Nguyễn Phúc Thiên Ân - 1652039

The numbers in a very matrix will represent knowledge, and that they can even represent mathematical equations.. In several time-sensitive engineering applications, multiplying matrices

 Phạm Đăng Khôi 1651125

 Trần Quốc Nhân 1651127

 Nguyễn Phúc Thiên Ân 1652039

 Võ Minh Hiếu 1651034

 Trần Viết An 1651003

PART 1: MATLAB

Electrical Engineers are associated with design of complex systems

This involves rigorous mathematical calculations and analysis with manual approach being a obsolete one

MATLAB can be used in many effective ways:

As a calculator: Any calculation can be done with the help of MATLAB

(some of which are not even possible with the help of latest CASIO Calculator), to find the value of Eigen value, Eigen vector…

MATLAB could do something more powerful: find Laplace transform, inverse Laplace transform, coefficients of Fourier series, Taylor series and plot any functions

We have one particular example about how MATLAB is used to plot the function:

Example: Given the signal x t( ) 6cos(100 ) t , write a MATLAB program to plot

the signal

(Present, explain your codes and provide the plot)

Solution:

The code in Matlab to illustrate the function in graph:

t=[-0.1:0.0005:0.1];

x=6*cos(100*pi*t);

plot(t,x);

xlabel('t')

ylabel('x(t)')

title('Signal x(t)=6*cos(100*pi*t)');

Explanation:

1 At first, the graph could be drawn from t = -0.1 to 0.1, and divided by 0.0005 for each step or unit, so we got t=[-0.1:0.0005:0.1]

2 After that, we write the function to express x in terms of t, that is the

fuction: x t( ) 6cos(100 ) t .

3 Then, ‘plot’ statement represent the sketch of graph

4 xlabel('t'), ylabel('x(t)') is represent the x-axis and y-axis, respectively

5 Finally, we have to name the graph’s function, because we want to make it clearly and perhaps easily for reading

Below is our result of matlab:

As can be seen, MATLAB is extremely useful for any student to face any difficult problems in Math Besides, it could help us understand clearly about how the elements work

PART 2: COMPLEX NUMBER:

We will focus intensively on the application in Electrical Circuit:

The elements are in Partial Differential Circuit, so the Reponses Vc, VL,VR are expressed in form:

Typical RLC circuit in steady-state, plugged in an AC-Voltage

We assume the complex form of the Responses:

Therefore, the impedance of Conductor: Zc =

Vs= 4sin(2

R=10Ὡ C=1F L=3H

The impedance of Inductor: ZL=2Lj

The input voltage Vs= 4sin(2can be transformed into module and argument of

complex number:

4 /_

And

= 4 sin(2 t + )

= = =>

-= wLj -=6 j -=> 6

Total Resistance

Z= 10 Ω + Zc + ZL

= 10 + + 6 π

=> Z= 21.19 1.08

I= = = 0.188 1.27

Response:

= I x Zc = 0.188 1.27 x -

= 0.03 -0.3

= I x ZL = 0.188 1.27 x 6

= 3.54 2.84

Thus, we can find numerical responses of RLC circuits

• = 0.03 sin2 t – 0.3 rad )

• = 3 sin( 2 t + 2.84 rad)

PART 3: MATRICES

Among the most widely recognized devices in electrical designing and software engineering are rectangular networks of numbers known as matrices The numbers

in a very matrix will represent knowledge, and that they can even represent

mathematical equations In several time-sensitive engineering applications,

multiplying matrices will offer fast however smart approximations of rather more sophisticated calculations

Matrices arose originally as the simplest way to explain systems of linear

equations, a kind of drawback acquainted to anyone United Nations agency took grade-school pure mathematics “Linear” simply means the variables within the equations don’t have any exponents, therefore their graphs can continually be straight lines

The equation x - 2y = zero, as an example, has associate degree infinite variety of solutions for each x and y, which may be pictured as a line that passes through the points (0,0), (2,1), (4,2), and so on however, if you mix it with the equation x - y = one, then there’s {only one|just one|only one} solution: x = a pair of and y = 1 the purpose (2,1) is additionally wherever the graphs of the 2 equations meet

The matrix that depicts those 2 equations would be a two-by-two grid of numbers: the highest row would be [1 -2], and therefore the bottom row would be [1 -1], to correspond to the coefficients of the variables within the 2equations

In a vary of applications from image process to genetic analysis, computers are typically known as upon to unravel systems of linear equations — typically with more than 2 variables Even additional overtimes, they’re known as upon to

multiply matrices

Matrix multiplication may be thought of as determination linear equations for specific variables Suppose, as an example, that the expressions t + 2p + 3h; 4t + 5p + 6h; and 7t + 8p + 9h describe 3 completely different mathematical operations involving temperature, pressure, and wetness measurements they might be drawn

as a matrix with 3 rows: [1 2 3], [4 5 6], and [7 8 9]

Now suppose that, at 2 completely different times, you're taking 

temperature, pressure, and wetness readings outside your home. Those  readings might be drawn as a matrix further, with the primary set of 

readings in one column and therefore the second within the different. 

Multiplying these matrices along means that matching up rows from the  primary matrix — the one describing the equations — and columns from  the second — the one representing the measurements — multiplying the  corresponding terms, adding all up, and getting into the leads to a 

replacement matrix. The numbers within the final matrix would possibly, as 

an example, predict the flight of an unaggressive system

Every graph will be depicted as a matrix, however, wherever every column and every row represents a node, and therefore the price at their intersection represents the strength of the affiliation between them (which may oft be zero) Often, the foremost economical thanks to analyze graphs is to convert them to matrices initial, and therefore the solutions to issues involving graphs are oft solutions to systems of linear equations

PART 4: APPLICATION OF LINEAR SYSTEMS:

Through this exercise, we could understand more about the benefit of matrices to solve the particular problem:

i 4

i 3

i 2

i 1

Set I12 = I1 + I2 R10// 5=

10*5

10 5  =

10

3 () KCL at v1: I1 + I2 = I3 +6  I12 = I3 +6 (1)

KCL at v2: I3 +6 + 3 = I4 (2)

Ohm’s Law for R10// 5: I12 = 10 /

1 / 5

0

R

v

 



=

1 3 10

v



(3) Ohm’s Law for 2: I3 =

1 2 2

v v

(4) Ohm’s Law for 4: I4 =

2 0 4

=

2 4

v

(5) (1) (2)(3)(4)(5):

1 3 10

v



=

1 2 2

v v

+ 6  8v1 - 5v2 = -60

2 4

v

=

1 2 2

v v

+6 + 3 2v1 - 3v2 = -36

( )

=>> V1 = 0V and V2 = 12V

PART 5: APPLICATION OF DETERMINANTS

The determinant easily describe the unambiguousness’s degree inside a matrix While the matrix usually represent for linear transformations, the common case in 3D graphics

The matrix can be inverted because the components do not “cancel out” each other,

if determinant is non-zero

In a similar setting, transpose of a 3x3 symmetrical pivot network is adequately its opposite This works on the grounds that the vectors inside the 3x3 grid speak to the per-heading scaling factors caused by pivot, and if the vectors speak to one of a kind bearings as to one another (symmetry), those scaling elements can be just flipped around to drop the turn that the first lattice speaks to

In conclusion, a full transpose of a 4x4 matrix can be solved to supply some GPU systems This is involed to the physical register display and the instructions

required to multiply matrices

PART 6: VECTORSPACE

We could mention about Calculations:

Common algorithms: LMS (Least Mean Square), RLS (Recursive Least

Square), ZF (zero forcing) etc

 Based on Vector Space Theory

They are connected in the structure of evening out circuits at the recipient

These calculations have a target work which should be boosted or limited The target capacity can be the otherworldly effectiveness (bits/second/Hertz),

impedance (between image, or multi-client), vitality productivity

(Watts/bits/second/Hertz) and so on

The minimization/augmentation of the target work continues along one or a

few Vector Spaces

PART 7: ESPACE

Aside from incalculable uses in principal science, a Euclidean model of the

physical space can be utilized to take care of numerous many practical problems with sufficient precision Two regular methodologies are a settled, or stationary reference outline (i.e the depiction of a movement of items as their positions that change consistently with time), and the utilization of Galilean space-time

symmetry, (for example, in Newtonian mechanics)

space of Galilean speeds is itself a Euclidean space

PART 8: EIGENVALUES AND EIGENVECTORS APPLICATION

Eigenvalues were utilized by Claude Shannon to decide as far as possible to how much data can be transmitted through a correspondence medium like your phone line or through the air

PART 9: QFORM

QForm programming can reenact most metal procedures including: chilly and hot manufacturing, open bite the dust fashioning, ring and wheel moving, reducer moving, cross-wedge moving, screw moving, profile expulsion, stream shaping, hydroforming, sheet framing, orbital framing and powder producing QForm can even mimic the framing of a few work pieces with various material sorts together

Additional modules permit reenactment of stage transformations in warmth

treatment, flexible plastic critical thinking at warming and cooling and additionally microstructure reproduction to follow grain estimate through misshaping

Information can be effectively transported in from throwing reproduction

programs

The assortment of assignments QForm can unravel is ceaselessly being extended

on account of the utilization of client subroutines