From Basic to Involved Mathematics
Notation
One confusing aspect of the whole calculus thing is the different notation that is used. You will have to get used to a variety of different types of notation. The following is a list of the main types - remember that they all mean the same thing - the value which the fraction (the change in y divided by the change in x) approaches as that fraction becomes infinitely smaller.
- dy/dx
-
f
1(x) - d/dx[f(x)]
- D
It is important to remember what we mean when we refer to the term 'function'. The following example may serve to highlight the issue.
A function states that one value is dependent on another or a range of other factors. Take the function q = f(30 - 5p + 18Y). This states that the value of q is dependent on the values and factors in the brackets - in this case it could be price (p) and incomes (Y). If incomes rise then the quantity demanded will be affected and if price changes the level of demand will also be affected.
The x and y terms can also change depending on the nature of the function. If you are working with a consumption function you will find the value which represents the change in consumption in relation to infinitesimally small changes in income; if it is a production function, changes in output with respect to infinitessimally small changes in capital or labour or land or a combination of all three.