- #1
Jhenrique
- 685
- 4
If dr = (dx, dy, dz) so, which is the correct form for d²r? Is (d²x, d²y, d²z) or (dy^dz, dz^dx, dx^dy) ?
tiny-tim said:what is d²r ?
tiny-tim said:what is d²r ?
Jhenrique said:you must be joking
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.
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) ?
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) ?
Mandelbroth said:The correct form of ##\mathrm{d}^2r=\mathrm{d}(\mathrm{d}r)## is 0.
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.
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.
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).
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.
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.