ObsidianVault/.trash/Class 10-28.md

Calculus 3

• Similar idea for multiplication, cross products and dot products with derivatives \frac{d}{dt} [r(t) \times u(t)] = r'(t) \times u(t) + r(t) \times u'(t) \frac{d}{dt} [r(t) \cdot u(t)] = r'(t) \cdot u(t) + r(t) \cdot u'(t)
• If r(t) \cdot r(t) = c, then r(t) \cdot r'(t) = 0
• Principle unit tangent vector is defined as T(t) = \frac{r'(t)}{||r'(t)||} as long as ||r'(t)|| \ne 0
• When there is a function of two variables with all real numbers as domain, it is written as \mathbb{R}^2
  • Can also write "domain: ${(x,y) | x^2+y^2 \leq 9}$"