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The eq operator is used to write equations. It is used in the same way as any other operator. That is, itis the first child of an apply. It takes two (or more) children which are the two quantities that are equal to eachother. For example, " a times b plus a times c equals a times the quantity b plus c " would be written as shown. <m:math> <m:apply> <m:eq/> <m:apply> <m:plus/> <m:apply> <m:times/> <m:ci>a</m:ci> <m:ci>b</m:ci> </m:apply> <m:apply> <m:times/> <m:ci>a</m:ci> <m:ci>c</m:ci> </m:apply> </m:apply> <m:apply> <m:times/> <m:ci>a</m:ci> <m:apply> <m:plus/> <m:ci>b</m:ci> <m:ci>c</m:ci> </m:apply> </m:apply> </m:apply> </m:math> This will display as a b a c a b c .

Integrals

The operator for an integral is int . However, unlike the operators and functions discussed above, it haschildren that define the independent variable that you integrate with respect to ( bvar ) and the interval over which the integral is taken (use either lowlimit and uplimit , or interval , or condition ). lowlimit and uplimit (which go together), interval , and condition are just three different ways of denoting the integrands. Don't forget that the bvar, lowlimit , uplimit , interval , and condition children take token elements as well. The following is "the integral of f of x with respect to x from 0 to b ." <m:math> <m:apply> <m:int/> <m:bvar><m:ci>x</m:ci></m:bvar> <m:lowlimit><m:cn>0</m:cn></m:lowlimit> <m:uplimit><m:ci>b</m:ci></m:uplimit> <m:apply> <m:ci type='fn'>f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as x 0 b f x .

Derivatives

The derivative operator is diff . The derivative is done in much the same way as the integral. That is, youneed to define a base variable (using bvar ). The following is "the derivative of the function f of x , with respect to x ." <m:math> <m:apply> <m:diff/> <m:bvar> <m:ci>x</m:ci> </m:bvar> <m:apply> <m:ci type="fn">f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as x f x .

To apply a higher level derivative to a function, add a degree tag inside of the bvar tag. The degree tag will contain the order of the derivative. Thefollowing shows "the second derivative of the function f of x , with respect to x ." <m:math> <m:apply> <m:diff/> <m:bvar> <m:ci>x</m:ci> <m:degree><m:cn>2</m:cn></m:degree> </m:bvar> <m:apply><m:ci type="fn">f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as x 2 f x .

Vector and matrices

Vectors are created as a combination of other elements using the vector tag. <m:math> <m:vector> <m:apply> <m:plus/> <m:ci>x</m:ci> <m:ci>y</m:ci> </m:apply> <m:ci>z</m:ci> <m:cn>0</m:cn> </m:vector> </m:math> This will display as x y z 0 .

Matrices are done in a similar manner. Each matrix element contains several matrixrow elements. Then each matrixrow element contains several other elements. <m:math> <m:matrix> <m:matrixrow> <m:ci>a</m:ci> <m:ci>b</m:ci> <m:ci>c</m:ci> </m:matrixrow> <m:matrixrow> <m:ci>d</m:ci> <m:ci>e</m:ci> <m:ci>f</m:ci> </m:matrixrow> <m:matrixrow> <m:ci>g</m:ci> <m:ci>h</m:ci> <m:ci>j</m:ci> </m:matrixrow> </m:matrix> </m:math> This will display as a b c d e f g h j .

There are also operators to take the determinant and the transpose of a matrix as well as to select elements fromwithin the matrix.

Entities

The use of MathML character entity references in Connexions content is deprecated .

MathML defines its own entities for many special characters used in mathematical notation. While the entity references have the advantage of being mnemonic with respect to the characters they stand for, they also entail some technical limitations, and so their use in Connexions content is deprecated. Please use the UTF-8-encoded Unicode characters themselves where possible, or, failing that, the XML Unicode character references for the characters. At some time in the future, the Connexions repository system will likely convert entity references and character references silently to the UTF-8-encoded Unicode characters they stand for. See 6.2.1 Unicode Character Data from the XML Specification for more information. The MathML specification contains a list of character entities with their corresponding Unicode code points .

There are character picker utilities available to help you select and paste UTF-8 characters into applications like Connexions. If you are running Microsoft Windows, the Windows accessory Character Map can help you. The "Lucida Sans Unicode" font seems to have a good selection of mathematical operators and special characters. Under Linux, the charmap utility and GNOME applet provide access to all Unicode characters.

Other resources

There is a lot more that can be done with Content MathML. Especially if you are planning on writing a lot of ContentMathML, it is well worth your time to take a look at the MathML specification .

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Cnxml tutorial. OpenStax CNX. Jul 08, 2009 Download for free at http://cnx.org/content/col10121/1.10
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