Usually, people are always scared of the word mathematics, especially ‘mathematical equations’. Equations always have variables and this is the main reason for the fear.
Variables are unknown quantities. They are either in terms of y or x, normally. Sometimes, variables can also be in z, r, θ and so on. Basically a mathematician represents any unknown quantity using a small alphabet. Some alphabets like a, b, c or p, q etc. will be used as constants. The basic difference between a constant and a variable is clearly seen from their literal meanings. Constants can be assigned only one value (fixed) where as variables can be assigned different (varying) values. These variables along with some constants and numbers make an equation.
An equation is simply a relation between two variables. If one variable (say, y) changes its values as a result of change of values of another variable (say, x), then y is called a depended variable, depending on x and since x takes its own values, it is called an independent variable. A formula which connects y and x, defining the relation between them is called ‘an equation’.
The simplest equation would be y = x, which says that y takes the values of x as it is. If we have an equation like y = 2x then, it means that y takes double the values of x. There can be more such equations like this, e.g., y = 3x + 4, y = 5x – 2 etc. These are simpler equations which give a direct relation between x and y and ultimately forms a straight line on a graph sheet.
More complex equations are also possible. The dependent variable y can vary inversely with x, ( y = 1/x), vary as the square of x ( y = x2), vary as the square root of x (y = √x) etc. These equations are called polynomial equations. y = sin(x), y = cos (x) etc are called trigonometric equations since the variables are related by trigonometric functions. The other equations are logarithmic( y = log(x)), exponential (y=ex), hyperbolic (y = sinh(x)) etc.
Though equations are scary, they play a very major role in almost every industry and technology. Without equations, it is impossible to even think about anything ranging from driving a car to sending a rocket to space. Even making a bicycle wheel needs an equation. Making a coca-cola bottle is done basically using mathematical equations.
The mathematical equations are not only used in mathematical concepts but also in other subject areas like chemistry, physics, biology and even literature and sports. All chemical equations are basically mathematical. Physics involves majority of mathematical equations for e.g. E = mc2. Literature sometimes needs mathematical calculations as to the relation to the number of pages written per hour/day. Of course, the motion of a football is a wonderful mathematical equation called quadratic or projectile. In biology, mathematical equations play a very important role. They are used in finding the pH values, in determining the location of genes, finding the growth rate of organisms etc. The common types of equations used in bio-technology are logarithmic, exponential, simple linear simultaneous, differential etc.
If one can understand that equations are nothing but simple relations between two quantities involved in a discussion, then there is no need to dread this concept. It starts with our basic everyday life activity. One can make lots of equations every day. For e.g. a mathematical equation can be formed between the days and the temperature. Every industry needs equations to chart their progress and profit/loss. There is no business without mathematical equations involved. Even for cooking, in every house hold, one needs to interpret the ingredients to his requirements using an equation in some way or the other.
All equations can be graphed for better understanding. Graphing an equation gives a good perception of the equation, same like a bar graph or pie chart in statistics gives a better understanding than a table of values. Usually the dependent variable is taken on the y-axis and the independent variable is taken on the x- axis. For example, a biologist draws the graph of an equation relating to the growth rate of particular bacteria in an organism. It will be easy for him to interpret the results and their consequences through the graph than just by looking into the equation. A steeper curve will be more alarming to the biologist
Presently, many softwares have been developed to interpret the data and make an appropriate equation which will satisfy the given data. This is very helpful, since sometimes it is humanly impossible to interpret certain data like distances of planets from the sun etc.
Hence, mathematical equations form part of our life and it should be taken as an interesting and essential concept, and not as a frightening, evil spirit. Smarter people can solve any problems in life if they can interpret the situation and make an equation out of it. Though solving equations is another major concept in mathematics, making an equation by itself is considered as a very first step to solve many problems. Making equations from a given data is usually called ‘modelling’ in mathematical terms. Henceforth, we can call an equation, a model, if it gives less terror!
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