From: Andrew Lorimer Date: Sat, 6 Jul 2019 04:12:29 +0000 (+1000) Subject: [spec] start vector calculus X-Git-Tag: yr12~100 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/42fe40b2a22f8f23ffd56684e4a2a31b111e6869?hp=5727605c4011fe198b16d530c572c71212945457 [spec] start vector calculus --- diff --git a/spec/vectors.md b/spec/vectors.md index 3a940e3..ef987fa 100644 --- a/spec/vectors.md +++ b/spec/vectors.md @@ -193,3 +193,11 @@ $$\boldsymbol{r}(t)=x\boldsymbol{i}+y\boldsymbol{y}$$ - If $\boldsymbol{r}(t)$ represents position with time, then the graph of endpoints of $\boldsymbol{r}(t)$ represents the Cartesian path. - Domain of $\boldsymbol{r}(t)$ is the range of $x(t)$ - Range of $\boldsymbol{r}(t)$ is the range of $y(t)$ + +## Vector calculus + +### Derivative + +Let $\boldsymbol{r}(t)=x(t)\boldsymbol{i} + y(t)\boldsymmbol(j)$. If both $x(t)$ and $y(t)$ are differentiable, then: + +$$\boldsymbol{r}(t)=x(t)\boldsymbol{i}+y(t)\boldsymbol{j}$$