By David H. von Seggern
Since the book of this book’s bestselling predecessor, Mathematica® has matured significantly and the computing energy of computer desktops has elevated drastically. The Mathematica® typesetting performance has additionally develop into sufficiently powerful that the ultimate replica for this variation should be remodeled at once from Mathematica R notebooks to LaTex input.
Incorporating those elements, CRC commonplace Curves and Surfaces with Mathematica®, 3rd Edition is a digital encyclopedia of curves and services that depicts the majority of the traditional mathematical capabilities and geometrical figures in use at the present time. the final layout of the publication 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 nearly each chapter
- Several chapters which were reorganized
- Better graphical representations for curves and surfaces throughout
- A CD-ROM, together with the complete ebook in a suite of interactive CDF (Computable rfile structure) files
The e-book provides a entire choice of approximately 1,000 illustrations of curves and surfaces frequently used or encountered in arithmetic, pix layout, technology, and engineering fields. One major swap with this version is that, rather than featuring quite a number realizations for many capabilities, this version provides just one curve linked to each one functionality.
The picture output of the control functionality is proven precisely as rendered in Mathematica, with the precise parameters of the curve’s equation proven as a part of the image exhibit. this allows readers to gauge what a cheap variety of parameters may be whereas seeing the results of one specific number of parameters.
Read or Download CRC Standard Curves and Surfaces [mathematical] PDF
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Additional resources for CRC Standard Curves and Surfaces [mathematical]
3. 28. y = e(a + bx)jx 2 1. 04 2. 04 3. 29. y = e(a + bX)2jx 2 1. 01 2. 01 3. 30. y = e(a 1. 2. 3. 31. y = c(a + bx)/x 3 1. 02 2. 02 3. 32. y = c(a + bX)2/X 3 1. 01 2. 01 3. 33. y 1. 2. 3. = c(a + bx? 3. 1. Y = e/(a 2 + x 2 ) a2y + x 2y - e 3 Special case: e = a gives witeh of Agnesi 1. 2. 3. 2. y = ex/(a 2 Serpentine 1. 2. 3. 3. 1. 2. 3. 4. 1. 2. 3. 5. Y = c/[x(a 2 + x 2 )] 1. 02 2. 02 3. 6. 1. 2. 3. 7. 1. 2. 3. 02 2. 3. 8. y 1. 4. 1. Y = c/(a 2 1. 2, c = 2. 5, c = 3. 2. Y = cx/(a 2 - x 2 ) 1.
Classification of Surfaces In general, surfaces may follow the same classification scheme as curves (Figure 6). Many commonly used surfaces are rotations of two-dimensional curves about an axis, thus giving axial, or possibly point, symmetry. In this case the independent variable x of the two-dimensional curve's equation can be replaced with the radial variable r = (x 2 + y2)1/2 to form the equation of the surface. Other commonly used surfaces are merely a continuous translation of a given two-dimensional curve along a straight line.
A translation by u and v in the x and y directions is then written using a 3-by-3 matrix (x' y' l)=(x o y 1 v ~) 21 where, explicitly, x' = x +u y' = y +v l' = 1 With this representation, a radial translation by s units of a curve given in f)) coordinates is effected by (r, o ( r' so that r' = r f)' + sand f) 1)=(r f) 1 o ~) is unchanged. Table 1 Operation Matrix Rotation ( Linear scaling (~ ~) Reflection Weighting Nonlinear scaling cos 0 -sin 0 sin 0) cos 0 ( :1 ) ~1 (; (; Un Notes o is counterclockwise angle from positive x axis.