Chapter15Sec4

# Chapter15Sec4 - Initialization Cells(Code Needed for Most...

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Initialization Cells (Code Needed for Most Plot3D Statements) ticks @ min_, max_ D : = Join @ Table @8 i,If @ i 0, ,Style @ i,12 DD , 8 0.01,0 << , 8 i,Ceiling @ min D ,Floor @ max D , 2 <D , H * Numbered ticks * L Table @8 j, , 8 0.01,0 << , 8 j,Round @ min D ,Round @ max - 1 D ,1 <DD H * Un - numbered ticks * L H * Some 2D code to generate polar rectangles * L H * Limitation to the module: Assume that r < R and Α<Β * L myPolarRectangle @ r0_, R0_, Α 0_, Β 0_ D : = Module @ 8 r = r0, R = R0, Α = Α 0, Β = Β 0 < , H * List of variables passed to the module * L Show @ PolarPlot @ r, 8 Θ , Α , Β < , PlotStyle fi 8 Thick, Black <D , PolarPlot @ R, 8 Θ , Α , Β < , PlotStyle fi 8 Thick, Black <D , Graphics @8 Thick, Black, Line @88 rCos @ Α D , rSin @ Α D< , 8 RCos @ Α D , RSin @ Α D<<D <D , Graphics @8 Thick, Black, Line @88 rCos @ Β D , rSin @ Β D< , 8 RCos @ Β D , RSin @ Β D<<D <D D D H * Assumptions: r < R, Α<Β * L myPolarGrid @ m0_,n0_,r0_,R0_, Α 0_, Β 0_ D : = Module @8 m = m0,n = n0,r = r0,R = R0, Α = Α 0, Β = Β 0 < , dr = H R - r L m; dtheta = H Β - Α L n; Show @ Table @ myPolarRectangle @ r + idr,r + H i + 1 L dr, Α + Θ dtheta, Α + H Θ + 1 L dtheta D , 8 i, 0, m - 1 < , 8 Θ , 0,n - 1 <D D D

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H * Assumptions: r < R, Α<Β * L myPolarGridwithPoints @ m0_,n0_,r0_,R0_, Α 0_, Β 0_ D : = Module @8 m = m0,n = n0,r = r0,R = R0, Α = Α 0, Β = Β 0 < , dr = H R - r L m; dtheta = H Β - Α L n; Show @ Table @ myPolarRectangle @ r + idr,r + H i + 1 L dr, Α + Θ dtheta, Α + H Θ + 1 L dtheta D , 8 i, 0, m - 1 < , 8 Θ , 0,n - 1 <D , Table @ Graphics @ 8 PointSize @ Large D , Point @8H 1 + H i + 1 2 L dr L Cos @ Pi 6 + H Θ + 1 2 L dtheta D , H 1 + H i + 1 2 L dr L Sin @ Pi 6 + H Θ + 1 2 L dtheta D<D<D , 8 i, 0, 5 - 1 < , 8 Θ , 0, 4 - 1 < D D D H * 2D Options * L SetOptions @ Plot, ImageSize fi 350, AxesOrigin fi 8 0,0 < ,
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