Chapter12Sec6ShowCode

Chapter12Sec6ShowCode - 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[42]:= 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 Chapter12Sec6.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 12 : Vectors and the Geometry of Space Chapter12Sec6.nb Section 12.6: Cylinders and Quadric Surfaces Cylinders Definition A cylinder is a surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given plane (i.e. 2D) curve. 3 4 Chapter12Sec6.nb In[48]:= GraphicsGrid Show ContourPlot3D x ^ 2 y ^ 2 9, x, 4.5, 4.5 , y, 4.5, 4.5 , z, 5, 5 , Graphics3D Text Style x, Large , 5.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 5, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0, 6.2 , Label the z axis PlotLabel Style "Circular Cylinder", Large Label the plot , Show ContourPlot3D z y ^ 2 3, x, 4.5, 4.5 , y, 4.5, 4.5 , z, 5, 5 , Graphics3D Text Style x, Large , 5.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 5, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0, 6.2 , Label the z axis PlotLabel Style "Parabolic Cylinder", Large Label the plot , ImageSize 600 Circular Cylinder z Parabolic Cylinder z 5 5 3 3 1 Out[48]= 4 2 x 21 4 3 5 4 1 2 2 4 4 2 y x 21 4 3 5 4 2 2 4 y Chapter12Sec6.nb 5 Quadric Surfaces Definition A quadric surface is the graph of a second-degree equation in three variables, x, y, z. The most general such equation is Ax2 By2 Cz2 Dxy Eyz Fxz Gx Hy Iz J, where A,B,C,D,E,F,G,H,I,J are constants. In[49]:= GraphicsGrid Show ContourPlot3D x^2 y^2 9 z ^ 2 4 1, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 3, 3 , Mesh 3 Draws the grid on the surface , Graphics3D Text Style x, Large , 4.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 4, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0.6, 3.2 , Label the z axis PlotLabel Style "Ellipsoid", Medium Label the plot , Show ContourPlot3D z 4 x ^ 2 y ^ 2, x, 2.5, 2.5 , y, 3.5, 3.5 , z, 2, 5 , Mesh 3 , Graphics3D Text Style x, Large , 3.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 3.8, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0, 5.7 , Label the z axis PlotLabel Style "Ellipitic Paraboloid", Medium Label the plot , Show ContourPlot3D z ^ 2 4 x ^ 2 4 y ^ 2 4, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 3, 3 , Mesh 3 Draws the grid on the surface , Graphics3D Text Style x, Large , 4.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 4, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0.6, 3.2 , Label the z axis PlotLabel Style "Cone", Medium Label the plot , Show ContourPlot3D x ^ 2 4 y ^ 2 z ^ 2 4 1, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 3, 3 , Mesh 3 Draws the grid on the surface , 6 Chapter12Sec6.nb , Graphics3D Text Style x, Large , 4.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 4, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0.6, 3.2 , Label the z axis PlotLabel Style "Hyperboloid of One Sheet", Medium Label the plot , Show ContourPlot3D x^2 y^2 4 z^2 2 1, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 3, 3 , Mesh 3 Draws the grid on the surface , Graphics3D Text Style x, Large , 4.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 4, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0.6, 3.2 , Label the z axis PlotLabel Style "Hyperboloid of Two Sheets", Medium Label the plot , Show ContourPlot3D z y ^ 2 x ^ 2, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 5, 5 , Mesh 3 , Graphics3D Text Style x, Large , 4.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 3.8, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0, 5.7 , Label the z axis PlotLabel Style "Hyperbolic Paraboloid", Medium Label the plot , ImageSize 600 Chapter12Sec6.nb 7 Ellipsoid 3 Ellipitic Paraboloid Cone z z 3 z 4 1 3 x 1 11 1 3 1 3 1 2 3 y 3 2 3 3 1 x 1 3 22 x y 1 11 1 3 1 3 3 3 Out[49]= Hyperboloid of One Sheet 3 Hyperboloid of Two Sheets z 3 Hyperbolic Paraboloid z z 5 3 1 3 x 1 11 1 3 3 1 1 3 3 y 3 x 1 11 1 3 3 1 3 1 3 y 3 x 11 1 1 33 5 1 3 3 8 Chapter12Sec6.nb Cone Properties of the Canonical Example z2 Horizontal traces are ellipses. Vertical traces in the planes x k and y x2 y2 c2 a2 b2 k are hyperbolas if k 0 but are pairs of lines if k 0. Chapter12Sec6.nb 9 In[50]:= GraphicsGrid Show ContourPlot3D z^2 4 x^2 4 y^2 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style 4, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis z2 x2 y2 4 PlotLabel 4 4 Style " ", Large Label the plot , Show ContourPlot3D y ^ 2 4 x ^ 2 4 z ^ 2, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 3, 3 , Mesh 3 Draws the grid on the surface , Graphics3D Text Style x, Large , 4.2, 0, 0 , Label the x axis Graphics3D Text Style y, Large , 0, 4, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0.6, 3.2 , Label the z axis y2 x2 4 PlotLabel 4 Style " z2 ", Large Label the plot , Show ContourPlot3D x^2 4 y^2 4 z^2 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style 2, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis x2 , ImageSize 600 y2 z2 4 PlotLabel 4 2 Style " ", Large Label the plot 10 Chapter12Sec6.nb z2 4 x2 4 3 y2 4 1 3 x 3 1 3 3 x y2 4 3 z2 2 z 1 1 x 3 1 1 1 3 3 1 z 3 y 3 1 1 1 3 3 Out[50]= 3 1 y 3 x2 4 z2 1 3 1 1 1 x2 4 z 1 3 y2 4 1 3 y Chapter12Sec6.nb 11 Ellipsoid Properties of the Canonical Example x2 All traces are ellipses. If r : a b y2 z2 a2 b2 c2 1 c , then the ellipsoid is a sphere of radius r . In[51]:= Show ContourPlot3D x^2 y^2 9 z^2 4 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style "x2 1, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis y2 z2 9 4 1", Large Label the plot 12 Chapter12Sec6.nb x y2 z2 1 94 2 3 z 1 3 1 3 1 Out[51]= 1 1 3 x 3 1 3 y Chapter12Sec6.nb 13 Elliptic Paraboloid Properties of the Canonical Example z x2 y2 c a2 b2 Horizontal traces are ellipses. Vertical traces are parabolos. The variable raised to the first power indicates the axis of the paraboloid. In[52]:= GraphicsGrid Show ContourPlot3D z 4 x ^ 2 y ^ 2, x, 2.5, 2.5 , y, Mesh 3 , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style "z 3.5, 3.5 , x, y, z, 4 Large , Large , Large , x2 y2 ", z, 2, 5 , 3.2, 0, 0 0, 3.8, 0 0, 0, 5.7 Large , , , Label Label the x axis Label the y axis Label the z axis the plot , Show ContourPlot3D y 4 x ^ 2 z ^ 2, x, 2.5, 2.5 , y, Mesh 3 , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style "y 3.5, 3.5 , x, y, z, 4 Large , Large , Large , x2 z2 ", z, 2, 2 , 3.2, 0, 0 0, 3.8, 0 0, 0.5, 2 Large , , , Label Label the x axis Label the y axis Label the z axis the plot , Show ContourPlot3D x 4 z ^ 2 y ^ 2, x, 2.5, 2.5 , y, Mesh 3 , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style "x , ImageSize 600 3.5, 3.5 , x, y, z, 4 Large , Large , Large , z2 y2 ", z, 2, 2 , 3.2, 0, 0 0, 3.8, 0 0, 0.5, 2 Large , , , Label Label the x axis Label the y axis Label the z axis the plot 14 Chapter12Sec6.nb 4 x2 y2 z z y 4 x2 z2 2 z 4 2 2 3 1 2 3 2 1 2 1 3 y 2 Out[52]= 4 z2 y2 2 z 2 3 1 1 2 x 2 x 2 x x 1 3 y 3 y Chapter12Sec6.nb 15 Hyperboloid of One Sheet Properties of the Canonical Example x2 y2 z2 a2 b2 c2 1 Horizontal traces are ellipses. Vertical traces are hyperbolas. The axis of symmetry is based upon the variable whose coefficient is negative. 16 Chapter12Sec6.nb In[53]:= GraphicsGrid Show ContourPlot3D x^2 4 y^2 z^2 4 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style " x 2 4 1, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis y2 z2 4 1", Large Label the plot , Show ContourPlot3D x^2 2 y^2 z^2 2 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style x2 PlotLabel Style " 1, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis y2 2 z2 1", Large Label the plot 2 , Show ContourPlot3D x^2 4 y^2 z^2 4 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel , ImageSize 600 Style " x2 4 1, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis y2 z2 4 1", Large Label the plot Chapter12Sec6.nb 17 x2 4 z2 4 y2 3 x2 2 z2 y 1 2 2 3z 1 z 1 3 1 1 3 1 x 1 1 1 3 y x z2 4 y2 3 1 z 1 3 1 1 x 1 1 3 3 1 3 y 3 1 1 1 3 3 Out[53]= 3 1 3 3 x2 4 3 1 3 y 18 Chapter12Sec6.nb Hyperboloid of Two Sheets Properties of the Canonical Example x2 y2 z2 a2 b2 c2 Horizontal traces in z k are ellipses if k c or k Vertical traces are hyperbolas. The two minus signs indicate two sheets. The plus sign indicates the axis. c. 1 Chapter12Sec6.nb 19 In[54]:= GraphicsGrid Show ContourPlot3D x^2 2 y^2 z^2 2 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style " x2 2 1, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis z2 2 y2 1", Large Label the plot , Show ContourPlot3D x^2 2 y^2 z^2 2 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style x2 PlotLabel Style " 1, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis y2 2 z2 1", Large Label the plot 2 , Show ContourPlot3D x^2 4 y^2 z^2 4 x, 3.5, 3.5 , y, Mesh 3 Draws the , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel , ImageSize 600 Style " x2 4 1, 3.5, 3.5 , z, 3, 3 , grid on the surface x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 4, 0 , Label the y axis z, Large , 0, 0.6, 3.2 , Label the z axis y2 z2 4 1", Large Label the plot 20 Chapter12Sec6.nb x2 2 z2 2 y2 3 x2 2 z2 y 1 2 2 3z 1 z 1 3 1 1 3 1 x 1 1 1 3 y x z2 4 y2 3 1 z 1 3 1 1 x 1 1 3 3 1 3 y 3 1 1 1 3 3 Out[54]= 3 1 3 3 x2 4 3 1 3 y Chapter12Sec6.nb 21 Hyperbolic Paraboloid Properties of the Canonical Example z x2 y2 c a2 b2 Horizontal traces are hyperbolas. Vertical traces are parabolas. The varaible c may be positive or negative! In[55]:= GraphicsGrid Show ContourPlot3D z y ^ 2 x ^ 2, x, 3.5, 3.5 , y, Mesh 3 , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style "z 3.5, 3.5 , x, y, z, y2 z, 5, 5 , Large , 4.2, 0, 0 , Label the x axis Large , 0, 3.8, 0 , Label the y axis Large , 0, 0, 5.7 , Label the z axis 2 x ", Large Label the plot , Show ContourPlot3D x y ^ 2 z ^ 2, x, 3.5, 3.5 , y, Mesh 3 , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style "x 3.5, 3.5 , z, 5, 5 , x, Large , 4.2, 0, 0 , Label the x axis y, Large , 0, 3.8, 0 , Label the y axis z, Large , 0, 0, 5.7 , Label the z axis y 2 z2 ", Large Label the plot , Show ContourPlot3D y z ^ 2 x ^ 2, x, 3.5, 3.5 , y, Mesh 3 , Graphics3D Text Style Graphics3D Text Style Graphics3D Text Style PlotLabel Style "y 3.5, 3.5 , x, y, z, z2 z, 5, 5 , Large , 4.2, 0, 0 , Label the x axis Large , 0, 3.8, 0 , Label the y axis Large , 0, 0, 5.7 , Label the z axis x2 ", Large Label the plot , Show ContourPlot3D z y ^ 2 x ^ 2, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 5, 5 , 22 Chapter12Sec6.nb x, 3.5, Mesh 3 , Graphics3D Graphics3D Graphics3D PlotLabel 3.5 , y, 3.5, 3.5 , z, 5, 5 , Text Style x, Large , 4.2, 0, 0 Text Style y, Large , 0, 3.8, 0 Text Style z, Large , 0, 0, 5.7 Style "z x2 y2 ", Large Label , , , the Label the x axis Label the y axis Label the z axis plot ContourPlot3D x y ^ 2 z ^ 2, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 5, 5 , Mesh 3 , Graphics3D Text Style x, Large , 4.2, 0, 0 , Graphics3D Text Style y, Large , 0, 3.8, 0 , Graphics3D Text Style z, Large , 0, 0, 5.7 , 2 2 PlotLabel Style "x z y ", Large Label the Label the x axis Label the y axis Label the z axis plot , Show , Show ContourPlot3D y z ^ 2 x ^ 2, x, 3.5, 3.5 , y, 3.5, 3.5 , z, 5, 5 , Mesh 3 , Graphics3D Text Style x, Large , 4.2, 0, 0 , Graphics3D Text Style y, Large , 0, 3.8, 0 , Graphics3D Text Style z, Large , 0, 0, 5.7 , 2 2 PlotLabel Style "y x z ", Large Label the , ImageSize 600 Label the x axis Label the y axis Label the z axis plot Chapter12Sec6.nb 23 y2 x2 z 5 z y2 z2 z 5 x 3 3 x z2 x2 z 5 y 3 3 1 1 11 1 1 3 33 5 y 3 x 3 3 1 1 11 1 1 3 33 5 y 3 x 3 1 1 11 1 1 3 33 5 y Out[55]= z x2 y2 z 5 x z2 y2 z 5 y x2 z2 z 5 3 3 3 1 3 x 11 1 1 33 5 1 3 1 3 y 3 x 11 1 1 33 5 1 3 1 3 y 3 x 11 1 1 33 5 1 3 3 y 24 Chapter12Sec6.nb Example Classify and graph the equation 4 y 2 z2 x 16 y 4z 20 0. In[56]:= Show Plot3D 0, x, 5.5, 5.5 , y, 5.5, 5.5 , PlotRange 5.5, 5.5 , PlotStyle Directive Opacity 0 Mesh None, BoundaryStyle None , Graphics3D Text Style x, Large , Graphics3D Text Style y, Large , Graphics3D Text Style z, Large , , 5.62, 0.4, 0 0.4, 5.5, 0 0, 0.6, 5.2 , , Label the x axis Label the y axis Label the z axis Chapter12Sec6.nb 25 5 z 3 5 1 3 5 1 3 1 1 1 Out[56]= 5 3 5 3 x 1 3 5 y 26 Chapter12Sec6.nb Mathematica Solution In[57]:= Show ContourPlot3D 4 y ^ 2 z ^ 2 x 16 y 4 z 20 0, x, 5.5, 5.5 , y, 5.5, 5.5 , z, 5, 5 , Mesh 3 Draws the grid on the surface , Graphics3D Text Style x, Large , 5.62, 0.4, 0 , Label the x axis Graphics3D Text Style y, Large , 0.4, 5.5, 0 , Label the y axis Graphics3D Text Style z, Large , 0, 0.6, 5.2 , Label the z axis 2 2 PlotLabel Style "x 4y 2 z 2 ", Large Label the plot Chapter12Sec6.nb 27 x 4y 2 2 z 2 2 z 5 3 5 1 5 3 1 3 1 Out[57]= 1 1 3 5 x 3 5 1 3 5 y 28 Chapter12Sec6.nb Homework Pages: 857 - 858 1, 3, 11, 15, 17, 19, 23, 27, 31, 33, 41 ...
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