Essentials of Mathematica: With Applications to Mathematics by Nino Boccara

By Nino Boccara

This e-book teaches how one can use Mathematica to unravel a wide selection of difficulties in arithmetic and physics. it's in line with the lecture notes of a direction taught on the collage of Illinois at Chicago to complex undergrad and graduate scholars. The ebook is illustrated with many distinct examples that require the coed to build meticulous, step by step, effortless to learn Mathematica courses. the 1st half, within which the reader learns easy methods to use numerous Mathematica instructions, includes examples, no longer lengthy factors; the second one half comprises beautiful functions. The CD-ROM offers the whole textual content content material and interactive examples.

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Example text

Limit[Abs[x] / x, x -> 0] The result is not correct. If x approaches 0 from the right, the limit is indeed 1 but from the left the limit is - 1 . Prom a purely mathematical point of view, the limit does not exist. Actually the wrong limit was obtained because Mathematica assumed that 0 was approached from the right. To obtain the limit when 0 is approached from the left, we have to specify the Direction. Limit[Abs[x] / x, x -> 0, D i r e c t i o n -> 1] - 1 The option D i r e c t i o n -> 1 means that we have to approach 0 going in the direction of 1 that is from the left of 0.

More... D[0, Pi] Because f [x] has been defined using : = , t h e right-hand side is kept in an unevaluated form. W h e n we enter f [ P i ] , Mathematica tries actually to evaluate D[Pi Sin[Pi], Pi] which has no meaning. If, on the contrary, we define f [x] using = and not : =, Mathematica immediately evaluates f [x] and replacing X by P i gives t h e correct result. 26 1 Panorama of Mathematica Clear[f] f [ x j = D[x S i n [ x ] , x] f[x] f[Pi] X Cos[x] + Sin[x] X Cos[x] + Sin[x] -Pi The command I n t e g r a t e [f, x] gives the indefinite integral / f{x) dx\ I n t e g r a t e [f, {x, a, b}] gives the definite integral/^/(x) dx.

Attributes[Plot] = {HoldAll, Protected} Options [Plot] = {AspectRatio -^ 1/GoldenRatio, Axes —> Automatic, AxesLabel -^ None, AxesOrigin -^ Automatic, AxesStyle -^ Automatic, Background —^ Automatic, ColorOutput —> Automatic, Compiled -^ True, DefaultColor —^ Automatic, DefaultFont :-^ $DefaultFont, DisplayFimction r^" $DisplayFunction, Epilog ^ { }, FormatType :-^ $FormatType, Frame -^ False, FrameLabel —> None, FrameStyle —^ Automatic, FrameTicks -^ Automatic, GridLines -^ None, ImageSize -^ Automatic, 12 1 Panorama of Mathematica MaxBend - ^ 1 0 .

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