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Chapter15Sec9ShowCode

Chapter15Sec9ShowCode - Initialization Cells(Code Needed...

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Initialization Cells (Code Needed for Most Plot3D Statements) In[1390]:= 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 ; 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 < 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,
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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 @ SphericalPlot3D, 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 ; Chapter 15: Multiple Integrals 2 Chapter15Sec9.nb
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Section 15.9: Triple Integrals in Spherical Coordinates ª Definition Consider a point in rectangular coordinates H x , y , z L . This point can be described using spherical coordinates as H Ρ , Θ , Φ L where L Ρ is the length of the vector X x , y , z \ , that is Ρ = X x , y , z \/ = x 2 + y 2 + z 2 . Hence, Ρ ‡ 0. L Θ is the angle measured counterclockwise in the xy -plane starting from the x -axis. L Φ is the angle measured from the positive z -axis to the vector X x , y , z \ and we assume that 0 £ Φ £ Π . L Note that r = Ρ sin H Φ L L Note that x = r cos H Θ L = Ρ sin H Φ L cos H Θ L and x = r sin H Θ L = Ρ sin H Φ L sin H Θ L L Note that z = Ρ cos H Φ L L Finally, the distance formula gives us Ρ 2 = x 2 + y 2 + z 2 . In[1397]:= myRho = 2; myTheta = Pi 3; myPhi = Pi 4; Show @ Plot3D @ 0, 8 x, 0, 2 < , 8 y, 0, 2 < , PlotRange fi 8 0,2 < , PlotStyle fi Directive @ Opacity @ 0 DD , Mesh fi None,BoundaryStyle fi None D , Graphics3D @8 PointSize @ Large D ,Point @ 8 myRhoSin @ myPhi D Cos @ myTheta D , myRhoSin @ myPhi D Sin @ myTheta D , myRhoCos @
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