Student handout: Murder Mystery Method

Vector Calculus II 2023
For each of the following vector fields, find a potential function if one exists, or argue that none exists.
  • \(\boldsymbol{\vec{F}} = (3x^2 + \tan y)\,\boldsymbol{\hat{x}} + (3y^2 + x\sec^2 y) \,\boldsymbol{\hat{y}}\)
  • \(\boldsymbol{\vec{G}} = y\,\boldsymbol{\hat{x}} - x\,\boldsymbol{\hat{y}}\)
  • \(\boldsymbol{\vec{H}} = (2xy + y^2 \sin z) \,\boldsymbol{\hat{x}} + (x^2 + z + 2xy\sin z) \,\boldsymbol{\hat{y}} + (y + z + xy^2 \cos z) \,\boldsymbol{\hat{z}}\)
  • \(\boldsymbol{\vec{K}} = yz \,\boldsymbol{\hat{x}} + xz \,\boldsymbol{\hat{y}}\)

Keywords
Constructing potential functions for conservative vector fields
Learning Outcomes