(*^ ::[paletteColors = 128; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e8, 24, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e6, 18, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, L1, e6, 14, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, L1, a20, 18, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, L1, a15, 14, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, L1, a12, 12, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = input, noPageBreakInGroup, 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, L1, 12, "Courier"; ; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, L1, 10, "Geneva"; ; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = Left Header, inactive, 12, "Times"; ; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, L1, 12, "Times"; ; fontset = Left Footer, inactive, 12, "Times"; ; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Times"; ;] :[font = title; inactive; preserveAspect; startGroup; ] Mathematica as an Engineering Tool ;[s] 2:0,1;12,0;36,-1; 2:1,25,18,Times,1,24,0,0,0;1,25,18,Times,3,24,0,0,0; :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] Description :[font = text; inactive; noPageBreak; preserveAspect; ] While Mathematica is an infinitely extensible programmable tool, many of the functions that engineers need on a day-to-day basis are just a few keystrokes away. Here are a few examples. ;[s] 3:0,0;6,1;17,0;187,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0; :[font = text; inactive; preserveAspect; endGroup; ] Compiled by: Ben W. Friedman Wolfram Research, Inc. :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] Log and Log-Log Graphing :[font = text; inactive; preserveAspect; ] Log Plotting is one of many advanced functions that reside in one of the many external packages that come with Mathematica.. These packages may be loaded into Mathematica as their functionality is needed. They also provide a style guide as you begin to write your own packages. ;[s] 6:0,2;12,0;112,1;123,0;160,1;171,0;281,-1; 3:3,13,9,Times,0,12,0,0,0;2,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Set Up :[font = text; inactive; preserveAspect; ] Load the package. :[font = input; preserveAspect; ] Needs["Graphics`Graphics`"] :[font = text; inactive; preserveAspect; ] Define the function to be graphed. :[font = input; preserveAspect; ] eqn[x_] := Abs[100/( (I x)^2 + 2 I x +100)]; :[font = text; inactive; preserveAspect; ] Generate point data to be plotted. :[font = input; preserveAspect; endGroup; ] data = Table[ eqn[x], {x, .1, 20, .4}]; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Log Plot of a Function :[font = input; preserveAspect; startGroup; ] plot1 = LogPlot[eqn[x], {x,1,20}, GridLines ->{Automatic, LogGridMinor}, PlotStyle ->Thickness[0.01]] :[font = postscript; PostScript; 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output; inactive; preserveAspect; endGroup; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Log-Log List Plot of Data :[font = input; preserveAspect; startGroup; ] plot4 = LogLogListPlot[ data, GridLines -> {LogGridMinor, LogGridMinor}, PlotStyle -> PointSize[0.015]] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.560564 0.250645 0.508962 [ [(1)] 0.02381 0 0 2 Msboxa [(2)] 0.19256 0 0 2 Msboxa [(5)] 0.41563 0 0 2 Msboxa [(10.)] 0.58437 0 0 2 Msboxa [(20.)] 0.75312 0 0 2 Msboxa [(50.)] 0.97619 0 0 2 Msboxa [(1)] -0.0125 0.25065 1 0 Msboxa [(1.5)] -0.0125 0.34027 1 0 Msboxa [(2)] -0.0125 0.40386 1 0 Msboxa [(3)] -0.0125 0.49348 1 0 Msboxa [(5)] -0.0125 0.60639 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.02381 0 moveto 0.02381 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.19256 0 moveto 0.19256 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.29127 0 moveto 0.29127 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.3613 0 moveto 0.3613 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.41563 0 moveto 0.41563 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.46001 0 moveto 0.46001 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.49754 0 moveto 0.49754 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 0.001 setlinewidth 0.53005 0 moveto 0.53005 0.61803 lineto stroke grestore gsave 0 0 0.5 setrgbcolor 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[(1)] 0.02381 0 0 2 Mshowa gsave 0.002 setlinewidth 0.19256 0 moveto 0.19256 0.00625 lineto stroke grestore [(2)] 0.19256 0 0 2 Mshowa gsave 0.002 setlinewidth 0.41563 0 moveto 0.41563 0.00625 lineto stroke grestore [(5)] 0.41563 0 0 2 Mshowa gsave 0.002 setlinewidth 0.58437 0 moveto 0.58437 0.00625 lineto stroke grestore [(10.)] 0.58437 0 0 2 Mshowa gsave 0.002 setlinewidth 0.75312 0 moveto 0.75312 0.00625 lineto stroke grestore [(20.)] 0.75312 0 0 2 Mshowa gsave 0.002 setlinewidth 0.97619 0 moveto 0.97619 0.00625 lineto stroke grestore [(50.)] 0.97619 0 0 2 Mshowa gsave 0.001 setlinewidth 0.29127 0 moveto 0.29127 0.00375 lineto stroke grestore gsave 0.001 setlinewidth 0.3613 0 moveto 0.3613 0.00375 lineto stroke grestore gsave 0.001 setlinewidth 0.46001 0 moveto 0.46001 0.00375 lineto stroke grestore gsave 0.001 setlinewidth 0.49754 0 moveto 0.49754 0.00375 lineto stroke grestore gsave 0.001 setlinewidth 0.53005 0 moveto 0.53005 0.00375 lineto stroke grestore gsave 0.001 setlinewidth 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stroke grestore gsave 0.001 setlinewidth 0 0.30864 moveto 0.00375 0.30864 lineto stroke grestore gsave 0.001 setlinewidth 0 0.32502 moveto 0.00375 0.32502 lineto stroke grestore gsave 0.001 setlinewidth 0 0.35453 moveto 0.00375 0.35453 lineto stroke grestore gsave 0.001 setlinewidth 0 0.36794 moveto 0.00375 0.36794 lineto stroke grestore gsave 0.001 setlinewidth 0 0.38057 moveto 0.00375 0.38057 lineto stroke grestore gsave 0.001 setlinewidth 0 0.39252 moveto 0.00375 0.39252 lineto stroke grestore gsave 0.001 setlinewidth 0 0.55707 moveto 0.00375 0.55707 lineto stroke grestore gsave 0.002 setlinewidth 0 0 moveto 0 0.61803 lineto stroke grestore grestore 0 0 moveto 1 0 lineto 1 0.61803 lineto 0 0.61803 lineto closepath clip newpath gsave gsave 0.015 setlinewidth 0.02381 0.25067 Mdot 0.19256 0.25119 Mdot 0.29127 0.25241 Mdot 0.3613 0.25434 Mdot 0.41563 0.25699 Mdot 0.46001 0.2604 Mdot 0.49754 0.2646 Mdot 0.53005 0.26962 Mdot 0.55872 0.27553 Mdot 0.58437 0.28238 Mdot 0.60758 0.29026 Mdot 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Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Combining Plots :[font = text; inactive; preserveAspect; startGroup; ] We can combine these graphs in one cell by using "GraphicsArray" :[font = input; preserveAspect; startGroup; ] Show[ GraphicsArray[ {{plot1 ,plot2}, {plot3, plot4}}]] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 31; pictureTop = 3; pictureWidth = 361; pictureHeight = 223; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 -0.0479942 0.952381 [ [ 0 0 0 0 ] [ 1 0.618034 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave grestore 0 0 moveto 1 0 lineto 1 0.61803 lineto 0 0.61803 lineto closepath clip newpath gsave % 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Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -GraphicsArray- :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] Curve Fitting :[font = text; inactive; preserveAspect; ] Several types of curve fitting can be done by Mathematica with little or no programming. ;[s] 3:0,0;46,1;57,0;89,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Set Up :[font = text; inactive; preserveAspect; ] Here are the data we will work with. In practice, data can be generated in many ways or read from an external file. :[font = input; preserveAspect; ] data ={ {1.25, 55.60}, {1.00, 51.00}, {0.75, 46.84}, {0.50, 35.89}, {0.40, 29.21}, {0.30, 19.70}, {0.20, 10.00}, {0.10, 2.67}}; :[font = text; inactive; preserveAspect; ] For linear curve fitting, we will use the Mathematica Fit function. We will use an implementation of the Levenberg-Marqaurdt nonlinear fit algorithm by Pakka Janhunan to do a nonlinear fit. This package is in the public domain and is available by anonymous ftp from the Mathematica files at ftp.ncsa.uiuc.edu in the directory UNIX/Symbolic/Mathematica/packages/JANHUNAN This is how you would load the package if you had stored it in a directory named "packages". ;[s] 5:0,0;42,1;53,0;270,1;281,0;466,-1; 2:3,13,9,Times,0,12,0,0,0;2,13,9,Times,2,12,0,0,0; :[font = input; preserveAspect; endGroup; ] Needs["packages`NonlinearFit`"] :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Linear Fitting :[font = input; preserveAspect; startGroup; ] pointplot = ListPlot[ data, PlotStyle -> {PointSize[ 0.02], RGBColor[1,0,0]}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations -0.0590062 0.828157 -0.0149764 0.0111204 [ [(0.2)] 0.10663 0.07399 0 2 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Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Non-linear Fitting :[font = text; inactive; dontPreserveAspect; ] The function gaussian defines the measured energy of a laser beam with a Gaussian spatial profile passing through an aperture of radius r, where xi is the peak energy density. This will be our model. ;[s] 7:0,0;12,1;21,0;135,1;137,0;145,1;148,0;200,-1; 2:4,13,9,Times,0,12,0,0,0;3,13,9,Times,1,12,0,0,0; :[font = input; dontPreserveAspect; ] gaussian[{xi_, r_}, x_] = xi N[Pi] r^2 (1- Exp[-(x/r)^2]); :[font = text; inactive; preserveAspect; ] Now we are ready to try to fit the experimental data to the Gaussian profile. :[font = input; preserveAspect; startGroup; ] NonlinearFit[ data, gaussian[{xi,r}, x], {xi,r}, {x}, ProgressTrace -> True] :[font = print; inactive; preserveAspect; ] NonlinearFit::trace params = {1., 1.}, lambda = -1. NonlinearFit::trace params = {1., 1.}, lambda = 0.01. NonlinearFit::trace params = {1., 1.}, lambda = 0.1. NonlinearFit::trace params = {25.4964, 0.328939}, lambda = 0.01. NonlinearFit::trace params = {25.4964, 0.328939}, lambda = 0.1. NonlinearFit::trace params = {25.4964, 0.328939}, lambda = 1.. NonlinearFit::trace params = {62.3382, 0.611647}, lambda = 0.1. NonlinearFit::trace params = {61.392, 0.541947}, lambda = 0.01. NonlinearFit::trace params = {73.3786, 0.471666}, lambda = 0.001. NonlinearFit::trace params = {79.9997, 0.457014}, lambda = 0.0001. 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Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] Fourier Transforms :[font = text; inactive; preserveAspect; ] The Fourier Transform and Inverse Fourier Transform are basic engineering tools. ;[s] 5:0,0;4,1;21,0;26,1;51,0;82,-1; 2:3,13,9,Times,0,12,0,0,0;2,13,9,Times,1,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] General Example :[font = text; inactive; preserveAspect; ] First, we generate a 300-item list containing a periodic signal with random noise added. :[font = input; preserveAspect; ] fourierdata = Table[ N[ Sin[25 2 Pi n/300] + Random[]], {n, 300}]; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup; ] A First Look at the Data :[font = text; inactive; preserveAspect; ] From this plot, the data look random. :[font = input; preserveAspect; startGroup; ] ListPlot[ fourierdata, PlotJoined -> True, 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Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup; ] Apply the Fourier Transform :[font = text; inactive; preserveAspect; ] The Fast Fourier Transform shows a strong peak at 25 (the frequency of the original periodic signal) and another at 300-25. ;[s] 3:0,0;4,1;27,0;124,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0; :[font = input; preserveAspect; startGroup; ] ListPlot[ Abs[ Fourier[ fourierdata]], PlotJoined -> True, PlotRange -> All, PlotStyle -> RGBColor[ 1, 0,.5]] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.0206243 0.00318522 0.0138876 0.0688303 [ [(50)] 0.17989 0.01389 0 2 Msboxa [(100)] 0.33915 0.01389 0 2 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Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = section; inactive; Cclosed; dontPreserveAspect; startGroup; ] FET Picture :[font = smalltext; inactive; dontPreserveAspect; ] by Alfy Riddle Macalan Consulting Author of: Nodal2.0: A package for ciruit analysis in Mathematica ;[s] 2:0,0;90,1;102,-1; 2:1,12,9,Times,0,10,0,0,0;1,12,9,Times,2,10,0,0,0; :[font = text; inactive; preserveAspect; ] By combining a few of Mathematica's built-in drawing commands, an engineer can build a precise representation of any system. Here is an example from electrical engineering. ;[s] 3:0,0;22,1;33,0;173,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Code :[font = input; dontPreserveAspect; endGroup; ] fetPict[] := ( Block[ {Rgs,Rds,Cgs,Cgd,Cds,gm,tau}, Show[ Graphics[{ Line[{{1,0},{-.3,0},{-.3,.1},{-.3,-.1}}], Line[{{-1,0},{-.4,0},{-.4,.1},{-.4,-.1}}], Line[{{.8,0},{.8,-.2},{.7,-.2},{.9,-.2}}], Line[{{.5,-.5},{.5,0}}], Line[{{0,-.5},{.8,-.5},{.8,-.3},{.7,-.3},{.9,-.3}}], Line[{{-.8,0},{-.8,-.2},{-.7,-.2},{-.9,-.2}}], Line[{{-.8,-.5},{-.8,-.3},{-.7,-.3},{-.9,-.3}}], Line[{{-.8,-.5},{0,-.5},{0,-.65}}], Line[{{.1,-.45},{0,-.25},{.1,-.05},{.2,-.25},{.1,-.45}}], Line[{{.1,-.5},{.1,0}}], Polygon[{{.1,-.4},{.07,-.3},{.135,-0.3}}], Text[1, {-.95,0.05}], Text[2, {.1,-.65}], Text[3, {.95,0.05}], Text[Rgs, {-0.5,-0.38}], Text[Rds, {0.35,-.37}], Text[Cgs, {-.93,-.37}], Text[Cgd, {-.15,0.05}], Text[Cds, {0.95,-.37}], Text[gm, {-.1,-.17}], Text[tau, {-.1,-.37}], GrayLevel[0.5], Rectangle[{-.7,-.45},{-.3,-.55}], Rectangle[{.45,-.1},{.55,-.4}] }], AspectRatio->Automatic ] ]) ;[s] 2:0,1;955,0;956,-1; 2:1,13,10,Courier,1,12,0,0,0;1,11,9,Courier,1,10,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Graphic :[font = input; dontPreserveAspect; startGroup; ] fetPict[] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 1; pictureTop = 2; pictureWidth = 455; pictureHeight = 170; endGroup; endGroup; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.375 MathPictureStart % Scaling calculations 0.5 0.47619 0.31845 0.47619 [ [ 0 0 0 0 ] [ 1 0.375 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave grestore grestore 0 0 moveto 1 0 lineto 1 0.375 lineto 0 0.375 lineto closepath clip newpath 0 setgray gsave 0.004 setlinewidth 0.97619 0.31845 moveto 0.35714 0.31845 lineto 0.35714 0.36607 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Clear[g] :[font = input; preserveAspect; startGroup; ] g[s] = 1/(s^2 + 2 xi w0 s + w0^2) :[font = output; output; inactive; preserveAspect; endGroup; endGroup; ] (s^2 + w0^2 + 2*s*w0*xi)^(-1) ;[o] 1 -------------------- 2 2 s + w0 + 2 s w0 xi :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Example :[font = input; preserveAspect; startGroup; ] g[t] = InverseLaplaceTransform[g[s],s,t] :[font = output; output; inactive; preserveAspect; endGroup; ] -E^(-(t*w0*xi) - t*w0*(-1 + xi)^(1/2)*(1 + xi)^(1/2))/ (2*w0*(-1 + xi)^(1/2)*(1 + xi)^(1/2)) + E^(-(t*w0*xi) + t*w0*(-1 + xi)^(1/2)*(1 + xi)^(1/2))/ (2*w0*(-1 + xi)^(1/2)*(1 + xi)^(1/2)) ;[o] -(t w0 xi) - t w0 Sqrt[-1 + xi] Sqrt[1 + xi] -E ---------------------------------------------- + 2 w0 Sqrt[-1 + xi] Sqrt[1 + xi] -(t w0 xi) + t w0 Sqrt[-1 + xi] Sqrt[1 + xi] E --------------------------------------------- 2 w0 Sqrt[-1 + xi] Sqrt[1 + xi] :[font = input; preserveAspect; startGroup; ] 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Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -SurfaceGraphics- :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] Bode Plots :[font = smalltext; inactive; dontPreserveAspect; ] by Art Low, The Leading Edge of Domain Systems Research :[font = text; inactive; preserveAspect; ] Bode Plots are an extremely useful function for control and electrical engineers. Basically consisting of two parametric plots, this function is quite straightforward. ;[s] 2:0,1;10,0;168,-1; 2:1,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] The BodePlot Function :[font = input; preserveAspect; endGroup; ] BodePlot[f_,s_,lo_,hi_,type_]:= Block[{W,v,p}, v=20; p=10; magplot = ParametricPlot[ {Log[10,W], type Log[10,Abs[f /. s-> I W]] }, {W,lo,hi}, PlotRange->All, AxesLabel->{Log[W],dB}, DisplayFunction->Identity ]; phaseplot = ParametricPlot[ {Log[10,W], 360/(2 Pi) Arg[f /. s->I W] }, {W,lo,hi}, PlotRange->All, AxesLabel->{Log[W],Degrees}, DisplayFunction->Identity ]; Show[GraphicsArray[ {{magplot},{phaseplot}}, DisplayFunction->$DisplayFunction ],Frame->True,PlotLabel->"Bode Magnitude & Phase Plots" ] ] :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Example :[font = input; preserveAspect; startGroup; ] BodePlot[(x+1)/(x+3)^2,x,.1,10,v] :[font = postscript; PostScript; 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