COLLEGE ALGEBRA-DISCUSSION BOARD - Essay Example

College Algebra-Discussion Board The Euler’s number e is one of the most important constants in mathematics. The constant is approximately 2.71828182845…; however, the number has been estimated to a fairy high degree of accuracy. Being a rational number implies that e has indeterminate decimals. The Euler’s numbers servers as the base to the natural logarithm. The Euler’s constant can be derived through several methods and each of these methods depends on the intended use. The first method is based on the infinite series theory.

From this method e is the limit of (1 + 1/n) {n± 0} or (1 + 1/n!) as n tends to infinity. Therefore e = 1 + 1/1 + ½ + 1/3 + ¼ …. Alternatively, e =1 + 1 + 1/ (1× 2) + 1/ (1 × 2 × 3) …. This makes e to have special characteristics that makes it a useful constant in mathematics. The first property of e is that it is a transcendental number. This implies that, e cannot be a root of any non-zero polynomial f (x) that has rational coefficients. Other useful mathematical constants are π and i.

The number e has many uses that result directly from its characteristics. The number is useful in calculus where it is used to perform integral and differential operations that involve exponential functions. The number is of particular interest in indefinite integrals since it enables calculation of lower and upper bound for such integrals. The number is also applied in complex analysis as Euler’s identity. In this case cos x + i sin x = eix. In business arithmetic, the function is applied in the calculation of compound interest.

Finally, the constant is applied in statistics to calculate Bernoulli trials. Work CitedRemmert, Reinhold. Theory of Complex Functions. New York: Springer-Verlag, 1991. Print.