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# A Maclaurin’s series is a Taylor series expansion of a function about 0, Maclaurin series are named after the Scottish mathematician Colin Maclaurin.

BTEC Level 5 HND in Electrical and Electronic Engineering

Student Id: 11678

Fabrice Bassele

HNEE 159 Advanced Mathematics for Engineering

Tutor: S Majmudar

Discuss briefly the theory and application of each of the following:

·        Maclaurin’s series Taylor’s series

·        Leibnitz theorem

·        Bessel’s and Legendre equation

·        Euler and Runge- kutta differential equation.                [LO P1.1]

Solution:

Maclaurin’s series:

A Maclaurin’s series is a Taylor series expansion of a function about 0, Maclaurin series are named after the Scottish mathematician Colin Maclaurin.

Using the above maclaurin’s series mixed function containing say algebraic, trigonometric and exponential functions, may be expressed only as algebraic function. Differentiation and integration can also be performed more easily and fast.

Maclaurin’s series gives the solution to complex function where simple algebraic calculation will be difficult. Some examples which can be solved using maclaurin’s series are shown below:

Maclaurin’s series can be used to represent any function say

As a power series provided that at the following three conditions are met.

Condition no.1

Example:  if then meets the condition however if  then