Chapter14Sec6ShowCode

Chapter14Sec6ShowCode - Initialization Cells (Code Needed...

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Unformatted text preview: Initialization Cells (Code Needed for Most Plot3D Statements) In[160]:= 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 ; Chapter 14 : Partial Derivatives 2 Chapter14Sec6.nb Section 14.6: Directional Derivatives and the Gradient Vector Directional Derivatives ª Definition Recall that if z = f H x , y L , then f x H x , y L = lim h fi f H x + h , y L- f H x , y L h and f y H x , y L = lim h fi f H x , y + h L- f H x , y L h are the rates of change of z in the x- and y- directions, that is along the unit vectors i and j . The directional derivative of f at the point H x , y L in the direction of a unit vector u = X a , b \ is D u f H x , y L = lim h fi f H x + h , y + h L- f H x , y L h provided the limit exits. This represents the rate of change in z = f H x , y L in the direction of the unit vector u ; that is, the slope of the tangent line to the curve of intersection of the surface and the vertical plane containing u . Note that when u = X 1, 0 \ we obtain f x and when u = X 0, 1 \ we obtain f y . Thus, the concept of directional derivatives generalizes the idea of partial derivatives....
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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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Chapter14Sec6ShowCode - Initialization Cells (Code Needed...

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