Math 240 Spring 2005, Victor Matveev
Binary system, round-off errors, loss of confidence, and double precision accuracy.
1. Bits and the binary number system
A bit is one digit in a binary representation of a number, and can assume only one of
two possibl
Math 240 Spring 2005
Midterm Examination
March 9, 2005
All work must be shown in order to receive full credit. Calculators are not allowed.
1 (10pts) Find the 3rd order Taylor polynomials for each of these function around
point a=0. (hint: both are very e
Lecture Notes Math 240-002
Victor Matveev
March 30, 2005
Application of Difference Equations:
Root Finding
Last week we learned that a 1st order difference equation yn +1 = f ( yn ) approaches an
equilibrium value determined by yeq = f ( yeq ) , if such a
Math 240 Spring 2005
Homework #12
Due date: April 29
All work must be shown in order to receive full credit
1. Since random numbers produced by a computer cannot be truly random, they are
usually called pseudorandom. One of the simplest methods of generat
Math 240 Spring 2005
Homework #11
Due date: April 18
All work must be shown in order to receive full credit
1. The following integral cannot be calculated analytically:
/2
cos x
2
dx
0
Use the midpoint rule to numerically evaluate this integral, with N=
Math 240 Spring 2005
Homework #10
Due date: April 11
All work must be shown in order to receive full credit
1. Equation x2 = cos x has one root on the interval (0, /2). Find this root with a tolerance
of 10-9 (use the difference between successive root ap
Math 240 Spring 2005
Homework #6
Due date: March 28
All work must be shown in order to receive full credit
Solve each of the difference equations given below, and check your analytic solution
against the numeric solution computed directly using the differ
Math 240 Spring 2005
Homework #5
Due date: February 28
All work must be shown in order to receive full credit
1. In this problem you will examine how loss of confidence leads to function
evaluation errors. Recall the simple trigonometric identity sin( x +
Math 240 Spring 2005
Homework #4
Due date: February 21
All work must be shown in order to receive credit; you have to hand in both the
MATLAB code and the corresponding results.
1. You can easily show analytically that the following two functions are equi
Math 240 Spring 2005 Homework #3 Due date: February 14
All work must be shown in order to receive credit; you have to hand in both the MATLAB code and the corresponding results. Be sure to include proper titles, labels and legends with all figures and tab