Chapter15Sec9ShowCode

- Initialization Cells(Code Needed for Most Plot3D Statements In[1390:= ticks min max D = Join [email protected] i If i 0 Style i 12 DD 8 0.01 0<< 8 i

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Unformatted text preview: 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, 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 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 ....
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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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- Initialization Cells(Code Needed for Most Plot3D Statements In[1390:= ticks min max D = Join [email protected] i If i 0 Style i 12 DD 8 0.01 0<< 8 i

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