CSc 30100 – Scientific Programming
Assignment
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0
Calculate the Taylor polynomials centered at 0,
0 , !
for cos for the following 4 values of ,
1234 , , , which is equivalent to 10 10 10 10
, for 1,2,3,4. 10
For each value of ,
k n
k
n
k
f T x x
k
f x x
x
j x j
j
=
=
=
∈
= =
∑
12
find the smallest integer such that
cos 10 .
10 10 n
n
j j T −
− <
2
.
3
Calculate the "exact" value using np.cos(x). Present your results
in a table and discuss them. How do your errors compare to the
error bounds for Taylor polynomials that we discussed in class?
Rememb
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1
1
er that the error for a Taylor polynomial is given by its
remainder term
=
1 !
Include all of your analysis and discussion in an .ipynb file
and submit the file through Blackbo
n
n
n n
f c R x fx T x x a
n
+
+
= − − +
ard. The name of the
file you submit should be lastname_firstname_AS03.ipynb.
Do not clear your results after your last run so that I will be
able to see your results without rerunning your file.
4
If you collaborate with anyone on this assignment, be sure to
follow the collaboration guidelines in the syllabus including
listing with whom you collaborated in your ipynb file.
While collaboration is fine, DO NOT submit exactly the same
file as your collaborations. Your code and your discussion must
be your own.
