Basic Calculus in R. reference: -http://www2.uaem.mx/r-mirror/web/packages/mosaic/vignettes/Calculus.pdf -http://user2007.org/program/presentations/kaplan.pdf function,Derivative,Integral(Andi derivative), Solving Equation, Plotting, Diferential Equations,Differentiation

1. Prepared by VOLKAN OBAN
Basic Calculus in R.
install.packages("mosaic")
library(mosaic)
Example:
> f <- makeFun(m * x + b ~ x, m = 3.5, b = 10)
>
> f(x = 2)
[1] 17
>
> g <- makeFun(A * x * cos(pi * x * y) ~ x + y, A = 3)
> g
function (x, y, A = 3)
A * x * cos(pi * x * y)
>
> g(x = 1, y = 2)
[1] 3
> > plotFun(A * exp(k * t) * sin(2 * pi * t/P) ~ t + k, t.lim = range(0, 1
0), k.lim = range(-0.3,
+
0), A = 10, P = 4)

2. Example
Example:
> library(manipulate)
> plotFun(A * exp(k * t) * sin(2 * pi * t/P) ~ t + k, t.lim = range(0, 10),
k.lim = range(-0.3,
+
0), A = 10, P = 4, surface = TRUE)

4. Example:
> plotFun(dt(t, df) ~ t + df, t.lim = range(-3, 3), df.lim = range(1, 10))
Derivative:
>library(mosaic)
> D(sin(x) ~ x)
function (x)
cos(x)
> D(A * x^2 * sin(y) ~ x)
function (x, A, y)
A * (2 * x) * sin(y)
> D(A * x^2 * sin(y) ~ x + y)
function (x, y, A)
A * (2 * x) * cos(y)

5. Example:
> F = antiD(a * x^2 ~ x, a = 1)
> F
function (x, a = 1, C = 0)
a * 1/3 * x^3 + C
> F = antiD(dnorm(x, mean = 6000, sd = 0.01) ~ x, lower.bound = 6000)
> F(Inf) - F(-Inf)
[1] 1
>
Solving..
findZeros(sin(t) ~ t, t.lim = range(-5, 1))
> findZeros(sin(t) ~ t, t.lim = range(-5, 1))
t
1 -6.2832
2 -3.1416
3 0.0000
4 3.1416
Example:
> solve(4 * sin(3 * x) == 2 ~ x, near = 0, within = 1)
x
1 0.1746
2 0.8726
Example:
> f <- rfun(~x, seed = 345)
> g <- rfun(~x)
> h <- rfun(~x)
> plotFun(f(x) ~ x, x.lim = range(-5, 5))
> plotFun(g(x) ~ x, add = TRUE, col = "red")
> plotFun(h(x) ~ x, add = TRUE, col = "darkgreen")
>

6. Example:
> Water <- data.frame(mass = c(57, 76, 105, 147, 181, 207, 227, 231, 231, 2
31), time = c(0,
+
3, 6, 9, 12, 15, 18, 21, 24, 27))
>
> xyplot(mass ~ time, data = Water)

7. Example:
> data(CPS85)
>
> xyplot(wage ~ age, data = CPS85)
> f <- smoother(wage ~ age, span = 0.9, data = CPS85)
> plotFun(f(age) ~ age, add = TRUE, lwd = 4)
>

8. Fitted Functions:
> data(CPS85)
> model <- lm(log(wage) ~ age * educ + 1, data = CPS85)
> g <- makeFun(model)
> g(age = 40, educ = 12)
1
7.494671
>
Example:
> plotPoints(temp ~ time, data = CoolingWater)
> mod <- fitModel(temp ~ A + B * exp(-k * time), start = list(A = 30, k = l
og(2)/30),data = CoolingWater)
> plotFun(mod(time) ~ time, add = TRUE, col = "red")
>

9. Mixed Examples:
1
> f = function(x){ x^2 + 2*x }
>
> f(pi)
[1] 16.15279
2-
> findZeros( sin(x)-0.35 ~ x, x.lim=range(-20,20) )
x
1 -12.2088
2 -9.7823
3 -5.9256
4 -3.4991
5 0.3576
6 2.7840
7 6.6407
8 9.0672
9 12.9239
10 15.3504
3-
> findZeros(sin(x^2)*(cos(sqrt(x^4+3)-x^2))-x+1~x,x.lim=range(1,2))
x
1 1.5576
4-
> f3 = makeFun( sin(x^2) - 100~x)
> f3(x=2)
[1] -100.7568

10. 5-
> F = antiD( exp(x^2) ~ x )
> F(x=2) - F(x=-1)
[1] 17.91528
6-Dif.Eq.
> soln <- integrateODE( dx ~ r*x*(1-x/K),x=1, K=10, r=.5, tdur=list(from=0,
to=20))
> soln$x(0:5)
[1] 1.000000 1.548281 2.319693 3.324279 4.508531 5.751209
7-
> plotFun( exp(-t/10)*sin(2*pi*x/5) ~ x&t,x.lim=range(0,5), t.lim=range(0,1
0) )
8-
> newF = antiD(exp(x)*x^2 ~ x, x.from=1)
> F(x=2) #default lower bound is 0
[1] 16.45263