Page 455 - Excel for Scientists and Engineers: Numerical Methods

432 EXCEL: NUMERICAL METHODS

Chapter 4 Number Series

1. (a) Sum of 24 terms = 2 (b) Sum of 100 terms = 1.6349839.
(c) Sum of24 terms = 1.71828182845899

2 0.632120558828558, one of the so-called incomplete gamma functions.

3. It's interesting to experiment with different values for a and x.

4. Answer: 1.5 5. Answer: 0.5

6. Summing the first 100 terms, the series sum is 7c = 3.133787 (0.2% error).

7

The formula in cell 18 is
{=2*PRODUCT((2*ROW( I NDIRECT("1 :"&H8)))A2/(2*ROW( lNDl RECT("1 :"&H
8))-1)/(2*ROW(INDIRECT("I :"&H8))+1))}

8. The spreadsheet answer also incorporates the formula for the initial estimate
(problem 9).

9. Here is one possible formula. The number is in cell C2; the initial estimate
formula is

=LEFT(C2,0.!5*(LEN(C2)+1))

10. The series is described in Edward Kasner and James R. Newman,
Mathematics and the Imagination, Simon & Schuster, 1940; Harper & Row,
1989. The sum (10 terms) is 'II = 3.14159265359 (9 x % error).

Chapter 5 Interpolation

1. Interpolated values: 6.04, 0.59. The formula uses an external reference to
refer to the data table on a different worksheet.

2. This problem requires you to "lookup" to the left. You can either use a linear
interpolation formula using MATCH and INDEX, like the one illustrated in
Figure 5-3, or reorganize the data table so that the freezing point data is on
the left of the wt% data. The latter approach permits the use of cubic