{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter14Sec6ShowCode

Chapter14Sec6ShowCode - Initialization Cells(Code Needed...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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,
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 2
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 0 , y 0 L = lim h fi 0 f H x 0 + h , y 0 L - f H x 0 , y 0 L h and f y H x 0 , y 0 L = lim h fi 0 f H x 0 , y 0 + h L - f H x 0 , y 0 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 0 , y 0 L in the direction of a unit vector u = X a , b \ is D u f H x 0 , y 0 L = lim h fi 0 f H x 0 + h , y 0 + h L - f H x 0 , y 0 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. Chapter14Sec6.nb 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ª Example Consider the curve is f H x , y L = - H x - 1 L 2 + H y - 1 L 2 + 4. In[166]:= myF @ x_, y_ D = - H x - 1 L ^2 - H y - 1 L ^2 + 4; myFx @ x_, y_ D = D @ myF @ x,y D , x D ; myFy @ x_, y_ D = D @ myF @ x,y D , y D ; Manipulate @ Show @ Plot3D @ H * Plot the surface * L myF @ x,y D , 8 x, - 1,3 < , 8 y, - 1,3 < , PlotRange fi 8 - 4,4 < , PlotStyle fi Opacity @ 0.4 D D , ContourPlot3D @ H * Plot the plane * L 0 - rSin @ Θ D x + rCos @ Θ D y, 8 x, - 8,8 < , 8
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}