CSc 30100 – Scientific Programming

Assignment

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( )

( )

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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.