Mathematical tools for natural sciences

In R, we can assign integer and floating point values to variables directly. The mathematical operations can be performed with variables and operators exactly similar to languages like C, C++, java, python and perl. We have already performed a simple operation c = a+b in the previous section.

For example, we can perform the operation $$ c = \frac{(a + b)}{(a \times b)}$$ by assigning values directly at declaration

> a = 7.5 > b = 6 > c = (a+b)/(a*b) > c

[1] 0.3

The following four letters are allotted for the four basic numerical operations:
'+' for addition '-' for subtraction '*' for multiplication '/' for division

In another example, we apply the formula $$y = 1.0 + {\large (\frac{z}{r})}^{0.38} $$ as,

> z = 22.9 > r = 6.7 > y = 1.0 + (z/r)^0.38 > y

[1] 2.595251

where the symbol "^" reresents "to the power". Thus, "(z/r)^0.38" "divides z by r and raises the resulting number to the power 0.38". Note the explicit usage of brackets for grouping the terms to remove ambiguity.

In order to carry out certain standard mathematical operations, R has internal *library functions*. In programming languages, a *function* is a collection of code statements that can perform a task. A functtion can take one or more input parameter values, and should give an output result.

For example, if we want to find the natural logarithm of a variable x, we can call the function called log as follows:

> x = 42.5 > y = log(x) > y

[1] 3.749504

In the above R codelines, variable x is assigned a value of 42.5. The function call y = log(x) passes the value of x to the function and the value returned by the function is assigned to the variable y. When we print y, we get 3.749504, which is the natural logarithm of 42.5.

A list of important math library functions in R are given below. many more will be introduced in the coming sections.

---------------------------------------------- Function name Description ---------------------------------------------- abs(x) absolute value sqrt(x) square root ceiling(x) ceiling(3.475) is 4 floor(x) floor(3.475) is 3 trunc(x) trunc(5.99) is 5 round(x, digits=n) round(3.475, digits=2) is 3.48 signif(x, digits=n) signif(3.475, digits=2) is 3.5 cos(x),sin(x),tan(x) Triginomteric sine, cosine and tan functions acos(x),asin(x),atan(x) arcsine, arccosine and arctangent functions log(x) natural logarithm log10(x) common logarithm log2(x) logarithm to the bse of 2 exp(x) exponential of x -----------------------------------------------

Let us now translate some mathematical expressions into R code lines:

> A = 120.5 > m = 2.0 > n = 3.2 > > Q = A * log(m^2 + n^2) > > Q

[1] 320.0546

> a = 33.5 > b = 50.0 > x = 4.1 > l = 2.3 > > M = (a/(a+b)) * sin(x/l) * cos(x/l) > > M

[1] -0.08245964

> z = 22.9 > r = 6.7 > y = sqrt(1.0 + (z/r)^0.38) > y

[1] 1.610978