Chapter13Sec3

Chapter13Sec3 - Initialization Cells (Code Needed for Most...

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Initialization Cells (Code Needed for Most Plot3D Statements) In[23]:= 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 350, AxesOrigin 8 0, 0 < , AspectRatio 1, AxesStyle Directive @ Medium, Bold D , Ticks ticks D ; H * 3D Options * L SetOptions @ Plot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None, ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; SetOptions @ ContourPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None, ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; SetOptions @ ParametricPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None,
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ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; SetOptions @ RegionPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None, ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; Chapter 13: Vector Functions 2 Chapter13Sec3.nb
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Section 13.3: Arc Length and Curvature ± Arc Length ª Definition Consider the vector equation r H t L = X f H t L , g H t L , h H t L\ over the interval a £ t £ b . Suppose the functions f , g , h , f ', g ', h ' are all continuous on the interval and the curve is traversed exactly once as t increases from a to b . Then, the length traversed is L = ± a b @ f ' H t LD 2 + @ g ' H t LD 2 + @ h ' H t LD 2 ± t = ± a b I dx dt M 2 + J dy dt N 2 + I dz dt M 2 ± t = ± a b r ' H t L ± t . The
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This note was uploaded on 01/13/2012 for the course MATH 333 taught by Professor Keithemmert during the Fall '11 term at Tarleton.

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Chapter13Sec3 - Initialization Cells (Code Needed for Most...

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