By Stan Wagon (auth.), Stan Wagon (eds.)
In this 3rd variation of Mathematica® in Action, award-winning writer Stan Wagon courses newbie and veteran clients alike via Mathematica's strong instruments for mathematical exploration. The transition to Mathematica 7 is made gentle with lots of examples and case experiences that make the most of Mathematica's most recent instruments, reminiscent of dynamic manipulations and adaptive 3-dimensional plotting. Mathematica in Action additionally emphasizes the breadth of Mathematica and the outstanding result of combining innovations from diverse components. This fabric permits the reader to exploit Mathematica to unravel various advanced problems.
Case stories starting from straight forward to stylish are supplied all through. each time attainable, the ebook exhibits how Mathematica can be utilized to find new issues. impressive examples contain the layout of a street on which a sq. wheel motorbike can journey, the layout of a drill that could drill sq. holes, an indication of the Banach—Tarski Paradox through hyperbolic geometry, new and mind-blowing formulation for p, the invention of shadow orbits for chaotic structures, and using robust new features for 3-dimensional portraits. Visualization is emphasised all through, with finely crafted portraits in every one chapter.
Wagon is the writer of 11 books on arithmetic, together with A direction in Computational quantity Theory, named one of many ten top math books of 2000 via the yank Library organization. He has written greatly at the academic purposes of Mathematica, together with the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory.
From stories of the second one edition:
"In a blinding variety of examples Stan Wagon indicates how such positive aspects as animation, three-dimensional photos and high-precision integer mathematics can give a contribution to our realizing and delight of mathematics."
—Richard Walker, The Mathematical Gazette
"The base line is that Mathematica in Action is an exceptional publication containing many examples of actual makes use of of Mathematica for the amateur, intermediate, and specialist user."
—Mark McClure, Mathematica in schooling and Research
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Additional info for Mathematica in Action: Problem Solving Through Visualization and Computation
CityData "Magenta" Magenta, Lombardy, Italy , Magenta, ChampagneArdenne, France Mathematica can provide web links to maps for these two cities. 97&z 12&t h 22 Chapter 0 A Brief Introduction There is also much useful data in the standard packages. Get "PhysicalConstants`" ? 6704 10 8 N Watt Kelvin4 Meter2 Get "Units`" If one wants to know how much water a 1000 cubic-foot-per-second stream will generate in a year, in gallons, that is simply done as follows. 1000. 35906 10 , Gallon Year Gallon Year And of course there is much mathematical information in these data bases.
It is not immediately obvious why the speeds 1, 7, and 17 should lead to such symmetry; Farris provides an explanation in his paper. Next we define the function and use Manipulate to study the effect of changing the parameters. f1 t_, s1_ : Cos s1 t , Sin s1 t ; f2 t_, r2_, s2_ : r2 Cos s2 t , Sin s2 t ; f3 t_, r3_, s3_, offset_ : r3 Cos s3 t offset , Sin s3 t offset ; epi r2_, r3_, s1_, s2_, s3_, offset_ t_ : f1 t, s1 f2 t, r2, s2 f3 t, r3, s3, offset ; We will let the reader experiment with the output of the following manipulation.
Here's an example. RSolve F n F n 1 aF n 2 ,F 0 0, F 1 1 ,F n ,n 40 Chapter 1 Plotting 2 n 1 1 4a n 1 1 4a n F n 1 Setting a 4a 2 shows a very simple form for that Fibonacci generalization. But we digress. Let's return to ListPlot and its use. Here is an interesting little puzzle: what is the rightmost nonzero digit of n ? Here we will examine only a few modest values of this function. The IntegerDigits function gives us the list of digits. ] 1, 5, 5, 1, 1, 2, 1, 0, 0, 4, 3, 3, 3, 0, 9, 8, 5, 9, 8, 4, 0, 0, 0, 0, 0, 0 DeleteCases is a handy way to erase what we don't want.