BAB 9 DINAMIKA

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
## 
##     count, tally

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
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##     D

DINAMIKA

Strategi dasar dalam kalkulus adalah membagi masalah yang menantang menjadi bagian-bagian yang lebih mudah, dan kemudian mengumpulkan bagian-bagian tersebut untuk menemukan solusi keseluruhan.

Memecahkan persamaan diferensial “Memecahkan” persamaan diferensial sama dengan menemukan nilai keadaan sebagai fungsi dari variabel bebas. Dalam “persamaan diferensial biasa”, hanya ada satu variabel bebas, biasanya disebut waktu. Dalam “persamaan diferensial parsial”, ada dua atau lebih variabel dependen, misalnya waktu dan ruang.

Fungsi tersebut integrateODE()menyelesaikan persamaan diferensial biasa yang dimulai dari kondisi awal keadaan tertentu. Fungsi integrateODE()mengambil persamaan diferensial sebagai input, bersama dengan nilai awal keadaan.

library(mosaic)
library(mosaicCore)
library(mosaicData)

"soln <- integrateODE(dx ~ r * x * (1 - x / K),
                     x = 1, K = 10, r = 0.5,
                     tdur = list(from=0, to=20))"

## [1] "soln <- integrateODE(dx ~ r * x * (1 - x / K),\n                     x = 1, K = 10, r = 0.5,\n                     tdur = list(from=0, to=20))"

"soln$x(0:5)"

## [1] "soln$x(0:5)"

"slice_plot(soln$x(t) ~ t, domain(t=0:20))"

## [1] "slice_plot(soln$x(t) ~ t, domain(t=0:20))"

Sistem Persamaan Diferensial

"epi <- integrateODE(dS ~ -a * S * I,
                    dI ~ a * S * I - b * I,
                    a = 0.0026, b = 0.5, S=762, I = 1,
                    tdur = 20)"

## [1] "epi <- integrateODE(dS ~ -a * S * I,\n                    dI ~ a * S * I - b * I,\n                    a = 0.0026, b = 0.5, S=762, I = 1,\n                    tdur = 20)"

"slice_plot(epi$S(t) ~ t, domain(t=0:20)) %>%
  slice_plot(epi$I(t) ~ t, color = red)"

## [1] "slice_plot(epi$S(t) ~ t, domain(t=0:20)) %>%\n  slice_plot(epi$I(t) ~ t, color = red)"

```

## DAFTAR PUSTAKA Computer-age Calculus with R. https://dtkaplan.github.io/RforCalculus/modeling-with-linear-combinations.html#example-atomic-bomb-data.