session_2b_interactive.Rmd

---
title: "session_2a"
author: "Joe DeCesaro"
date: "8/3/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(palmerpenguins)
```

### Plot a function in `ggplot2`

```{r}
eq <- function(x) {
  
  3 * x ^ 2 + 4
}

# Use stat_function()

ggplot(data = data.frame(x = c(1, 100)), aes(x = x)) + 
  stat_function(fun = eq)

```

### Task

Plot $f(x)=2.4-5x^3+2.1x^2$

Over a range from -50 to +50

```{r}
eq_2 <- function(x) { 
  
  2.4 - (5 * x ^ 3) + (2.1 * x ^ 2)
  }

ggplot(data = data.frame(x = c(-50, 50)), aes(x = x)) + 
  stat_function(fun = eq_2)

```

### `penguins` body mass and flipper lengths

Basic ggplot scatterplot of body mass (y) and flipper length (x)

```{r}
ggplot(data = penguins, aes(x = flipper_length_mm, y = body_mass_g)) + 
  geom_point(aes(color = species)) + 
  scale_color_manual(values = c("red", "purple", "cyan")) + 
  labs(x = "Flipper length (mm)",
       y = " Body Mass (g)",
       title = "Palmer Penguins size measurements",
       caption = "Data collected by KB Gorman et al. at Palmer Station",
       color = "species")
```


The 'missing' data sets mentioned by the console are just letting us know that we have two penguins where 1 or both data points that are being called are missing or incomplete.

### `penguins` body mass and flipper lengths now seperated by island and another theme

Basic ggplot scatterplot of body mass (y) and flipper length (x)

```{r}
ggplot(data = penguins, aes(x = flipper_length_mm, y = body_mass_g)) + 
  geom_point(aes(color = species)) + 
  scale_color_manual(values = c("red", "purple", "cyan")) + 
  labs(x = "Flipper length (mm)",
       y = " Body Mass (g)",
       title = "Palmer Penguins size measurements",
       caption = "Data collected by KB Gorman et al. at Palmer Station",
       color = "species") + 
  facet_wrap(~island) + 
  theme_grey()
```

### Higher Order Derivative

```{r}
gt <- expression(2.2 + 3.1 * t - 5.6 * t ^ 4)

dg_dt <- D(expr = gt, name = 't')

dg_dt
```

```{r}
d2g_dt2 <- D(expr = dg_dt, 't')

d2g_dt2
```

### Partial Derivatives

```{r}
f_xyz <- expression(2*x*y - 3*(x^2)*(z^3))

df_dx <- D(expr = f_xyz, 'x')

df_dx

df_dy <- D(expr = f_xyz, 'y')

df_dy

df_dz <- D(expr = f_xyz, 'z')

df_dz

```