MATH 2153 Final: Math 2153 Final Exam solutions

• School: Ohio State University
• Department: Mathematics
• Course: MATH 2153
• Professor: All

Document Summary

Practice final exam math 2153: decide if the following statements are true or false and circle your answer. You do not need to justify your answers. (a) (1 point) if line integrals in the continuous vector eld f(x, y) are path independent then f is a conservative vector eld. Solution: t (path independence of line integrals in f is equivalent to f being conservative. ) (b) (1 point) if f is a conservative vector eld then line integrals in the continuous vector eld f(x, y) are path independent. Solution: f (the vector eld f = h y, xi is source-free since the 2-dimensional divergence of f is 0. However f is not irrotational since the 2-dimensional curl of f is 2. : give examples of the following. You do not need to justify your answers. (a) (2 points) give an example of a scalar function f (x, y) whose implicit domain is connected but not simply connected.