(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. 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[ 127482, 3476]*) (*NotebookOutlinePosition[ 128232, 3502]*) (* CellTagsIndexPosition[ 128188, 3498]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ " ", StyleBox[" ", "Subtitle", FontSize->16, FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}], StyleBox["Basic Calculation and Graphing ", "Subtitle", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", "Subtitle", FontSize->16, FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", "Subtitle", FontSize->16, FontVariations->{"CompatibilityType"->0}], StyleBox[" ", "Subtitle", FontSize->16] }], "Text"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox[" Mathematica", FontSlant->"Italic"], " " }], "Subtitle", CellMargins->{{Inherited, -22}, {Inherited, Inherited}}, TextAlignment->Left, TextJustification->0], Cell["\<\ Dr. Andrzej Korzeniowski Department of Mathematics, UTA\ \>", "Subsubtitle"] }, Open ]], Cell[CellGroupData[{ Cell["Lesson 1", "Subtitle"], Cell[CellGroupData[{ Cell["Preliminaries", "Section", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[TextData[{ StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic"], StyleBox[" ", FontWeight->"Bold"], " operations are based on the concept of a list {a, b, ..., c} where a, \ b,... are symbols or numbers. Use built-in palettes : BasicInput (shown as \ default next to the notebook) found in Files\[Rule]Palettes\[Rule]BasicInput. \ To put an expression of choice in a given place click the cursor in that \ place and then click the desired item from palette. Use Format\[Rule] Show \ ToolBar to see in the left-upper corner the attribute of the cell containing \ the active cursor. Input cells hold commands that execute mathematical \ operations while Output", StyleBox[" ", "Program"], "cells", StyleBox[" ", "Program"], "store the answer. Other layout options are: Text, Title, Section, etc. \ (word processing only and not to be executed). Expressions are stored in \ cells displayed as blue brackets on the right-hand side. Cells can be \ formatted or operated on by being selected (clicking on cell bracket to \ highlight it in black) then going to Cell (main menu) and using pull-down \ menus. Most useful initially are: Cell Grouping (first choose Manual \ Grouping \[Rule]Ungroup Cells) so each executable expression is entered in a \ separate single Input cell for easy corrections, Divide Cell (put cursor in a \ desired place in the cell), Merge Cell (highlight cells to be merged). Use \ the online HELP in the main menu to familiarize yourself with many other \ features. To delete a cell highlight the cell and press Delete key. Use copy, \ cut, paste, undo, from Edit to avoid unnecessary typing. " }], "Text"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MULTIPLICATION", FontWeight->"Bold", FontVariations->{"Underline"->True}], StyleBox[".", FontVariations->{"Underline"->True}], " ", "'"}], "*", "'", " ", "in", " ", "multiplication", " ", "of", " ", "symbols", " ", "x", "*", "y", " ", "may", " ", "be", " ", "substituted", " ", "by", " ", "a", " ", "blank"}], ",", " ", \(i . e . \), ",", \(x* y = \(x\ y . \ \ \ If\ first\ factor\ is\ a\ number\ then\ 5 x = \(5\ x = 5*x\)\)\)}], TraditionalForm]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(2 + 2\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(4\)], "Output"] }, Open ]], Cell[BoxData[ FormBox[ RowBox[{\( (*\ comment\ by\ notebook\ user\ *) \), " ", RowBox[{"is", " ", "ignored", " ", StyleBox[ RowBox[{"by", StyleBox["Mathematica", FontSlant->"Italic"]}]], " ", "while", " ", "executing", " ", "the", " ", "cell", " ", "containing", " ", \(\(comment\)\(.\)\)}]}], TraditionalForm]], "Text", CellMargins->{{Inherited, 106}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Factor[\ 24 - 50\ x + 35\ x\^2 - 10\ x\^3 + x\^4]\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\)\)], "Input", CellMargins->{{Inherited, 101}, {Inherited, Inherited}}], Cell[BoxData[ \(\((\(-4\) + x)\)\ \((\(-3\) + x)\)\ \((\(-2\) + x)\)\ \((\(-1\) + x)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Together[1\/x + x\^2 - 1]\)], "Input"], Cell[BoxData[ \(\(1 - x + x\^3\)\/x\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Apart[\((x - 1)\)\ \((x - 2)\)\ \((x - 3)\)\ \((x - 4)\)]\)], "Input"], Cell[BoxData[ \(24 - 50\ x + 35\ x\^2 - 10\ x\^3 + x\^4\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(Expand[\((a + b)\)\^5]\)\)\)], "Input"], Cell[BoxData[ \(a\^5 + 5\ a\^4\ b + 10\ a\^3\ b\^2 + 10\ a\^2\ b\^3 + 5\ a\ b\^4 + b\^5\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(Simplify[ 1\/\(x - 1\) - 1\/\(x + 1\)]\)\(\ \ \ \ \ \)\)\(\[IndentingNewLine]\)\(\ \[IndentingNewLine]\)\( (*\ \(\(Shortcuts\)\(:\)\)\ // Factor, \(\(...\) \(\(,\)\(\ \)\(\(//\)\(Simplify\ or\ FullSimplify\)\ \)\)\)\ *) \)\)\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(2\/\(\(-1\) + x\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(5!\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\)\( (*\ \ n\ \(factorial : \ \ n\) = \(1*2\ * ... \) \((n - 1)\)* n\ \ *) \)\)\)], "Input"], Cell[BoxData[ \(120\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(k = 1\)\%n k\^5\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(1\/12\ n\^2\ \((1 + n)\)\^2\ \((\(-1\) + 2\ n + 2\ n\^2)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]Sin[x]\ Tan[x] \[DifferentialD]x\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(\(-Log[Cos[x\/2] - Sin[x\/2]]\) + Log[Cos[x\/2] + Sin[x\/2]] - Sin[x]\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["TYPING TEXT.", FontWeight->"Bold", FontVariations->{"Underline"->True}], " To type a text highlight a cell and choose Text from the ToolBar. \n\n\ ", StyleBox["NUMERICAL EVALUATION.", FontWeight->"Bold", FontVariations->{"Underline"->True}], " To evaluate an expression Expr numerically use N[Expr] or Expr//N. To \ evaluate with n digit of accuracy use N[Expr,n]" }], "Text", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[Pi]\)\(//\)\(\(N\)\(\ \ \ \ \)\)\( (*\ shortcut\ for\ N[\[Pi]], \ i . e . \ to\ evaluate\ numerically\ *) \)\)\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(3.141592653589793`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(N[\[Pi], 100]\)\(\ \ \ \ \ \ \ \ \ \ \ \ \)\)\( (*\ with\ accuray\ of\ 100\ decimal\ places\ *) \)\)\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(3.1415926535897932384626433832795028841971693993751058209749445923078164\ 0628620899862803482534211706798214808651`100\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["FUNCTIONS", FontWeight->"Bold", FontVariations->{"Underline"->True}], StyleBox[".", FontVariations->{"Underline"->True}], " All elementary functions ", StyleBox["MUST", FontColor->RGBColor[1, 0, 0]], " begin with a", StyleBox[" CAPITAL LETTER\n", FontColor->RGBColor[1, 0, 0]], "followed by ", StyleBox["BRACKET [x]", FontColor->RGBColor[1, 0, 0]], " in place of parenthesis (x). 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", FontVariations->{"Underline"->True}], "\nMost equations (e.g., polynomials of degree 5 or higher) cannot be \ solved symbolically. \nOne uses in those cases the built-in functions to \ obtain approximate numerical solution." }], "Text", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(NSolve[Sin[x] == 1, x]\)\(\ \ \)\)\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(Solve::"ifun" \(\(:\)\(\ \)\) "Inverse functions are being used by \!\(Solve\), so some solutions may \ not be found."\)], "Message"], Cell[BoxData[ \({{x \[Rule] 1.5707963267948966`}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(NRoots[x\^6 - 1 == x, x]\)\(\ \ \ \)\)\( (*\ polynomial\ equations\ only\ *) \)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\)\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(x == \(-0.778089598678601`\) || x == \(-0.6293724284703148`\) - 0.7357559529997764`\ \[ImaginaryI] || x == \(-0.6293724284703148`\) + 0.7357559529997764`\ \[ImaginaryI] || x == \(\(0.4510551586088556`\)\(\[InvisibleSpace]\)\) - 1.002364571587165`\ \[ImaginaryI] || x == \(\(0.4510551586088556`\)\(\[InvisibleSpace]\)\) + 1.002364571587165`\ \[ImaginaryI] || x == 1.1347241384015194`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(NSolve[Log[x] + Sin[x] == 1, x]\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\)\( (*\ unable\ to\ solve\ *) \)\)\)], "Input", CellMargins->{{Inherited, 174}, {Inherited, Inherited}}], Cell[BoxData[ \(Solve::"tdep" \(\(:\)\(\ \)\) "The equations appear to involve the variables to be solved for in an \ essentially non-algebraic way."\)], "Message"], Cell[BoxData[ \(NSolve[Log[x] + Sin[x] == 1, x]\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["GRAPH TRACING.", FontWeight->"Bold", FontVariations->{"Underline"->True}], StyleBox[" ", FontWeight->"Bold"], "One can change the position and size of the graph by using the mouse: \ Click on the graph+hold+drag \n(= moving), click+hold corners+drag (= \ sizing). 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