L3.Rmd

---
title: "L3"
author: "Xiaoting Chen"
date: "2023-08-09"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(purrr)
library(dplyr)
library(ggplot2)
library(tidyr)
```

## Transform data for plotting

purrr::map* function
```{r}
x <- 1:10
y <- x |> 
  map(\(x) runif(n=100, min=x,max=15)) |>
  map_dbl(mean)
# "\(x)" equals to creating a new function taking x as input
## name(x) <- function(x) { }

y
```


```{r}
rates <- seq(0.05, 0.2, length = 10)
p <- 100
time <- seq(1, 50, length = 50)

Pe <- function(A, r, t) A*exp(r * t)
d <- time |>
  map(\(x) Pe(A=p, r = rates, t = x))
#str(d)
```

practice
```{r}
data("Arbuthnot")
# head(Arbuthnot)

dat_p <- Arbuthnot[, 1:3] %>%
  pivot_longer(cols = c(Males, Females),names_to = "gender", values_to = "christening")

ggplot(dat_p, aes(x = Year, y = christening, color = gender)) +
  geom_line()
```

## integration

### Riemann Sum
```{r}
riemann <- function(f, lower, upper, step_size) {
  step <- seq(lower, upper, by = step_size)
  s <- 0 # initialize the sum
  for (i in 2:length(step)) {
    # multiply base by the height of the rectangle
    area <- step_size * f(step[i]) 
    s <- s + area
  }
  return(s)
}
```

evaluate the method
```{r}
f <- function(x) x * sin(x^2)

riemann(f, 1, 3, 0.01)
integrate(f, 1, 3)
```


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