Understanding d²r: Exploring the Correct Form for dr with (dx, dy, dz)

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In summary, the conversation discusses the correct form for d²r, with one person suggesting it may be 0 and another mentioning it as an alternative to dS in surface integrals. The components of the vector d²r are also questioned, with some confusion surrounding whether they are (d²x, d²y, d²z) or (dydz, dzdx, dxdy).
  • #1
Jhenrique
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If dr = (dx, dy, dz) so, which is the correct form for d²r? Is (d²x, d²y, d²z) or (dy^dz, dz^dx, dx^dy) ?
 
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  • #2
what isr ? :confused:
 
  • #3
tiny-tim said:
what isr ? :confused:

you must be joking
 
  • #4
tiny-tim said:
what isr ? :confused:

Jhenrique said:
you must be joking

Seems like a reasonable question to me.
 
  • #5
I imagine he's referring to the "numerator" of a second derivative such as ##\frac{d^2 \vec{r}}{dt^2}## in analogy with his identification of the differential form ##d\vec{r}## with the "numerator" of a first derivative.
 
  • #6
MuIotaTau said:
I imagine he's referring to the "numerator" of a second derivative such as ##\frac{d^2 \vec{r}}{dt^2}## in analogy with his identification of the differential form ##d\vec{r}## with the "numerator" of a first derivative.

Is this even. No doubts.
 
  • #7
Jhenrique said:
If dr = (dx, dy, dz) so, which is the correct form for d²r? Is (d²x, d²y, d²z) or (dy^dz, dz^dx, dx^dy) ?

I've seen d²r used as an alternative to dS in surface integrals.
 
  • #8
Jhenrique said:
If dr = (dx, dy, dz) so, which is the correct form for d²r? Is (d²x, d²y, d²z) or (dy^dz, dz^dx, dx^dy) ?

The correct form of ##\mathrm{d}^2r=\mathrm{d}(\mathrm{d}r)## is 0. Your question is incredibly ambiguous, and I wouldn't expect anyone to understand what you're asking without clarification.
 
  • #9
Mandelbroth said:
The correct form of ##\mathrm{d}^2r=\mathrm{d}(\mathrm{d}r)## is 0.

This is theoretical identity that in the practice is useless.

I just asking which are the components of the vector d²r.

The components of the vector r is (x, y, z);

of dr is (dx, dy, dz)

But, I have doubt if the components of vector d²r is (d²x, d²y, d²z) or (dydz, dzdx, dxdy) or other...
 

What is d²r?

d²r is a mathematical notation used to represent the derivative of a function with respect to a vector, specifically (dx, dy, dz). It is commonly used in fields such as physics and engineering to calculate rates of change.

Why is it important to understand d²r?

Understanding d²r is essential for accurately calculating rates of change in vector functions. It allows us to analyze and predict how a system will behave over time, making it a crucial concept in many scientific applications.

What is the correct form for dr with (dx, dy, dz)?

The correct form for dr with (dx, dy, dz) is written as d²r = (∂r/∂x)dx + (∂r/∂y)dy + (∂r/∂z)dz. This notation represents the derivative of a function r with respect to the vector (x,y,z).

How is d²r different from other mathematical notations?

D²r differs from other mathematical notations because it specifically represents the derivative of a function with respect to a vector, rather than a single variable. It is commonly used in vector calculus and tensor calculus, while other notations may be used for different types of derivatives.

What are some real-world applications of d²r?

D²r has many applications in various fields of science and engineering. For example, it can be used to calculate the velocity and acceleration of an object in motion, model fluid flow in pipes and channels, and analyze the behavior of electromagnetic fields.

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