Chapter16Sec4ShowCode

# Chapter16Sec4ShowCode - Initialization Cells(Code Needed...

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Initialization Cells (Code Needed for Most Plot3D Statements) In[841]:= 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 * 2D Options * L SetOptions @ Plot, ImageSize fi 350, AxesOrigin fi 8 0,0 < , AspectRatio fi 1, AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks D ; SetOptions @ ParametricPlot, ImageSize fi 350, AxesOrigin fi 8 0,0 < , AspectRatio fi 1, AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks D ; SetOptions @ VectorPlot, ImageSize fi 350, AxesOrigin fi 8 0,0 < , AspectRatio fi 1, Frame fi False, Axes fi True, AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks D ; H * 3D Options * L SetOptions @ Plot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 <

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D ; SetOptions @ ContourPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ ParametricPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ RegionPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ VectorPlot3D, ImageSize fi 350, AxesOrigin fi 8 0,0 < , AspectRatio fi 1, BoxRatios fi 1, Axes fi True, AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; Needs @ "CurvesGraphics6`" D 2 Chapter16Sec4.nb
Chapter 16: Vector Calculus Chapter16Sec4.nb 3

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Section 16.4: Green’s Theorem Some Terminology ª Definition L A curve is called closed if its terminal point coincides with its initial point, that is, r H b L = r H a L . L A set D is open if for every point P Ε D , there is a disk with center P that lies entirely in D . (In particlu- lar, D does not contain its boundary points.) L A set D is connected if for any two points in D , there is a path joining them that lies entirely in D . L A curve is called a simple curve if it doesn’t intersect itself except, possibly, at the endpoints. L A simply-connected region is a connected region, D , such that every simple closed curve contained entirely in D encloses only points that are in D . L A simple closed curve C has positive orientation if it is traversed in a single counterclockwise manner. That is, if r H t L , a £ t £ b is the vector function representation of C , then the region D is always on the left as the point r H t L traverses C . 4 Chapter16Sec4.nb
In[851]:= GraphicsGrid @8 8 Show @ ParametricPlot @ 8 Cos @ x D + Sin @ 3x D 3,Sin @ x D< , 8 x,0,2 Π < , PlotStyle fi Directive @ Thick, Black, Arrowheads @ Large DD , Oriented fi True, H * Needs a package: Needs @ "CurvesGraphics6`" D * L HowManyArrows fi 4, H * Needs a package: Needs @ "CurvesGraphics6`" D * L AspectRatio fi Automatic, PlotLabel fi Style @ Text @ "Positively Oriented" D

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