# Application of Linear and Polynomial Functions

Algebra is a branch of mathematics involving the use of mathematical statements to describe the relationship between variables (Axler, 1997). Letters are used to denote variables; and relate them by algebraic terms, expressions or various types of equations. Linear and polynomial functions are a part of algebra; and the relationships they draw find application in various professions. In this research paper, I sought to identify two professions that employ linear functions and one that employs polynomial functions on a regular basis. I also describe the context in which these algebraic functions are applied in the respective professions identified.Linear functions are algebraic functions describing the relationship between two unknown variables raised to the power of 1 where the first is the input and the second is the output; and a constant (Axler, 1997). Linear functions derive their name from the fact that they yield straight lines when the relationship between the variables, usually depicted as y=mx+c where y is the result, x is the input, m is the gradient and c is a constant, is translated onto a graph (Axler, 1997). In my research, I identified economics as one of the professions in which linear functions are used. I also identified engineering as the other profession since linear functions are widely used in design engineering.Linear functions are widely used in economics. The attractiveness for their use in this profession is that they are simple and easy to deal with. Linear functions are used to calculate simple interest earned on money saved in a bank or simple interest on money borrowed (Axler, 1997). If, for example a customer saves a principal P in a bank that pays simple interest at a rate I for a number of years, say N, the interest accrued after the N years will be given by the expressionInterest = I.N.PThe total amount in the bank S will be the sum of the interest accrued plus the principal, orS = P + I.N.P = P (1+I.N) = IN + P.Since P, the principal and N, the interest rate are constants, the above expression is a linear function, taking the form described above. Having solved algebraic expressions concerned with hire purchase and interest rates earlier, I was already familiar with the application of linear functions in economics.Use of Linear Functions in EngineeringTwo or three dimensional vectors, which are linear functions, are widely used in design engineering. Matrices derived from vectors and their associated operations like eigenvalues, eigenvectors, and diagonals are extremely vital in the generation of two or multidimensional engineering models like trajectories, jet engines, fluid-flow systems and production lines (Cohn, 2000). Another example of linear functions finding application in engineering is Bernoulli’s Equations which are perhaps the most instrumental in the study of thermodynamics, fluid mechanics, heat transfer and air conditioning (Cohn, 2000).Laplace Transforms, which transforms into the z-transform if applied to the complex plane, is one of the most widely used techniques in all engineering disciplines (Cohn, 2000). Derived from linear algebra, it finds application in the design of both analogue and digital control systems where it aids engineers in the determination of characteristics of control system components like the initial and final value theorems, transfer functions and forced and natural frequencies of oscillation.I had limited knowledge of engineering principles before this research, and I was surprised to discover the relevance and importance of linear algebra in engineering. I now understand why engineering students have to be taught linear functions: they are very vital in the teaching and later the actual practice of the engineering profession.Use of Polynomial Functions in EngineeringPolynomial Functions assume the formn is referred to as the order of the equation.Functions in this form are widely used in engineering since they generate models with a simple form which are therefore easy to understand.An example of polynomial function being used in engineering is when determining the electric current passing through a variable resistance. Traditionally, current I and voltage E are linearly related by Ohm’s Law (Hamming, 1997):I=E/R.When the resistance is variable, the relationship is modified into: This is a polynomial function of degree n. Assuming that the circuit under examination has a linear resistance , the potential in the circuit is shared according to the rule of summation of voltages as(Hamming, 1997), after which the current flowing in the circuit is given asORSolving for the voltage across the variable resistor and the current flowing through it, the current and voltage values for the linear resistance can be established.I knew that polynomial functions are used in electrical engineering, but this was a new demonstration I came across during my research. Once again, I am surprised to see how relevant these functions are in so many professions. It goes a long way to illustrate the importance of all algebraic topics in professional disciplines outside academia.ConclusionThe above examples of linear and polynomial functions being applied in different professions to make work and research easier illustrate the importance of this subject. Learning algebra is not just as lacking in opinion and initiative as some people might think. It can evidently help a lot in understanding various principles outside one’s profession; or lead to a career in a variety of professional disciplines (Axler, 1997).

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