Assignment #1: Introduction to Accuracy and Precision; Errors; Rounding and Chopping;
Taylor Series Review; Getting Started with Matlab
Due date: Wednesday, September 15, 2010 (10:10am)
For full credit you must show all of your work.
1.
Round each of the following numbers to 4 significant digits; compute the absolute and
relative errors, both signed and unsigned, of the approximation in each case.
a)
x
= 0.12345
b)
x
= 98.7650
2.
Show in pseudocode how each of the functions below can be efficiently evaluated, using no
extra variables and no more than the specified number of arithmetic operations.
[Hint: use the
principles of nested multiplication wherever you can.]
a)
p
(
x
) =
x
4
;
two arithmetic operations
b)
p
(
x
) = 3(
x
+1)
2
+ 5(
x
+1)
4
; five arithmetic operations
3.
(1.1.C1)
Using Matlab, write and run a program that corresponds to the program
First
given
in pseudocode in our textbook, but with the extra error reporting shown here:
program
First
integer
i, imax, imin
←
2
31
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 Spring '08
 MEYER
 Taylor Series, Analytic function, Natural logarithm, Colin Maclaurin

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