapter are found in elementary algebra texts or tables of integrals and are likely familiar. Many have acquired common names in the mathematical literature and these names are included wherever appropriate.

    01 2. 01 3. 30 y Z cða C bxÞ3 =x2 x2 yKb3 cx3 K3ab2 cx2 K3a2 bcxKa3 c Z 0 1. 003 2. 003 3. 31 y Z cða C bxÞ=x3 x3 yKbcxKca Z 0 1. 02 2. 02 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. 1 y Z c=ða2 Kx2 Þ a2 yKx2 yKc Z 0 1. 03 2. 03 3. 2 y Z cx=ða2 Kx2 Þ a2 yKx2 yKcx Z 0 1. 1 2. 1 3. 3 y Z cx2 =ða2 Kx2 Þ a2 yKx2 yKcx2 Z 0 1. 2 2. 2 3. 4 y Z cx3 =ða2 Kx2 Þ a2 yKx2 yKcx3 Z 0 1. 2 2. 2 3. 5 y Z c=½xða2 Kx2 Þ a2 xyKx3 yKc Z 0 1. 001 2. 001 3. 6 y Z c=½x2 ða2 Kx2 Þ a2 x2 yKx4 yKc Z 0 1. 0003 2. 0003 3. 7 y Z cxða2 Kx2 Þ yKa2 cx C cx3 Z 0 1. 0 2. 0 3.

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