(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 4049744, 133458]*) (*NotebookOutlinePosition[ 4089173, 134781]*) (* CellTagsIndexPosition[ 4089129, 134777]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Examples of Commands in KNOXPACKAGES\ \>", "Subtitle"], Cell[CellGroupData[{ Cell["Examples from Functions", "Section"], Cell[TextData[{ "One of the basic limitations of ", StyleBox["Mathematica", FontSlant->"Italic"], " in precalculus and calculus is that it will not plot odd roots of powers \ of x when the interval contains negative values of x. Many folks have \ attempted to fix this problem. With the assistance of Robby Villegas (former \ Knox student and current developer at Wolfram Research), we have implemented \ an extension of the Power command which will request ", StyleBox["Mathematica", FontSlant->"Italic"], " to use the real roots instead of the principal complex root. We will \ illustrate the effect of setting PowerBehavior to Real in several of the \ examples below." }], "Text"], Cell[CellGroupData[{ Cell["Plotting commands", "Subsubsection"], Cell[TextData[{ "A severe drawback of ", StyleBox["Mathematica", FontSlant->"Italic"], "'s basis ", StyleBox["Plot", "Input"], " command is that it connect all points it generates for a plot, whether or \ not they should be connected. 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It returns expressions for the derivatives of \ order k which do not involve derivatives of lower order. Variables to be \ treated as constants can be specified with the option Constants as in Dt. \ Reduction rules may also be given as options of the form expr1 -> expr2."\)], \ "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ImplicitD[x\^2 + \ x\ y\ + \ y\^2 == \ 1, x, y]\)], "Input"], Cell[BoxData[ \({Dt[y, x] \[Rule] \(-\(\(2\ x + y\)\/\(x + 2\ y\)\)\)}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Mathematics 152: Calculus II", "Subsection"], Cell[CellGroupData[{ Cell["Approximate Integration", "Subsubsection"], Cell[TextData[{ "Our integral approximation commands plot the curve as well as the \ approximating objects and prints the approximate value of the integral. The \ option ", StyleBox["Graph\[Rule]False", "Input"], " will suppress the graph and return the approximation. 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