BTEC Level 5 HND in Electrical and Electronic Engineering
Student Id: 11678
Fabrice Bassele
HNEE 159 Advanced Mathematics for
Engineering
Tutor: S Majmudar
Task: 1
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