1.6 Round-off errors in floating point computations.
1.6.1
Round-off errors.
When people or computers do computations with floating point numbers, they usually round the result of
each arithmetic oper
1.8 Binary floating point numbers
Computers often use base 2 for their representation of floating point numbers. A number x is expressed in
binary (base 2) floating point form if it is written as a si
1.5 Floating point numbers and round-off errors.
1.5.1
Floating point numbers.
Round-off errors are due to the fact that people, calculators, and computers usually do not keep track of or
store number
Final Exam
Math 472/572
Fall 2010
Name: _ This is a closed book exam. You may use a calculator and the formulas handed out
along with the exam. Show your work so I can see how you arrived at your answ
Math 472
1.
Exam 1
Fall 2008
(25 points) The New Youth Plastic Surgery Clinic performs face-lifts. Currently the clinic
performs 50 face-lifts / week for which they charge $10,000 per face-lift. Curre
Formulas
Approximations and Errors
Measuring errors
x = true value of something
xa = approximate value of something (e.g. measured or computed)
x = x - xa = (signed) error in xa
= (x) = (x,xa) = | x
1.7 Other ways to specify errors.
1.7.1
Number of significant digits and intervals.
In section 1.3 we discussed how one could specify the error in an approximate value by means of the
absolute error a
1.4 The algebra of errors.
The function rule estimates the error in a computed value from the errors in the values it is computed from
in a single step. However, for simple functions it may be simpler
1
Approximations and Errors
1.1 Taylor series.
1.1.1
Taylor series and their error.
Mathematical approximations are necessary because on most computers the only built-in operations are
addition, subtr
1.2 Absolute and relative errors.
In mathematics, science, and engineering we calculate various numbers, such as the current in an electric
circuit, or the viscosity of the transmission fluid in a car