# Essentials

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Essential skills to use MATLAB effectively. Learning a new skill, especially a computer program in this case, can be overwhelming. However, if we build on what we already know, the process can be handled rather effectively. In the preceding chapter we learned about MATLAB Graphical User Interface (GUI) and how to get help. Knowing the GUI, we will use basic math skills in MATLAB to solve linear equations and find roots of polynomials in this chapter.

## Mathematical operators

The evaluation of expressions is accomplished with arithmetic operators as we use them in scientific calculators. Note the addtional operators shown in the table below:

Operator Name Description
- Minus Subtraction
* Asterisk Multiplication
/ Forward Slash Division
\ Back Slash Left Matrix Division
^ Caret Power
.* Dot Asterisk Array multiplication (element-wise)
./ Dot Slash Right array divide (element-wise)
.\ Dot Back Slash Left array divide (element-wise)
.^ Dot Caret Array power (element-wise)
The backslash operator is used to solve linear systems of equations, see [link] .
Matrix is a rectangular array of numbers and formed by rows and columns. For example $A=\begin{pmatrix}1 & 2 & 3 & 4\\ 5 & 6 & 7 & 8\\ 9 & 10 & 11 & 12\\ 13 & 14 & 15 & 16\\ \end{pmatrix}$ . In this example A consists of 4 rows and 4 columns and therefore is a 4x4 matrix. (see Wikipedia ).
Row vector is a special matrix that contains only one row. In other words, a row vector is a 1xn matrix where n is the number of elements in the row vector. $B=\begin{pmatrix}1 & 2 & 3 & 4 & 5\\ \end{pmatrix}$
Column vector is also a special matrix. As the term implies, it contains only one column. A column vector is an nx1 matrix where n is the number of elements in the column vector. $C=\begin{pmatrix}1\\ 2\\ 3\\ 4\\ 5\\ \end{pmatrix}$
Array operations refer to element-wise calculations on the arrays, for example if x is an a by b matrix and y is a c by d matrix then x.*y can be performed only if a=c and b=d. Consider the following example, x consists of 2 rows and 3 columns and therefore it is a 2x3 matrix. Likewise, y has 2 rows and 3 columns and an array operation is possible. $x=\begin{pmatrix}1 & 2 & 3\\ 4 & 5 & 6\\ \end{pmatrix}$ and $y=\begin{pmatrix}10 & 20 & 30\\ 40 & 50 & 60\\ \end{pmatrix}$ then $\mathrm{x.*y}=\begin{pmatrix}10 & 40 & 90\\ 160 & 250 & 360\\ \end{pmatrix}$

The following figure illustrates a typical calculation in the Command Window.

## Operator precedence

MATLAB allows us to build mathematical expressions with any combination of arithmetic operators. The order of operations are set by precedence levels in which MATLAB evaluates an expression from left to right. The precedence rules for MATLAB operators are shown in the list below from the highest precedence level to the lowest.

1. Parentheses ()
2. Power (^)
3. Multiplication (*), right division (/), left division (\)

## Mathematical functions

MATLAB has all of the usual mathematical functions found on a scientific calculator including square root, logarithm, and sine.

Typing pi returns the number 3.1416. To find the sine of pi, type in sin(pi) and press enter.
The arguments in trigonometric functions are in radians. Multiply degrees by pi/180 to get radians. For example, to calculate sin(90), type in sin(90*pi/180) .
In MATLAB log returns the natural logarithm of the value. To find the ln of 10, type in log(10) and press enter, (ans = 2.3026).

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
how did you get the value of 2000N.What calculations are needed to arrive at it
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