Block_0_Preliminaries.Rmd

---
title: "MOSAIC Calculus Workout"
output: html_notebook
---
Basic Dimensions:
- time, T
- length, L
- mass, M
- money, V ("value")
```{r}
108 - 22
sqrt(17)
b <- 7
b
```
Defining functions in R/mosaic
```{r}
h <- makeFun(a*t^2 - b ~ t, a = 1.5, b = 2)
h(1)
h(2)
```
Formulas in R
```{r}
3 + 2
3/2
6*4
sqrt(4)
log(5)
2*pi
(1/2)*17
17-5/2
3^2
exp(-2)
```
Draw a graph
```{r}
slice_plot(3*cos(z) + 7 ~ z, domain(z = 0:10))
```
```{r}
slice_plot(sin(x) ~ x, domain(x=0:5))
slice_plot(3 *y + b ~ y, domain(y=-3.5:3))
```
Functions with two inputs
```{r}
h <- makeFun(3*x - 2*x*y - y^2 ~x & y)
contour_plot(h(x,y) ~ x & y, domain(x = -1:1, y = 0:2))
```
Pattern functions in R
```{r}
x #identity: output is identical to input
x^2 #square: parabola
1/x #recoprocal
dnorm(x) #gaussian: normal
pnorm(x) #sigmoid
sin(x) #sinusoid
exp(x) #exponential
log(x) #logarithm
```