Geometric interpretation for d²f/dxdy

Jhenrique
Messages
676
Reaction score
4
If the following integral:
$$\\ \iint\limits_{a\;c}^{b\;d} f(x,y) dxdy$$ represents:

attachment.php?attachmentid=70578&stc=1&d=1402650671.png


So which is the geometric interpretation for ##f_{xy}(x_0, y_0)## ?
 

Attachments

  • 3.PNG
    3.PNG
    7.3 KB · Views: 487
Physics news on Phys.org
Would it be the rate of change of z with area, dz/dA at x0, y0?
 
Jilang said:
Would it be the rate of change of z with area, dz/dA at x0, y0?

Yeah! But which is the geometric interpretation?
 
I am taking my last guess back. If A is the shaded area
f(x,y) = dA/dR
So df/dR is a measure of the curvature. When it is zero the area A is flat.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
View full post »

Similar threads

Geometrical interpretation of this property
Replies
2
Views
3K
Insights The Amazing Relationship Between Integration And Euler’s Number
Replies
1
Views
2K
Why is the Jacobian for polar coordinates sometimes negative?
Replies
5
Views
1K
I Differentiability of a Multivariable function
Replies
1
Views
2K
I Non-Homogeneous Robin Boundary conditions and Interpretations of Signs
Replies
2
Views
2K
MHB Evaluate the surface integral $\iint\limits_{\sum}f\cdot d\sigma$
Replies
1
Views
3K
I Find the center manifold of a 2D system with double zero eigenvalues
Replies
4
Views
2K
Resultant force and centre of pressure in a tank
Replies
16
Views
2K
A Searching for radial part solution of Klein-Gordon type equation
Replies
1
Views
1K
I Geometries from Line Element $$dl^2=d\theta^2 + \sin^2\theta\, d\varphi^2$$
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top