TABLE OF CONTENTS A, B, and C are vectors and a and b are scalars.
| (A.1) |  |
| (A.2) |  |
| (A.3) |  |
| (A.4) |  |
| (A.5) |  |
| (A.6) |  |
| (A.7) |  |
| (A.8) |  |
| (A.9) |  |
| (A.10) |  |
| (A.11) |  |
| (A.12) |  |
| (A.13) |  |
| (A.14) |  |
| (A.15) |  |
Cartesian
| (A.16) |  |
| (A.17) |  |
| (A.18) |  |
| (A.19) |  |
Cylindrical
| (A.20) |  |
| (A.21) |  |
| (A.22) |  |
| (A.23) |  |
Spherical
| (A.24) |  |
| (A.25) |  |
| (A.26) |  |
| (A.27) |  |
Cartesian-cylindrical
| (A.28) |  |
| (A.29) |  |
Cartesian-spherical
| (A.30) |  |
| (A.31) |  |
Distance R = r 2 - r 1 in the three coordinate systems
Cartesian
| (A.32) |  |
Cylindrical
| (A.33) |  |
Spherical
| (A.34) |  |
Divergence theorem
| (A.35) |  |
Stokes's theorem
| (A.36) |  |
| (A.37) |  |
| (A.38) |  |
| (A.39) |  |
| Coordinate system | Cartesian ( x, y, z) | Cylindrical | Spherical ( r, ?, ?) |
|---|---|---|---|
| Unit vectors | u x u y u z | u ? u ? u z | u r u ? u ? |
| Differential length dl | dx u x +dy u y +dz u z | d ? u ? + ?d ? u ? +dz u z | d r u r +r d ? u ? +rsin ?d ? u ? |
| Differential surface area ds | dy dz u x dx dz u y dx dy u z | ?d ? dz u p d ? dz u ? ?d ? d ? u z | r 2sin ?d ?d ? u r rsin ?d rd ? u ? rd rd ? u |
