**Mathematics using Matlab**

For a long time, people have always predicted a time when everything about the school framework would go digital. Some of the predictions are that hard copy books will not be existent, and no longer will classes be carried out at the traditional classrooms. The truth is the prediction seems will come to pass but not as fast as the predictions are. It will take time. No one argues that this is just mere fantasies. There is enough evidence to suggest that the time will come. In today’s academic settings, students are being taught to use different software such as python, C, and C++. Institutions have adopted eLearning and online learning, but this is just a few numbers. The use of the software’s in the analysis is increasingly being used by so many institutions. One of them is Matlab.

Matlab.

Matlab is a mathematical computation high-level programming language. With Matlab, you can automate the mathematical tasks that normally take a long time to complete manually. The name Matlab is an acronym for matrix laboratory. In its initial years, Matlab was developed as a tool for matrix computation. As years and technology advanced, Matlab uses was increased. Today, with Matlab, you can do one of the most complex sums. All this transformation has happened just in less than a century. Who knows what Matlab capabilities will be in some other decades to come?

Academic institutions have incorporated Matlab into their curriculum. What would have warranty its application in these institutions? Here are the reasons for this.

- Debugging. Matlab has been developed in such a way that any user will find it easier to debug the code. As you write a line of code, it highlights where the problem is in. Rather than waiting to complete writing the code and then debug, you correct the errors as you move on.
- It’s a mathematical computing tool. Matlab was meant to be a mathematical computing tool. That is what its main role is. It only speaks math.
- Integrates well with other languages. With Matlab, you can develop a C code from Matlab that works in exactly the same way that the Matlab code works. This is automated and takes a shorter time. You could also load Matlab form excel and use its functions to do mathematical computations.
- Matlab has a large community. The scientific community supports it, and there are lots of free codes that anyone can use to develop their codes. There is also a lot of sharing. In case you do not know anything or encounters an error, simply ask, and you will get your answers.

Mathematics using Matlab.

Matlab is a mathematical computing tool that allows you to do a lot of computations with it. Let’s look at some of the mathematical problems you could solve using Matlab. Here we won’t develop the code.

Elementary mathematical

This is one of the most basic mathematics that anyone must learn irrespective of the course they are studying. Operations here include doing trigonometric sums, normal addition and subtraction, logarithmic operations, remainders, and rounding of values. In some cases, students will learn about complex numbers. In Matlab, it should be fairly easy to compute these operations as they are the most basic and won’t need specialized apps.

Linear algebra

This is one of the first steps in mathematics where we say a student is leaning real mathematics. It’s mostly taught before calculus as it’s not as advanced as to how calculus is. Linear algebra is a branch of mathematics which deals with linear equations. It’s mostly used to model linear equations of real-life data. Despite being very useful, it always comes short when nonlinear equations are involved.

The symbolic math toolbox is an app in Matlab that can be used for linear algebra. It contains all the functions that you can need.

Calculus.

Much like the linear algebra, calculus involves the use of equations. In most institutions, calculus is taught immediately after linear algebra. It’s more complex than linear algebra and can solve numerous real-life problems that linear algebra falls short of. Further, it takes any kind of equation linear or nonlinear. Primarily calculus is split into two: integral calculus and differential calculus. The latter deals with the rates of change of the curve, while the former deals with the accumulation of quantities. Integral calculus is also used to calculate the area between two curves. In Matlab, the symbolic math toolbox app is an important resource for both differential ad integral calculus.

Optimization.

Optimization comes from the word optimize, which means to make the best out of something or a situation. Optimization is a branch of mathematics that means getting the best element of a function.

It has a lot of applicators in disciplines such as economics and engineering. Mostly, it’s applied where there is a decision to be made. In mathematics, the optimal values are obtained by finding the maximum and the minimum values of the equation. The differential is a method that is employed to find the minimum and maximum of a curve. Matlab provides you with various functions that you can use to find the maximum and the minimum of a curve. For instance, you could find the minimum of a curve by keying in the function fminbnd in the Matlab console.

Computational geometry.

Geometry is a mathematics branch that deals with measurements, areas, and volumes of tools. When you studied how to find the volume of a cone in high school, you were studying geometry. It has a lot of applications in real life. Designers, social science, and engineers often apply geometry principles. Computational geometry is the branch of mathematics that deals with the development of geometry algorithms. The computational geometry toolbox has all the functions that you will need on this part.

Mathematical statistics.

In general terms, statistics is the science that involves the collection of data, analyzing all the way up to the interpretation of the data. Mathematical statistics is a branch of mathematics that is concerned with advanced mathematics such as probability theory. It deals with the interpretation part of the data. Note the difference between mathematical statistics and statistics itself. Mathematical statistics exclude the process of data collection. Symbolic math’s toolbox is an essential tool in computing Probability theory

Matlab assignment experts

Are you still wondering if it’s possible to solve mathematics using Matlab? You now know that it’s possible. Matlab has everything that you would require. Even the most complicated math problem can be solved using Matlab. In case you have any difficulties in solving mathematics using Matlab, you could ask for our help. We are a team of experts from different disciplines ready to help you with any Matlab relates challenging problems our expert’s team is the best in the field and have the necessary academic requirements and have experience working on such assignments. From us, you gain in the sense that you get plagiarism-free assignment solutions, timely deliveries, and high-quality assignment solutions. We promise you that you will get that quality grade that always seems elusive to you. Contact us at any time, and you will be pleased with the outcome.

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__Green’s theorem, Surf & Fsurf, Triplequad and Integral13__

__Green’s theorem, Surf & Fsurf, Triplequad and Integral13__

This is a sample Matlab assignment solution that involves the use of Surf & Fsurf Matlab function and Triplequad and Integral13 Matlab command. The expert has showcased the application of Green’s theorem. S(he) has computed the right and left side of Green’s theorem in two separate problems. In one of the problems movement of a particle is described. Also, the vector expression for force field acting on the particle is given, the expert has calculated the total work done during movement of the particle. In another problem, the equation of a sphere and cone is given. The tutor has shown, how to use “surf” & “fsurf” function to plot the ice cream cone cut out of the sphere. The same ice cream cone has been plotted by adding normal vectors. In the last part of the assignment, moments of a solid D are given about the coordinate axes, expert has calculated moments of inertia about the Z-axis of the same ice cream cone using “triplequad” & “integral13” matlab command.

** SOLUTION** : –

clear all

clc

Fxy=@(x,y)x+y ;

xmin=1;

xmax=5;

ymin=6;

ymax=@(x) 6+sqrt((2-0.5*(x-3).^2));

I1 = integral2(Fxy,xmin,xmax,ymin,ymax)

xi=xmin:0.1:xmax;

yi=ymax(xi);

scatter(xi,yi)

F2yx=@(y,x) x+y;

ymin=2;

ymax=6;

xmin=@(y) 4-y/2;

xmax=@(y) 2+y/2;

I2 = integral2(F2yx,ymin,ymax,xmin,xmax)

I=I1+I2;

fprintf(‘the required value is:[%d]\n’,I)

hold on

yj=2:0.1:6;

xj=xmin(yj);

scatter(xj,yj);

xj=xmax(yj);

hold on

scatter(xj,yj)

clear all

clc

a=2;

b=sqrt(2);

f = @(t) 0.5*(6+b*sin(t)).^2*a.*sin(t) + 0.5*(3+a*sin(t)).^2*b.*cos(t);

I1 = integral(f,0,pi/2)

f2 = @(t) (2+4*t).^2 + 2*(3-2*t).^2 ;

I2 = integral(f2,0,1)

f3 = @(t) -(2+4*t).^2 + (3+2*t).^2*2;

I3 = integral(f3,0,1)

I = I1+I2+I3;

fprintf(‘the first integral is:[%d]\n’,I1)

fprintf(‘the second integral is:[%d]\n’,I2)

fprintf(‘the third integral is:[%d]\n’,I3)

fprintf(‘the total integral is:[%d]\n’,I)

clear all

clc

% Path 1

Ft=@(t) 3*sin(9*t.^2);

I1t=integral(Ft,0,1)

% Path 2

Gt=@(t) 5*log(4+15*t);

I2t=integral(Gt,0,1)

Ht=@(t) -3*(sin((3-3*t).^2+(5-5*t).^2)) -5 * log(4+(3-3*t).*(5-5*t));

I3t=integral(Ht,0,1)

I = I1t+I2t+I3t;

fprintf(‘the work done is:[%d]\n’,I)

clear,clc

r=[0:0.2:2];

theta=[0:pi/50:2*pi];

[R,THETA]=meshgrid(r,theta);

X=R.*cos(THETA);

Y=R.*sin(THETA);

Z=3.5*R;

surf(X+8,Y+2,Z)

hold on

%surfnorm(X+8,Y+2,Z)

phi=[0:pi/50:pi];

theta=[0:pi/35:2*pi];

[THETA,PHI]=meshgrid(theta,phi);

radius=2;

X=radius*sin(PHI).*cos(THETA);

Y=radius*sin(PHI).*sin(THETA);

Z=radius*cos(PHI);

surf(X(1:26,:)+8,Y(1:26,:)+2,Z(1:26,:)+7)

xlabel(‘x’)

ylabel(‘y’)

zlabel(‘z’)

print(‘cone’,’-dpng’)

clear,clc

r=[0:0.2:2];

theta=[0:pi/50:2*pi];

[R,THETA]=meshgrid(r,theta)

X=R.*cos(THETA);

Y=R.*sin(THETA);

Z=3.5*R;

surf(X+8,Y+2,Z)

hold on

%surfnorm(X+8,Y+2,Z)

[U,V,W] = surfnorm(X+8,Y+2,Z);

quiver3(X+8,Y+2,Z,-U,-V,W,0.5);

hold on

phi=[0:pi/50:pi];

theta=[0:pi/35:2*pi];

[THETA,PHI]=meshgrid(theta,phi);

radius=2;

X=radius*sin(PHI).*cos(THETA);

Y=radius*sin(PHI).*sin(THETA);

Z=radius*cos(PHI);

surf(X(1:26,:)+8,Y(1:26,:)+2,Z(1:26,:)+7)

hold on

[U,V,W] = surfnorm(X(1:26,:)+8,Y(1:26,:)+2,Z(1:26,:)+8);

quiver3(X(1:26,:)+8,Y(1:26,:)+2,Z(1:26,:)+7,-U,-V,W,0.5);

xlabel(‘x’)

ylabel(‘y’)

zlabel(‘z’)

print(‘coneWithNormal’,’-dpng’)

clear all

clc

R=2;

fun=@ (r,theta) r.^3.*(7-7/2*r);

Qcone = integral2(fun,0,R,0,2*pi);

fun2=@(r,theta,phi) r.^4.*cos(phi).*sin(phi)

QSphere = integral3(fun2,0,2,0,2*pi,0,pi/2)

Inertia=Qcone+QSphere

fprintf(‘The inertia moment required is:[%d]\n’,Inertia)