446 CHAPTER 23. STOKES AND GREEN’S THEOREMS

23.4.2 Some TerminologyIf F = (P,Q,R) is a vector field. Then the statement that F is conservative is the same assaying the differential form Pdx+Qdy+Rdz is exact. Some people like to say things interms of vector fields and some say it in terms of differential forms. In Example 23.4.9, thedifferential form

(4x3 +2

(cos(x2 + z2

))x)

dx+dy+(2(cos(x2 + z2

))z)

dz is exact.

446 CHAPTER 23. STOKES AND GREEN’S THEOREMS23.4.2 Some TerminologyIf F = (P,Q,R) is a vector field. Then the statement that F' is conservative is the same assaying the differential form Pdx + Qdy + Rdz is exact. Some people like to say things interms of vector fields and some say it in terms of differential forms. In Example 23.4.9, thedifferential form (4x° + 2 (cos (x* +-z”)) x) dx + dy-+ (2 (cos (x? +z’)) z) dz is exact.