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2009-06-08-19-10 start
This file http://freeman2.com/tute0008.htm
is Freeman's reading notes. Although Freeman
always keep correct view point. But Freeman's
capability is limited, plus no one proofread
this file. Then you can still find wrong view
point. When read, please put question mark as
often as possible. If you suspect any view
point wrong, please ask a math expert near by.
<a name="docA02">
This file is a note for reading inequality
book written by ProfessorJ. MichaelSteeleThe Cauchy-Schwarz Master Class★★★★★
Below use 'textbook' as abbreviation.
Freeman also read web pages online, and will
indicate the source URL at discussion point.
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Freeman study mechanical engineering.
Engineering mathematics do not teach
inequality. Above book is first inequality
book. First time read, it was very hard.
Although high school time learned
a*a + b*b >= 2*a*b
But this little knowledge do not help.
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This file follow textbook chapter section
order, but not continuous, Freeman skip
those uncertain sections/problems.
This file first function is to learn
inequality. Second function is to learn
how to use html code to write math
equations.
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On 2009-01-27-10-08 Freeman accessed
the next page
http://www.sftw.umac.mo/~fstitl/10mmo/inequality.html
save as sftw.umac.mo_text_math_eqn_good.htm
Above page is the main reference for html
math equation.
In order to let reader to build html math
equation, previous file tute0007.htm page
end has math symbol and internal code.
This file third function is to display how
to draw curves in web page. The main engine
is XYGraph v2.3 - Technical Figures
Thank you for read Freeman's inequality page.
2009-06-08-19-47 stop
<a name="ch01b052">
2009-06-27-12-27 start write
Program verify page 13 line 14 equation
up to six sequences.
Each seq. has
numbers
If sequence 1 proportional to sequence 2,
inequality become equality.
proportional
=
(box2 change)
Box 1
Box 2
Box 3
Box 4
Box 5
Box 6
Example
2 and 3 are equality.
output to box7
Box 7, answer
Box 8, debug
2009-06-27-21-35 done goCauchy6()
In/out location display here
<a name="ch01b053">
2009-06-27-19-28 start
Above is six sequence Cauchy Inequality,
allow six sequence at one time.
Please pay attention to the following
First, If sequence one has five elements
other sequence read only five elements.
discard the remaining. If other sequence
do not have five elements, program fill
with zero.
Second, if work with two sequences, let box3
be empty.
Third, three sequences or more, the condition
for Cauchy inequality to become equality
is tight.
Product Sum related material
The Cauchy-Schwarz Master Class
ISBN 978-0-521-54677-5 chapter five.
Product 1st, sum 2nd get Same≧Rand≧Revs
chapter five, page 78,79,80 problem 5.3
Sum 1st, product 2nd get Same≦Rand≦Revs
chapter five, page 81 problem 5.4
What is first? what is second? Please click
"Test&Doc" and read Box23 second half.
"Same"=sequence_a and seq_b both monotone
increase, or both monotone decrease.
"Rand"=both sequence are random order
"Revs"=one monotone increase, the other
one monotone decrease.
Program assume Box21,Box22 initial data are both random.
<a name="sortnumb">
Sort number not text string
Output may contain error, Please verify first.
Program environment is MSIE 6.0, please use MSIE
Box11 accept only numbers, not name list, not non-number string.
Box 71, input number sequence
Box 72, output answer
This file sort numbers, not for sort text; upsidedown text ok.
2009-07-15-11-18 start sortNumb()
2009-07-15-18-40 done sortNumb()
2009-09-29-20-50 done upsidedown()
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Working record.
2009-06-10-09-45 Build Cauchy Inequality input box
2009-06-10-18-09 Done Cauchy Inequality
2009-06-11-12-00 Improve Cauchy Inequality program.
2009-06-27-12-27 Start six sequence Cauchy Inequality
2009-06-27-18-30 Done six sequence Cauchy Inequality
2009-07-02-09-51 Start generalized Cauchy Inequality
2009-07-02-13-22 Done generalized Cauchy Inequality
generalized Cauchy Inequality is in tute0009.htm
2009-11-21-16-55 create cauchy6e.htm for
Cauchy Inequality
6 sequence
English
include Cauchy Converse
<a name=docB02>
2009-11-25-17-47
"Update 2009-11-25" add link to tute0020.htm
"Update 2009-11-25" add [Sorted Seq. 123]
button.
Before one click get decrease number output
and two click get increase number output
Now one click get increase number output
2009-11-25-17-55
<a name=docB03>
2009-11-27-15-39
"Update 2009-11-27" add Cauchy converse 2
[[
above Cauchy converse 1, page 75, line -1
below Cauchy converse 2, page 84, line 5
The Cauchy-Schwarz Master Class
J. Michael Steele
ISBN 978-0-521-54677-5
]]
2009-11-27-15-40
Cauchy's Inequality, Six sequences; Cauchy Converse
http://freeman2.com/cauchy6e.htm
"Cauchy's Inequality, Six sequences" part
was from tute0008.htm and tute0009.htm
Cauchy Converse is new program
Product Sum is new program
cauchy6e.htm first upload 2009-11-22
Thank you for visiting Freeman's page.
Freeman
2009-11-21-19-37