Chapter15Sec10

Chapter15Sec10 - Initialization Cells (Code Needed for Most...

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Initialization Cells (Code Needed for Most Plot3D Statements) In[1]:= 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 ; SetOptions @ RegionPlot, 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 <
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D ; SetOptions @ ParametricPlot3D, 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 @ 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 15: Multiple Integrals 2 Chapter15Sec10.nb
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Section 15.10: Change of Variables in Multiple Integrals ± Recall ª One Dimensional Change of Variables In one dimensional calculus, when x = g H u L or more generally we might write x = x H u L , we can change the variable using the Substitution Rule and obtain ± a b f H x L ± x = ± c d f @ g H u LD g ' H u L ± u = ± c d f @ x H u LD dx du ± u . where a = g H c L and b = g H d L . ª Higher Dimensional Change of Variables L Changing to polar coordinates often simplifies a double integral when the region can be written as a polar rectangle such as R = 8H r , Θ L Α £ Θ £ Β , u 1 H Θ L £ r £ u 2 H Θ L < . L
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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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Chapter15Sec10 - Initialization Cells (Code Needed for Most...

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