Chapter13Sec1ShowCode

Chapter13Sec1ShowCode - Initialization Cells (Code Needed...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Initialization Cells (Code Needed for Most Plot3D Statements) In[146]:= ticks min_ , max_ : Join Table i, If i 0, , Style i, 12 , 0.01, 0 , i, Ceiling min , Floor max , 2 , Numbered ticks Table j, , 0.01, 0 , j, Round min , Round max 1 , 1 Un numbered ticks 2D Options SetOptions Plot, ImageSize 350, AxesOrigin 0, 0 , AspectRatio 1, AxesStyle Directive Medium, Bold , Ticks ticks ; 3D Options SetOptions Plot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin AxesStyle Directive Medium, Bold , Ticks ticks, Mesh None, ViewPoint 2, 0.9, 1 , ViewVertical 0, 0, 1 ; SetOptions ContourPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin AxesStyle Directive Medium, Bold , Ticks ticks, Mesh None, ViewPoint 2, 0.9, 1 , ViewVertical 0, 0, 1 ; SetOptions ParametricPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin AxesStyle Directive Medium, Bold , Ticks ticks, Mesh None, , 0, 0, 0 , 0, 0, 0 , 0, 0, 0 , 2 Chapter13Sec1.nb ViewPoint 2, 0.9, 1 , ViewVertical 0, 0, 1 ; SetOptions RegionPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin AxesStyle Directive Medium, Bold , Ticks ticks, Mesh None, ViewPoint 2, 0.9, 1 , ViewVertical 0, 0, 1 ; 0, 0, 0 , Chapter 13: Vector Functions Chapter13Sec1.nb 3 Section 13.1: Vector Functions and Space Curves Definition A vector valued function is a function whose domain is a set of real numbers and whose range is a set of vectors. In 3D, if f(t), g(t), h(t) are the compenents of the vector r(t), then rt f t, gt, ht . The parametric equations of a curve defined by the vector valued function are x ft, y gt, z ht. Thus, a vector valued function can be thought of as the position vector of the point P f t , g t , h t . The limit of a vector function is defined by taking the limits of its component parts as follows limt a rt limt a f t , limt a g t , limt a ht . A vector function is continuous at the number a if limt a rt r a. That is, if and only if the vector function’s components are all continuous at the number a. 4 Chapter13Sec1.nb Example Consider the vector function r t Sketch the curve over 0 t cos t , sin t , 8 Π. What surface does this curve live on? Find the limit as t approaches 0, Π 2 Π , and . 4 t. Chapter13Sec1.nb 5 Mathematica Solution In[152]:= GraphicsGrid Show Plot3D 0, x, 1.5, 1.5 , y, 1.5, 1.5 , PlotRange 0.5, 7 , PlotStyle Directive Opacity 0 , Mesh None, BoundaryStyle None , ParametricPlot3D Cos t , Sin t , Sqrt t , t, 0, 8 Pi , Graphics3D Text Style x, Large , 1.2, 0.2, 0 Graphics3D Text Style y, Large , 0.2, 1.4, 0 Graphics3D Text Style z, Large , 0, 0.2, 6.2 PlotLabel Style "Parametric Plot", Large , Show Plot3D 0, x, 1.5, 1.5 , y, 1.5, 1.5 , PlotRange 0.5, 7 , PlotStyle Directive Opacity 0 , Mesh None, BoundaryStyle None , ParametricPlot3D Cos t , Sin t , Sqrt t , t, 0, 8 Pi , PlotStyle Red, Tube 0.1 , PlotRange All , Graphics3D Text Style x, Large , 1.2, 0.2, 0 Graphics3D Text Style y, Large , 0.2, 1.4, 0 Graphics3D Text Style z, Large , 0, 0.2, 6.2 PlotLabel Style "Tube Plot", Large Label , Label the x axis , Label the y axis , Label the z axis Label the plot , Label the x axis , Label the y axis , Label the z axis the plot , Show Plot3D 0, x, 1.5, 1.5 , y, 1.5, 1.5 , PlotRange 0.5, 7 , PlotStyle Directive Opacity 0 , Mesh None, BoundaryStyle None, AxesOrigin None, Ticks Automatic, Boxed True Do this to put a box around the plot , 6 Chapter13Sec1.nb ParametricPlot3D Cos t , Sin t , Sqrt t , t, 0, 8 Pi , Graphics3D Text Style x, Large , 0.2, 1.4, 0 , Label the x axis Graphics3D Text Style y, Large , 1.2, 0.2, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 3, 6.2 , Label the z axis PlotLabel Style "Boxed Parametric Plot", Large Label the plot , Show Plot3D 0, x, 1.5, 1.5 , y, 1.5, 1.5 , PlotRange 0.5, 7 , PlotStyle Directive Opacity 0 , Mesh None, BoundaryStyle None , ContourPlot3D x^2 y ^ 2 1, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 0, 7 , ContourStyle Directive Opacity 0.4 , ParametricPlot3D Cos t , Sin t , Sqrt t , t, 0, 8 Pi , PlotStyle Black, Thick , Graphics3D Text Style x, Large , 1.2, 0.2, 0 , Label the x axis Graphics3D Text Style y, Large , 0.2, 1.4, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0.2, 6.2 , Label the z axis PlotLabel Style "The Surface", Large Label the plot , ImageSize 600 Chapter13Sec1.nb 7 Parametric Plot 6 Tube Plot z 6 4 z 4 2 2 1 1 1 x 1 1 1 y x 1 1 y 1 y Out[152]= Boxed Parametric Plot The Surface z 6 6 z 4 4 2 2 1 1 1 0 x y 0 x 1 1 0 1 In[153]:= Limit Limit Limit Out[153]= Out[154]= Cos t , Sin t , Sqrt t Cos t , Sin t , Sqrt t Cos t , Sin t , Sqrt t 1, 0, 0 Π 0, 1, 2 Out[155]= 1 1 , 2 Π , 2 2 ,t ,t ,t 0 Π Π 2 4 1 8 Chapter13Sec1.nb Example Show that the vector function (using parameter t) that represents the curve of intersection of the paraboloid z 4 x2 y 2 and the parabolic cylinder y x2 is given by rt t, t2, 4 t2 t4 . In[156]:= Show Plot3D 0, x, 3.5, 3.5 , y, 3.5, 3.5 , PlotRange 0.5, 7 , PlotStyle Directive Opacity 0 , Mesh None, BoundaryStyle None , ContourPlot3D z 4 x ^ 2 y ^ 2, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 0, 7 , ContourStyle Directive Red, Opacity 0.4 , ContourPlot3D y x ^ 2, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 0, 7 , ContourStyle Directive Blue, Opacity 0.4 , ParametricPlot3D t, t ^ 2, 4 t ^ 2 t ^ 4 , t, 3, 3 , PlotStyle Black, Thick , Graphics3D Text Style x, Large , 1.2, 0.2, 0 Graphics3D Text Style y, Large , 0.2, 1.4, 0 Graphics3D Text Style z, Large , 0, 0.2, 6.2 , , Label the x axis Label the y axis Label the z axis Chapter13Sec1.nb 9 6 z 4 Out[156]= 2 3 1 3 1 x 1 1 y 3 3 10 Chapter13Sec1.nb Homework Pages: 869 - 871 1, 3, 7, 9, 15, 19, 21, 25, 27, 29, 31 ...
View Full Document

This note was uploaded on 01/13/2012 for the course MATH 333 taught by Professor Keithemmert during the Fall '11 term at Tarleton.

Ask a homework question - tutors are online