HW1 assignment - HW#1 Note i ii iii EGM6341 Spring 2009 iv...

HW#1
EGM6341
Spring 2009
Note:
i) This set of HW comes from diverse aspects in calculus and math analyses.
ii) It is intended to serve as a review and to bring you up to speed in
mathematical analysis. Series expansion in various forms and acceleration of
series are extremely useful tools both analytically and computationally.
iii) I suggest that you first read over a dozen examples that I provide in the
Supplemental Reading Material (Chapter One) –they serve to bridge the gap
between your previous calculus background and the class discussions/
homework problems.
iv) If you still have difficulty to solve some problems in HW#1 after reading and
understanding the examples in Supplemental Reading Material , let me know
via phone call (if you are an EDGE student), visit to my office, or emails.
Due: 1/15/08 (tentative schedule)
Assignments :
From the textbook by Atkinson: pp.43-50:
#1a Assume ƒ(x) is continuous on a ≤ x ≤ b, and consider the average
∑
=
=
n
j
j
x f
n
S
1
) (
1
with all points x
j
in the interval [a, b]. Show that
) ( ζ f S =
for some ζ in [a, b].