MATH V1207 Midterm: MATH V1205 Columbia Fall01Mid2
31 Jan 2019
School
Department
Course
Professor
Document Summary
Write your name and my name on your exam booklet. You can earn partial credit only if you justify your steps. One point for a correct answer; minus one for an incorrect answer. ) In the following c is a closed curve, s is a closed surface, f is a vector eld and f is a function. 2. (8 points) let c be a simple closed curve in the plane. Show, using one of the theorems, that rc f dr is related to the area enclosed by c. 3. (30 points) let f be the vector eld (3y, 0, 0). Let be the lower unit hemisphere oriented with the downward normal and with boundary c: = {(x, y, z) | x2 + y2 + z 2 = 1; z 0}. (a) directly compute rc f dr. (b) by stokes" theorem this line integral is equal to a surface integral over .
