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THE USE OF POLYNOMIAL FUNCTIONS IN THE REAL WORLD
Transcript of THE USE OF POLYNOMIAL FUNCTIONS IN THE REAL WORLD
In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition,subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate (or variable), x, is x2 − 4x + 7, which is a quadratic polynomial.
Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic
"Education is the most wonderful weapon which we can use to change the world."
Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.
Polynomials come up often in chemistry. Gas equations relating diagnostic parameters can usually be written as polynomials, such as the ideal gas law: PV=nRT (where n is mole count and R is a proportionality constant).
Why put Polynomial Functions in the curriculum?
A polynomial function is a function that can be defined by evaluating a polynomial. A function of one argument is called a polynomial function if it satisfies
Although many of us don't realize it, people in all sorts of professions use polynomials every day. The most obvious of these are mathematicians, but they can also be used in fields ranging from construction to meteorology. Although polynomials offer limited information, they can be used in more sophisticated analysis to retrieve more data.
Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Engineers use polynomials to graph the curves of roller coasters and bridges.
Roller coasters are modeled using polynomial functions, specifically this one:
If we fill in the values, we get this graph:
That looks like a roller coaster, doesn't it?
Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales.
Assessment of present value is used in loan calculations and company valuation. It involves polynomials that back interest accumulation out of future liquid transactions, with the aim of finding an equivalent liquid (present, cash, or in-hand) value. Fortunately, numerous payments can be rewritten in a simple form, if the payment schedule is regular. Tax and economic calculations can usually be written as polynomials as well.
Motion of Particle Under
Influence of Gravity
To find the motion of a particle under the
influence of gravity, this equation is used:
x0 = initial position
v0 = initial velocity
a = acceleration due to gravity
t = time
Formulas of molecules in concentration at equilibrium also can be written as polynomials. For example, if A, B and C are the concentrations in solution of OH-, H3O+, and H2O respectively, then the equilibrium concentration equation can be written in terms of the corresponding equilibrium constant K: KC=AB.
Electronics use many polynomials. The definition of resistance, V=IR, is a polynomial relating the resistance from a resistor to the current through it and the potential drop across it.
This is similar, but not the same as, Ohm's law, which is followed by many (but not all) conductors. It states that the relation between voltage drop and current through a resistor is linear when graphed. In other words, resistance in the equation V=IR is constant.
Other polynomials in electronics include the relation of power loss to resistance and voltage drop: P=IV=IR^2. Kirchhoff's junction rule (describing current at junctions) and Kirchhoff's loop rule (describing voltage drop around a closed circuit) are also polynomials.
Polynomial regression in statistics is found
with the following formula:
Polynomial regression is "a form of linear regression in which the relationship between the independent variable x and the dependent variable y is modelled as an nth order polynomial."
Polynomials are fit to data points in both regression and interpolation. In regression, a large number of data points is fit with a function, usually a line: y=mx+b. The equation may have more than one "x" (more than one dependent variable), which is called multiple linear regression.
In interpolation, short polynomials are joined together so they pass through all the data points. For those who are curious to research this more, the name of some of the polynomials used for interpolation are called "Lagrange polynomials," "cubic splines" and "Bezier splines."
Nursing, psychiatric and home-health aides use polynomials to determine schedules and keep records of patient progress. People seeking employment in these areas require a keen mathematical background using polynomial computations.
To calculate the concentration, c, in parts per
million of a certain drug in the bloodstream
after t hours, we use this equation:
Weight of a Patient
The weight, w, of a sick patient can be
modeled with this equation:
n= number of weeks since
patient became ill
Converting measurements, using geometry to calculate area, and metric math apply to forestry employment in conservation work and logging. Forest engineers, conservationists and loggers use polynomials in managing the land, for example, calculating how many trees to replant after cutting down a section of forest.