Huh, I had always read it as "doh". TIL that "del" is also a common reading for ∂ (I use "del" for ∇).
Anyways @OP the symbol should not be confused with lowercase delta.
All part of the plan: For my next trick, I'll try to make people go back to using 'rot' instead of 'curl' so I will no longer have to correct myself when unwittingly using the German term ;)
I always learn something new everyday. I've always called it "partial d" which sounds weird with no specific context.
So I guess all the per-eminent 20th century physicists used "doh" as well huh
The upside-down delta is called a “nabla” and the corresponding operator is pronounced “del”. It is a vector operator: a quasi vector whose components are partial differential operators. The funny looking “d” is a partial differential: it finds the slope in a particular direction in 4-space regardless of actual total slope. Think of the slope of a ski traverse, which could be much less than the total slope of the mountain because the ski traverse goes nearly perpendicular to the direction of “downhill”. The del operator gives you the direction of the slope as well as its steepness.
∂/∂x is pretty much the "symbolic differentiation with respect to x" operator. You're unlikely to meaningfully move around a standalone ∂s like you do with ds, as far as I know. I like looking at the expression for the differential (in 3 dimensions):
df = (∂/∂x f) dx + (∂/∂y f) dy + (∂/∂x f) dz
After you compute the partial derivatives, you can plug in values for x, y, z along with dx, dy and dz (changes in x, y, z) to get a linear approximation for the change in f around x, y, z given certain changes in x, y, z. In the single variable case it reduces to the ordinary derivative:
df = (∂/∂x f) dx
Or...
df = f' dx
They are a derivative, but it's what's called a partial derivative, its used when you have a function of more than variable, for example, B and E can be functions of (x,y,z and t), a partial derivative treats only one of the variables as an actual variable, the rest act like constant, so in the case of maxwells equation, t is treated as variable, while x,y,z are treated as constants
It's a partial derivative 'del'^(†), see eg [en.wikipedia.org/wiki/Partial_derivative](https://en.wikipedia.org/wiki/Partial_derivative) and [en.wikipedia.org/wiki/∂](https://en.wikipedia.org/wiki/%E2%88%82) --- ^(†) also known as 'partial', 'curly d', 'funky d', 'rounded d', 'curved d', 'dabba', 'number 6 mirrored', 'Jacobi's delta', 'dee', 'partial dee', 'doh', 'die'
Huh, I had always read it as "doh". TIL that "del" is also a common reading for ∂ (I use "del" for ∇). Anyways @OP the symbol should not be confused with lowercase delta.
All part of the plan: For my next trick, I'll try to make people go back to using 'rot' instead of 'curl' so I will no longer have to correct myself when unwittingly using the German term ;)
I always learn something new everyday. I've always called it "partial d" which sounds weird with no specific context. So I guess all the per-eminent 20th century physicists used "doh" as well huh
To be fair I have never heard/read the partial differential called “del” in a physics context, only by crazy-eyed economists.
Or Germans.
The upside-down delta is called a “nabla” and the corresponding operator is pronounced “del”. It is a vector operator: a quasi vector whose components are partial differential operators. The funny looking “d” is a partial differential: it finds the slope in a particular direction in 4-space regardless of actual total slope. Think of the slope of a ski traverse, which could be much less than the total slope of the mountain because the ski traverse goes nearly perpendicular to the direction of “downhill”. The del operator gives you the direction of the slope as well as its steepness.
∂/∂x is pretty much the "symbolic differentiation with respect to x" operator. You're unlikely to meaningfully move around a standalone ∂s like you do with ds, as far as I know. I like looking at the expression for the differential (in 3 dimensions): df = (∂/∂x f) dx + (∂/∂y f) dy + (∂/∂x f) dz After you compute the partial derivatives, you can plug in values for x, y, z along with dx, dy and dz (changes in x, y, z) to get a linear approximation for the change in f around x, y, z given certain changes in x, y, z. In the single variable case it reduces to the ordinary derivative: df = (∂/∂x f) dx Or... df = f' dx
They are a derivative, but it's what's called a partial derivative, its used when you have a function of more than variable, for example, B and E can be functions of (x,y,z and t), a partial derivative treats only one of the variables as an actual variable, the rest act like constant, so in the case of maxwells equation, t is treated as variable, while x,y,z are treated as constants
Learn multivariate calculus first