7 lines
600 B
Markdown
7 lines
600 B
Markdown
#rs/notes #rs/class/math163
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- Similar idea for multiplication, cross products and dot products with derivatives $$ \frac{d}{dt} [r(t) \times u(t)] = r'(t) \times u(t) + r(t) \times u'(t)$$ $$ \frac{d}{dt} [r(t) \cdot u(t)] = r'(t) \cdot u(t) + r(t) \cdot u'(t)$$
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- If $r(t) \cdot r(t) = c$, then $r(t) \cdot r'(t) = 0$
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- Principle unit tangent vector is defined as $$T(t) = \frac{r'(t)}{||r'(t)||}$$ as long as $||r'(t)|| \ne 0$
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- When there is a function of two variables with all real numbers as domain, it is written as $\mathbb{R}^2$
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- Can also write "domain: $\{(x,y) | x^2+y^2 \leq 9\}$" |