(*^ ::[ frontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.1"; macintoshStandardFontEncoding; showRuler; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, e8, 24, "B Univers 65 Bold"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Garamond"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, e6, 14, "I Garamond LightItalic"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, a20, 18, "B Univers 65 Bold"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, a15, 14, "B Garamond Bold"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Garamond"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Garamond"; ; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Garamond"; ; 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, "Garamond"; ; fontset = leftheader, inactive, L2, 12, "Garamond"; ; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Garamond"; ; fontset = leftfooter, inactive, L2, 12, "Garamond"; ; 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, M18, N55, 12, "Garamond"; ; 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"; ; ] :[font = text; inactive; preserveAspect; leftWrapOffset = 17; leftNameWrapOffset = 1; ] Mathematics 162 Laboratory 4 Week of Feb. 15, 1993 Name: _____________________________ Lab Partner: ___________________________ Consulted with: ____________________________________________________________ :[font = title; inactive; preserveAspect; ] Direction Fields :[font = text; inactive; preserveAspect; ] Direction fields provide a simple graphical method for constructing solutions of first order differential equations. Geometrically, the differential equation y' = f(x, y) says that the slope of the solution curve through the point (x, y) is the value of f(x, y). We can indicate this on a graph by drawing a short line segment of slope f(x, y) through the point (x, y). The collection of all such line segments is called the direction field of the differential equation. ;[s] 31:0,0;159,1;160,0;164,1;165,0;166,1;167,0;169,1;170,0;233,1;234,0;236,1;237,0;255,1;256,0;257,1;258,0;260,1;261,0;338,1;339,0;340,1;341,0;343,1;344,0;365,1;366,0;368,1;369,0;428,1;443,0;474,-1; 2:16,14,9,Garamond,0,12,0,0,0;15,14,9,Garamond,2,12,0,0,0; :[font = section; inactive; preserveAspect; ] Part 1: Solution Curves :[font = subsubtitle; inactive; preserveAspect; ] You and your lab partner should work together in lab, using just one computer. You should also collaborate on writing the laboratory report and hand in just one report for your team. :[font = text; inactive; preserveAspect; ] As you learned in completing Part 0, drawing direction fields can be laborious. Therefore, in the lab we will let Mathematica do the work for us. A package of special Mathematica commands we will use is called DEGraphics.m; load it with this command ;[s] 5:0,0;169,1;180,0;212,2;224,0;252,-1; 3:3,14,9,Garamond,0,12,0,0,0;1,14,9,Garamond,2,12,0,0,0;1,13,10,Courier,1,12,0,0,0; :[font = input; preserveAspect; ] <