Tutorial #1: PHYS2100
Due 15/09/15
1) Write the first few terms of the Maclaurin series up to and including
x6
for
each of following functions:
a)
e
e)
b)
x3
f)
1 cos x
x2
c)
ln cos x
g)
1
d)
sin x
x
h)
x ln 3 x
1
2 x
1 x
1 x2
2) Write the Taylor se

1
STUDENT NOTES/LECTURE #4
Power Series
1.1
Application of common series
These lecture notes introduce some of the series of functions most commonly
used in mathematical physics. One of the most common series of functions is the power
series where th

1
STUDENT NOTES/LECTURE #3
Convergence of Series
1.1
Test for convergence
For a convergent series the th member of the sequence of partial sums will be a
good approximation to the series if is large enough. This is a simple but important
property of

1
STUDENT NOTES/LECTURE #1
Introduction to Series
1.1
Infinite Sequences
Methods of approximation play a central role in the sciences. All of the laws that
we deal with in the sciences are mathematical laws, and as such, they are exact. However,
once