- #1
Craptola
- 14
- 0
Hey, I'm studying for a physics degree and have a general curiosity about vector calculus. Having learned about surface and line integrals for scalar functions in multivariable calculus I've been having some issues translating them into vector calculus. Though conceptually I haven't had much trouble yet I find myself struggling to interpret some notation.
My main concern concerns have been with [itex]\vec{dl}[/itex] (I've sometimes seen it written [itex]\vec{dr}[/itex]) and [itex]\vec{ds}[/itex]. I've encountered [itex]dl[/itex] as a scalar when doing line integrals but not as a vector. After much searching I was able to discover that the vector [itex]\vec{ds}[/itex] is equal to [itex]ds\mathbf{\hat{n}}[/itex] where n is the unit vector normal to the surface. But I've still not been able to find such a definition for [itex]\vec{dl}[/itex]. I would appreciate if anyone could shed some light on what this actually is.
My main concern concerns have been with [itex]\vec{dl}[/itex] (I've sometimes seen it written [itex]\vec{dr}[/itex]) and [itex]\vec{ds}[/itex]. I've encountered [itex]dl[/itex] as a scalar when doing line integrals but not as a vector. After much searching I was able to discover that the vector [itex]\vec{ds}[/itex] is equal to [itex]ds\mathbf{\hat{n}}[/itex] where n is the unit vector normal to the surface. But I've still not been able to find such a definition for [itex]\vec{dl}[/itex]. I would appreciate if anyone could shed some light on what this actually is.