ABSTRACT

Maclaurin’s series One of the simplest kinds of function to deal with, in either algebra or calculus, is a polynomial (i.e. an expression of the form a + b x + c x 2 + d x 3 + . . . $ {\boldsymbol{a+bx+cx^2+dx^3+...}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351232876/7c39b375-15cb-4b0b-ad64-16e4787c18a4/content/inline-math22_1.tif"/> ). Polynomials are easy to substitute numerical values into, and they are easy to differentiate. One useful application of Maclaurin’s series is to approximate, to a polynomial, functions which are not already in polynomial form. In the simple theory of flexure of beams, the slope, bending moment, shearing force, load and other quantities are functions of a derivative of y $ {\boldsymbol{y}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351232876/7c39b375-15cb-4b0b-ad64-16e4787c18a4/content/inline-math22_2.tif"/> with respect to x $ {\boldsymbol{x}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351232876/7c39b375-15cb-4b0b-ad64-16e4787c18a4/content/inline-math22_3.tif"/> . The elastic curve of a transversely loaded beam can be represented by the Maclaurin series. Substitution of the values of the derivatives gives a direct solution of beam problems. Another application of Maclaurin’s series is in relating inter-atomic potential functions. At this stage, not all of the above applications will have been met or understood; however, sufficient to say that Maclaurin’s series has a number of applications in engineering and science.