Calculus
The rules of differentiation and integration are known to R. You will use them in modelling (e.g. in calculating starting values in non-linear regression) and for numeric minimization using optim. Read the help files for D and integrate to understand the limitations of these functions.
Derivatives
The R function for symbolic and algorithmic derivatives of simple expressions is D. Here are some simple examples to give you the idea. See also ?deriv.
D(expression(2*x^3),"x")
2 * (3 * x^2)
D(expression(log(x)),"x") 1/x D(expression(a*exp(-b * x)),"x") -(a * (exp(-b * x) * b)) D(expression(a/(1+b*exp(-c * x))),"x") a * (b * (exp(-c * x) * c))/(1 + b * exp(-c * x))^2 trig.exp <-expression(sin(cos(x + y^2))) D(trig.exp, "x") -(cos(cos(x + y^2)) * sin(x + y^2))
Integrals
The R function is integrate. Here are some simple examples to give you the idea:
integrate(dnorm,0,Inf) 0.5 with absolute error < 4.7e-05 integrate(dnorm,-Inf,Inf) 1 with absolute error < 9.4e-05 integrate(function(x) rep(2, length(x)), 0, 1) 2 with absolute error < 2.2e-14 integrand <-function(x) {1/((x+1)*sqrt(x))} integrate(integrand, lower = 0, upper = Inf) 3.141593 with absolute error < 2.7e-05 xv<-seq(0,10,0.1) plot(xv,integrand(xv),type="l")
The area under the curve is π = 3.141593.
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