Line integrals

Learning objectives

  • Define line integrals
    • vector notation: \int_C \vec{F} \cdot d\vec{r}
    • differential notation: \int_c p(x, y)\,dx + q(x, y)\,dy
    • relationship: \vec F = p\vec{i} + q\vec{j}; d\vec{r} = dx\vec{i} + dy\vec{j}
  • Understand 1-variable integrals \int_a^b f(x)\,dx as line integrals
  • Develop geometric intuition for line integrals
  • Compute line integrals geometrically
    • when vector field is orthogonal to the path
    • when vector field is tangent to the path and of constant magnitude on the path
  • Compute line integrals analytically using parameterizations
  • Compute line integrals of gradient vector fields

Before class

  • Read Hughes-Hallett sections 18.1, 18.2, 18.3.
  • Ponder Hughes-Hallett problems: 18.1: 1-13 odd,36; 18.2: 1, 9, 10, 25; 18-3:1, 13.

In class

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