Page 9 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Mathematics for Economists
Note
2 LOVELY PROFESSIONAL UNIVERSITY
With the change of value of one number, the rate of change in the value of other number and
questions related to rate of such change and analysis and study of functions is referred to as Differential
Calculus.
1.1 Quantities
There are two types of quantities:
1. Variable 2. Constant
1. Variables – Changing quantities are referred to as variables. Quantities for which values keeps on
changing viz which can be given indefinite numerical values are Variables. These are general
expressed with the last characters such as x, y, z, u, v, w etc. of English Words.
2. Constants – Numbers for which value is unchangeable under any process of mathematics, are
constants. Constant Tuantities are of two types:
(i) Absolute constants
(ii) Arbitrary constants
Value of which in any problem is unchanged, is referred to as absolute constants e.g.
2
5, S 3, 1, 1, 5, , , e etc.
5
Value of which remains constant in a problem, but get different value in different problems, they
are called arbitrary constants. These are expressed with the beginning letters such as a, b, c, d, etc. of
English word.
1.2 Related Quantities
We know that the area of the circle depends on its radius. In other words, circles with different radii
have different areas. Similarly, square of any positive number increases or decreases with any
change in it. Here radius of circle and its area or number and its square are related quantities.
Notes Any two numbers, in which change in any one number affects another number, are
referred to as related quantities.
Although both these two numbers are constants, but value of any one number can be changed
liberally and the value of other number will change not independently but applying any rule. For
example if we assume liberally 1, 2, 3, 4 …….. for the radius of the circle (r), then its area (A) applying
the rule A = πr would be π, 4π, 9π, 16π,..... respectively.
2
There are two types of constants:
(i) Independent Variables, (ii) Dependent variables
If two constants x and y are related in a manner where one variable can be given any value liberally
and the value of y depends on it, then x will be referred to as independent variables and y would be
its dependent variables.
For example: Assume y = 2x + 5
Now giving x variable different values like 0, 1, 2, ….. etc. we get different results for y variable such
5, 7, 9, …… etc. respectively, which is completely depended on x.
Therefore, here x is independent variable and y is a dependent one.