manipulasi simpbolik

Bapak Prof. Dr. SUHARTONO, M.Kom || UIN Maulana Malik Ibrahim Malang

Beberapa fungsi buku pola begitu sering muncul dalam Kalkulus MOSAIK sehingga ada baiknya meninjau kembali cara memanipulasinya secara simbolis. Sebagai contoh, perhatikan fungsinya $$g(x)\equiv e^x{e}^x.$$ Ini adalah cara yang sangat bagus untuk mendefinisikan$g()$ , namun akan sangat membantu jika kita menyadari bahwa definisi berikut ini benar-benar setara

$$\begin{gathered} f(x)\equiv e^{x+x} \\ h(x)\equiv e^{2x}. \end{gathered}$$

Manipulasi simbolik yang kita bahas dalam bab ini melibatkan kemampuan mengingat dan menerapkan kesetaraan tersebut. kita hanya memerlukan sebagian kecil saja, semua atau sebagian besarnya dapat ditemukan dalam pelajaran aljabar sekolah menengah.

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

## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
## which was just loaded, will retire in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## The sp package is now running under evolution status 2
##      (status 2 uses the sf package in place of rgdal)

## 
## Attaching package: 'mosaicCalc'

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

reciprocal <- makeFun(1/t ~ t)
one <- makeFun(1 ~ z)
square <- makeFun(x^2 ~ x)


reciprocal(7)

## [1] 0.1428571

## [1] 0.1428571
one(123.67)

## [1] 1

## [1] 1
square(19)

## [1] 361

## [1] 361

library(mosaicCalc)
h <- makeFun(sin(t)*exp(-t) ~ t)
h

## function (t) 
## sin(t) * exp(-t)