(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 35659, 1862] NotebookOptionsPosition[ 33829, 1799] NotebookOutlinePosition[ 34164, 1814] CellTagsIndexPosition[ 34121, 1811] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Weekly Exercises (1)", "Title"], Cell["\<\ Assigned: January 22, 2009 Due: before class on January 29, 2009\ \>", "Subsubtitle", CellChangeTimes->{{3.44154520110165*^9, 3.441545216779632*^9}}], Cell[CellGroupData[{ Cell["Getting Help", "Subsection"], Cell[TextData[{ "Use the ", StyleBox["?", FontWeight->"Bold"], " command to find all commands that begin with the letters ", StyleBox["P ", FontWeight->"Bold"], "and", StyleBox[" Q", FontWeight->"Bold"], "." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Using the Help Browser", "Subsection"], Cell[TextData[{ "Use the Help Browser and describe the basic differences between ", StyleBox["Plot", FontWeight->"Bold"], " and ", StyleBox["ListPlot", FontWeight->"Bold"], ". In particular, describe the argument to each command in words." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Simple Evaluation", "Subsection"], Cell["\<\ Evaluate the following pairs of expressions and describe in words why they \ are different.\ \>", "Text"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"2", " ", "x"}], " ", "+", " ", RowBox[{"x", " ", "7"}]}], ",", " ", RowBox[{ RowBox[{"2", "x"}], " ", "+", " ", "x7"}]}], "}"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"2", " ", "meters"}], " ", "+", " ", RowBox[{"7", " ", "meters"}]}], ",", " ", RowBox[{ RowBox[{"1", " ", "meter"}], " ", "+", " ", RowBox[{"8", " ", "meters"}]}]}], "}"}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Working with Real numbers", "Subsection"], Cell[TextData[{ "(1) Find the numerical value for", StyleBox[" Sin[53 \[Degree]]", FontWeight->"Bold"], " to six significant figures." }], "Text"], Cell[TextData[{ "(2) Find the 2001st significant figure of ", StyleBox["\[Pi]", FontWeight->"Bold"], "." }], "Text"], Cell[TextData[{ "(3) Find ", StyleBox["Tan[50] - 1", FontWeight->"Bold"], " to 10 significant figures." }], "Text"], Cell[TextData[{ "(4) Find the real and imaginary parts of the complex number ", StyleBox["z = Exp[2 + 9 I]", FontWeight->"Bold"], "." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Procedures", "Subsection"], Cell["\<\ Construct a list of 30 random number using, the following\[Ellipsis]\ \>", "Text"], Cell[BoxData[ RowBox[{"list", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"RandomReal", "[", RowBox[{"{", RowBox[{"0", ",", "20"}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "30"}], "}"}]}], "]"}]}]], "CompatibilityInput"], Cell["\<\ Then, write a procedure that will retain only those elements having values \ between 6 and 15. Try sorting the list from largest to smallest.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Collision?", "Subsection"], Cell[TextData[{ "A train pulls out of a station. It moves along the tracks following the \ equation ", StyleBox["s = 0.1 t^2", FontWeight->"Bold"], ", where ", StyleBox["s", FontWeight->"Bold"], " is the distance along the track and ", StyleBox["t", FontWeight->"Bold"], " is time.\nAnother train arrives at the station at high-speed and moves \ along the track according to the equation", StyleBox[" s = -4 + 5 t - t^2 - t^3", FontWeight->"Bold"], ". The second train eventually comes to a stop and moves backwards." }], "Text"], Cell[TextData[{ "Question: Use ", StyleBox["Plot[\[Ellipsis]]", FontWeight->"Bold"], " to deter ine if the two trains collide." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Find the Function", "Subsection"], Cell[TextData[{ "Below you'll find four graphs generated using the ", StyleBox["Plot", FontWeight->"Bold"], " and ", StyleBox["ListPlot", FontWeight->"Bold"], " commands. 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