(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times"; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times"; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier"; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva"; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = leftheader, inactive, L2, 12, "Times"; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times"; fontset = leftfooter, inactive, L2, 12, "Times"; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; paletteColors = 128; automaticGrouping; currentKernel; ] :[font = subtitle; inactive; preserveAspect; startGroup] Numerical Calculations :[font = text; inactive; preserveAspect] Mathematica can perform ordinary arithmetic e.g. type the input 5 + 7 and the expected result 12 is obtained: ;[s] 3:0,0;1,1;12,0;113,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0; :[font = input; preserveAspect] 5+7 :[font = text; inactive; preserveAspect] Unlike a calculator, exact results, 3100, can be evaluated exactly: ;[s] 3:0,0;38,1;41,0;69,-1; 2:2,13,9,Times,0,12,0,0,0;1,21,13,Times,32,12,0,0,0; :[font = input; preserveAspect] 3^100 :[font = text; inactive; preserveAspect] Numerical results, e.g. of the previous expression, can also be computed: :[font = input; preserveAspect] N[%] :[font = text; inactive; preserveAspect] Calculate the square root of 10 to 50 decimal places: :[font = input; preserveAspect] N[Sqrt[10],50] :[font = text; inactive; preserveAspect] Complex numbers can be handled: Take the power of a complex number: :[font = input; preserveAspect] (3 + 4*I)^10 :[font = text; inactive; preserveAspect] Mathematica can evaluate all standard mathematical functions e.g. the Bessel function of the first kind J(n, z) at n=0 and z=14.5: ;[s] 3:0,0;1,1;12,0;133,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0; :[font = input; preserveAspect] BesselJ[0,14.5] :[font = text; inactive; preserveAspect] Find the numerical solution to the equation J(0, x) = 0 near x=14.5: :[font = input; preserveAspect] FindRoot[BesselJ[0,x], {x,14.5}] :[font = text; inactive; preserveAspect] Numerically evaluate the Riemann zeta function z(z) for z=1/2 + 13i: ;[s] 3:0,0;47,1;48,0;69,-1; 2:2,13,9,Times,0,12,0,0,0;1,18,13,Symbol,0,12,0,0,0; :[font = input; preserveAspect] N[ Zeta[1/2 + 13 I], 40] :[font = text; inactive; preserveAspect] Numerical Integration, e.g. numerically integrate Ú0 p dx sin(sin(x)): ;[s] 6:0,0;50,1;51,2;52,0;53,3;54,0;71,-1; 4:3,13,9,Times,0,12,0,0,0;1,18,13,Symbol,0,12,0,0,0;1,21,13,Times,64,12,0,0,0;1,26,17,Symbol,32,12,0,0,0; :[font = input; preserveAspect] NIntegrate[Sin[Sin[x]], {x,0,Pi}] :[font = text; inactive; preserveAspect] Exact computations with Integers, e.g. find the list of the prime factors of the integer 70612139395722186 together with their exponents: :[font = input; preserveAspect; endGroup] FactorInteger[70612139395722186] ^*)