โž—calculus ii review

key term - Area density

Definition

Area density, also known as surface density, is a measure of mass per unit area. It is typically denoted by the symbol $\sigma$ and has units of $\text{kg}/\text{m}^2$.

5 Must Know Facts For Your Next Test

  1. Area density is calculated as $\sigma = \frac{dm}{dA}$, where $dm$ is the infinitesimal mass element and $dA$ is the infinitesimal area element.
  2. In applications of integration, area density can be integrated over a surface to find total mass: $M = \int_A \sigma \, dA$.
  3. Area density problems often involve setting up integrals in polar or Cartesian coordinates depending on symmetry.
  4. Understanding transformations between coordinate systems (e.g., Cartesian to polar) is crucial when working with area densities on non-rectangular surfaces.
  5. The concept is important in physical applications such as calculating the mass of thin plates or membranes.

Review Questions

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