Math 308, Spring 1999
Assignment 1.
Given Friday, April 2; due Friday, April 9.
Objectives: (1) To practice solving linear systems by hand and
by computer, (2) To learn to use MATLAB by solving a fun problem.
Exercises from the text:
p. 25, #17, 18, 29, 30, 36.
p. 37, #8, 10, 22.
p. 43-44, #2, 6.
MATLAB exercise:
Following is census data showing the population of the U.S. between
1900 and 1980:
|
| population
|
year | in millions
|
1900 | 76.0
|
1920 | 105.7
|
1940 | 131.7
|
1960 | 179.3
|
1980 | 226.5
|
Plot this data using MATLAB by entering the years into a vector x
and the populations into a vector y and giving the command
plot(x,y,'o'). Set up a linear system to solve for the
coefficients of a fourth degree polynomial that passes through each
data point, and solve this linear system using MATLAB. Plot the
resulting polynomial on the same graph, and determine its value
in the year 2000. Is this a reasonable way to estimate the
population of the U.S. in future years? [To see a demonstration
of other methods of extrapolation, type census in MATLAB.]
Hand in: Your plot and output showing what linear system you solved
and the solution that you obtained, along with the value you estimated
for the population in the year 2000.
File translated from TEX by TTH, version 1.59.