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The line integral 
, where C is the boundary of the square 
oriented counterclockwise, can be evaluated in two ways:
, where C is the boundary of the square oriented counterclockwise, can be evaluated in two ways: Using the definition of the line integral:
% Initialize the integral sum
integral_sum = 0;
% Segment C1: x = -1, y goes from -1 to 1
y = linspace(-1, 1);
x = -1 * ones(size(y));
dy = diff(y);
integral_sum = integral_sum + sum(-x(1:end-1) .* dy);
% Segment C2: y = 1, x goes from -1 to 1
x = linspace(-1, 1);
y = ones(size(x));
dx = diff(x);
integral_sum = integral_sum + sum(y(1:end-1).^2 .* dx);
% Segment C3: x = 1, y goes from 1 to -1
y = linspace(1, -1);
x = ones(size(y));
dy = diff(y);
integral_sum = integral_sum + sum(-x(1:end-1) .* dy);
% Segment C4: y = -1, x goes from 1 to -1
x = linspace(1, -1);
y = -1 * ones(size(x));
dx = diff(x);
integral_sum = integral_sum + sum(y(1:end-1).^2 .* dx);
disp(['Direct Method Integral: ', num2str(integral_sum)]);
Plotting the square path
% Define the square's vertices
vertices = [-1 -1; -1 1; 1 1; 1 -1; -1 -1];
% Plot the square
figure;
plot(vertices(:,1), vertices(:,2), '-o');
title('Square Path for Line Integral');
xlabel('x');
ylabel('y');
grid on;
axis equal;
% Add arrows to indicate the path direction (counterclockwise)
hold on;
for i = 1:size(vertices,1)-1
% Calculate direction
dx = vertices(i+1,1) - vertices(i,1);
dy = vertices(i+1,2) - vertices(i,2);
% Reduce the length of the arrow for better visibility
scale = 0.2;
dx = scale * dx;
dy = scale * dy;
% Calculate the start point of the arrow
startx = vertices(i,1) + (1 - scale) * dx;
starty = vertices(i,2) + (1 - scale) * dy;
% Plot the arrow
quiver(startx, starty, dx, dy, 'MaxHeadSize', 0.5, 'Color', 'r', 'AutoScale', 'off');
end
hold off;
Apply Green's Theorem for the line integral
% Define the partial derivatives of P and Q
f = @(x, y) -1 - 2*y; % derivative of -x with respect to x is -1, and derivative of y^2 with respect to y is 2y
% Compute the double integral over the square [-1,1]x[-1,1]
integral_value = integral2(f, -1, 1, 1, -1);
disp(['Green''s Theorem Integral: ', num2str(integral_value)]);
Plotting the vector field related to Green’s theorem
% Define the grid for the vector field
[x, y] = meshgrid(linspace(-2, 2, 20), linspace(-2 ,2, 20));
% Define the vector field components
P = y.^2; % y^2 component
Q = -x; % -x component
% Plot the vector field
figure;
quiver(x, y, P, Q, 'b');
hold on; % Hold on to plot the square on the same figure
% Define the square's vertices
vertices = [-1 -1; -1 1; 1 1; 1 -1; -1 -1];
% Plot the square path
plot(vertices(:,1), vertices(:,2), '-o', 'Color', 'k'); % 'k' for black color
title('Vector Field (P = y^2, Q = -x) with Square Path');
xlabel('x');
ylabel('y');
axis equal;
% Add arrows to indicate the path direction (counterclockwise)
for i = 1:size(vertices,1)-1
% Calculate direction
dx = vertices(i+1,1) - vertices(i,1);
dy = vertices(i+1,2) - vertices(i,2);
% Reduce the length of the arrow for better visibility
scale = 0.2;
dx = scale * dx;
dy = scale * dy;
% Calculate the start point of the arrow
startx = vertices(i,1) + (1 - scale) * dx;
starty = vertices(i,2) + (1 - scale) * dy;
% Plot the arrow
quiver(startx, starty, dx, dy, 'MaxHeadSize', 0.5, 'Color', 'r', 'AutoScale', 'off');
end
hold off;
To solve a surface integral for example the
over the sphere 
easily in MATLAB, you can leverage the symbolic toolbox for a direct and clear solution. Here is a tip to simplify the process:
over the sphere easily in MATLAB, you can leverage the symbolic toolbox for a direct and clear solution. Here is a tip to simplify the process:- Use Symbolic Variables and Functions: Define your variables symbolically, including the parameters of your spherical coordinates θ and ϕ and the radius r . This allows MATLAB to handle the expressions symbolically, making it easier to manipulate and integrate them.
- Express in Spherical Coordinates Directly: Since you already know the sphere's equation and the relationship in spherical coordinates, define x, y, and z in terms of r , θ and ϕ directly.
- Perform Symbolic Integration: Use MATLAB's `int` function to integrate symbolically. Since the sphere and the function
are symmetric, you can exploit these symmetries to simplify the calculation.
Here’s how you can apply this tip in MATLAB code:
% Include the symbolic math toolbox
syms theta phi
% Define the limits for theta and phi
theta_limits = [0, pi];
phi_limits = [0, 2*pi];
% Define the integrand function symbolically
integrand = 16 * sin(theta)^3 * cos(phi)^2;
% Perform the symbolic integral for the surface integral
surface_integral = int(int(integrand, theta, theta_limits(1), theta_limits(2)), phi, phi_limits(1), phi_limits(2));
% Display the result of the surface integral symbolically
disp(['The surface integral of x^2 over the sphere is ', char(surface_integral)]);
% Number of points for plotting
num_points = 100;
% Define theta and phi for the sphere's surface
[theta_mesh, phi_mesh] = meshgrid(linspace(double(theta_limits(1)), double(theta_limits(2)), num_points), ...
linspace(double(phi_limits(1)), double(phi_limits(2)), num_points));
% Spherical to Cartesian conversion for plotting
r = 2; % radius of the sphere
x = r * sin(theta_mesh) .* cos(phi_mesh);
y = r * sin(theta_mesh) .* sin(phi_mesh);
z = r * cos(theta_mesh);
% Plot the sphere
figure;
surf(x, y, z, 'FaceColor', 'interp', 'EdgeColor', 'none');
colormap('jet'); % Color scheme
shading interp; % Smooth shading
camlight headlight; % Add headlight-type lighting
lighting gouraud; % Use Gouraud shading for smooth color transitions
title('Sphere: x^2 + y^2 + z^2 = 4');
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
colorbar; % Add color bar to indicate height values
axis square; % Maintain aspect ratio to be square
view([-30, 20]); % Set a nice viewing angle
I am often talking to new MATLAB users. I have put together one script. If you know how this script works, why, and what each line means, you will be well on your way on your MATLAB learning journey.
% Clear existing variables and close figures
clear;
close all;
% Print to the Command Window
disp('Hello, welcome to MATLAB!');
% Create a simple vector and matrix
vector = [1, 2, 3, 4, 5];
matrix = [1, 2, 3; 4, 5, 6; 7, 8, 9];
% Display the created vector and matrix
disp('Created vector:');
disp(vector);
disp('Created matrix:');
disp(matrix);
% Perform element-wise multiplication
result = vector .* 2;
% Display the result of the operation
disp('Result of element-wise multiplication of the vector by 2:');
disp(result);
% Create plot
x = 0:0.1:2*pi; % Generate values from 0 to 2*pi
y = sin(x); % Calculate the sine of these values
% Plotting
figure; % Create a new figure window
plot(x, y); % Plot x vs. y
title('Simple Plot of sin(x)'); % Give the plot a title
xlabel('x'); % Label the x-axis
ylabel('sin(x)'); % Label the y-axis
grid on; % Turn on the grid
disp('This is the end of the script. Explore MATLAB further to learn more!');
More than 500,000 people have subscribed to the MATLAB channel. MathWorks would like to thank everyone who has taken the time to watch one of our videos, leave us a comment, or share our videos with others. Together we’re accelerating the pace of engineering and science.
I keep getting this error, what do I do?
Error: File: convert_mnist_to_mat.m Line: 63 Column: 1
This statement is not inside any function.
(It follows the END that terminates the definition of the function
"read_mnist_labels".)
function convert_mnist_to_mat(mnist_dir, output_file)
% Function to convert MNIST dataset files into .mat format
% Check if the directory exists
if ~isfolder(mnist_dir)
error('MNIST directory does not exist.');
end
% Read training images
train_images = read_mnist_images(fullfile(mnist_dir, 'train-images-idx3-ubyte'));
% Read training labels
train_labels = read_mnist_labels(fullfile(mnist_dir, 'train-labels-idx1-ubyte'));
% Read test images
test_images = read_mnist_images(fullfile(mnist_dir, 't10k-images-idx3-ubyte'));
% Read test labels
test_labels = read_mnist_labels(fullfile(mnist_dir, 't10k-labels-idx1-ubyte'));
% Save data into .mat file
save(output_file, 'train_images', 'train_labels', 'test_images', 'test_labels');
disp('MNIST dataset converted successfully.');
end
function images = read_mnist_images(filename)
% Function to read MNIST image data
fid = fopen(filename, 'rb');
assert(fid ~= -1, ['Could not open ', filename, '']);
magic_number = fread(fid, 1, 'int32', 0, 'ieee-be');
assert(magic_number == 2051, ['Invalid magic number in ', filename]);
num_images = fread(fid, 1, 'int32', 0, 'ieee-be');
num_rows = fread(fid, 1, 'int32', 0, 'ieee-be');
num_cols = fread(fid, 1, 'int32', 0, 'ieee-be');
images = fread(fid, [num_rows, num_cols, num_images], 'uint8');
fclose(fid);
images = permute(images, [2, 1, 3]); % Convert from (rows, cols, images) to (cols, rows, images)
end
function labels = read_mnist_labels(filename)
% Function to read MNIST label data
fid = fopen(filename, 'rb');
assert(fid ~= -1, ['Could not open ', filename, '']);
magic_number = fread(fid, 1, 'int32', 0, 'ieee-be');
assert(magic_number == 2049, ['Invalid magic number in ', filename]);
num_labels = fread(fid, 1, 'int32', 0, 'ieee-be');
labels = fread(fid, [num_labels, 1], 'uint8');
fclose(fid);
end
% Usage example:
mnist_dir = 'C:\Users\gabep\Desktop\MNIST';
output_file = 'mnist_dataset.mat';
convert_mnist_to_mat(mnist_dir, output_file);
Hi All,
I'm trying to produce some nice figures from the graphical user interface and have a set of local sensitivity analyses that I'd like to combine.
I have two inputs that vary the sensitivies of my system and would like to plot them on top of each other like:
Is there either a way to do this natively in simbiology (when you try and use 'keep results from each run' it plots them both as a time series) or to export the sensitivity data to the normal matlab programatic UI where I can combine them by hand?
Thank you for your help!
Hi everyone, I need help for transfering the data from a ThingSpeak' channel to Google Sheets. Please help me.
Suppose I want to use tiledlayout to draw a 4*6 figure. Now I want to let the first and second row of figures share the same ylabels, and so do the third and the fourth. But I did not find a way to do this. I tried to create two different tiledlayout on one figure, but tiledlayout did not allow me to do so. Thus, any suggestions?
Englisch Translate Französisch Deutsch Deutsch Russisch PONS Deepl übersetzer Spanisch Deutsch DeepL kostenlos Deutsch Englisch hallo, ich bitte um Hilfe! Seit Jahren habe ich Konto auf Thingspeak, den ich für meinen Zweck nicht richtig nutzen kann. Ich kann "Upoad to meine private Chanel", aber das lesen funktioniert nicht, weder in ArdunioIDE, noch Ardunio iot kann ich die gesendete Daten (Temperatur) von einem anderen Board lesen, es ist egal, ob ESP8266, ESP32, MKR, oder UnoWifi Rev2. Nichts! Die Beispiele im Bibliotek sind eine Katastrophe, "wetter-chanel" und diese funktionieren auch nicht. Auch nicht die von GitHub. Es sollte aber einfach sein, denn auf meiner Seite sehe ich ja "GET"+ url. inkl json+result.
Wo gibt es eine richtige sketch für "read private chanel/field" , welche funktioniert? Man braucht nicht die Wifi-Enstellungen, sondern den code für die Abfrage, "Serial.print"(value)"
Bitte um Hilfe, danke schön.
hello, I ask for help! I've had an account on Thingspeak for years, but I can't use it properly for my purpose. I can "Upoad to my private Chanel", but reading doesn't work, neither in ArdunioIDE nor Ardunio iot can I read the sent data (temperature) from another board, it doesn't matter whether ESP8266, ESP32, MKR, or UnoWifi Rev2. Nothing! The examples in the library are a disaster, "weather-chanel" and they don't work either. Not even the one from GitHub. But it should be easy, because on my site I see “GET”+ url. including json+result.
Where is there a proper sketch for "read private chanel/field" that works? You don't need the WiFi settings, but the code for the query, "Serial.print"(value)"
Please help, thank you very much.
Hello Everyone,
I'm running an IoT project at my university using a free . Basically, my system uploads the sensor data to 4 different fields of a ThingSpeak channel and I'm reading from or writing to the channel through Simulink. I have a few questions regarding this topic:
- I'm trying to upload to the server every 3 seconds (which seemed to be providing the best results so far). Since the channel only accepts data transmit every 15 seconds, what is the optimized upload interval rate to match the interval rate of the channel? Because otherwise I have realized that my interval rate can go up to 1min sometimes for some reason.
- Is reading from/writing to the channel through simulink while the system is uploading data to the channel slow down th whole process? What is your overall suggestion in this case?
I'm excited to hear your suggestions and experiences!
Regards,
Ege
I would like to propose the creation of MATLAB EduHub, a dedicated channel within the MathWorks community where educators, students, and professionals can share and access a wealth of educational material that utilizes MATLAB. This platform would act as a central repository for articles, teaching notes, and interactive learning modules that integrate MATLAB into the teaching and learning of various scientific fields.
Key Features:
1. Resource Sharing: Users will be able to upload and share their own educational materials, such as articles, tutorials, code snippets, and datasets.
2. Categorization and Search: Materials can be categorized for easy searching by subject area, difficulty level, and MATLAB version..
3. Community Engagement: Features for comments, ratings, and discussions to encourage community interaction.
4. Support for Educators: Special sections for educators to share teaching materials and track engagement.
Benefits:
- Enhanced Educational Experience: The platform will enrich the learning experience through access to quality materials.
- Collaboration and Networking: It will promote collaboration and networking within the MATLAB community.
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By establishing MATLAB EduHub, I propose a space where knowledge and experience can be freely shared, enhancing the educational process and the MATLAB community as a whole.
In one line of MATLAB code, compute how far you can see at the seashore. In otherwords, how far away is the horizon from your eyes? You can assume you know your height and the diameter or radius of the earth.
Keep calm and study PDEs
Product Models:LPS8N dragino
Firmware Version: lgw--build-v5.4.1704801796-20240109-2005
Hi all
at the moment i can not work with CODE dragino lora to gateway LPS8N and MQTT thingSpeak.
with root commands i can send DATA to thingspeak
mosquito_pub -d -h mqtt3.thingspeak.com -p 1883 -u PSoyJxYWBTQ9Hx8cExMZ... -I PSoyJxYWBTQ9Hx8cExM.... -P hCEd77jdiziYzUV6ygl.... -t channels/2466703/publish -m “field1=100&field2=100&status=MQTTPUBLISH”
so my question there anybody that can work with LPS8N dragino to MQTT ThingSpeak? which code arduino are using?
thanks in advance to answer.
Nelson
Me at the beginning of every meeting
A bit late. Compliments to Chris for sharing.
Hey MATLAB Community! 🌟
March has been bustling with activity on MATLAB Central, bringing forth a treasure trove of insights, innovations, and fun. Whether you're delving into the intricacies of spline conversions or seeking inspiration from Pi Day celebrations, there's something for everyone.
Here’s a roundup of the top posts from the past few weeks that you won't want to miss:
Interesting questions
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Explore the challenges and solutions in tuning autopilot gains within a non-linear model of a business jet aircraft.
Popular discussions
Celebrate Pi Day with cool MATLAB implementations and code. A delightful read filled with π-inspired creativity.
Get a glimpse of fun with MATLAB through an engaging visual shared by Athanasios. A light-hearted thread that showcases the fun side of mathematics.
From File Exchange
Unlock the secrets of global climate data with MATLAB. This thread offers tools and insights for analyzing precipitation variability.
Interact with a numerical puddle in real-time and explore the dynamics of disturbances. A fascinating exploration of fluid dynamics simulation.
From the Blogs
Revisit Pi Day with Jiro's picks of the coolest π visualizations. A post that combines art, math, and the joy of exploration.
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These threads are just the tip of the iceberg. Each post is a gateway to new knowledge, ideas, and community connections. Dive in, explore, and don't forget to contribute your insights and questions. Together, we make MATLAB Central a vibrant hub of innovation and support.
Happy Coding!
sort(v)
8%
unique(v)
16%
union(v, [ ])
17%
intersect(v, v)
14%
setdiff(v, [ ])
12%
All return sorted output
33%
1193 votes
can you relate?
I am considering to use ThingSpeak for my use case which is electric motor drive where I want to do a predictive maintanace for.
Is it possible to use ThingSpeak to develop and evaluate the AI/ML model for such purpose and the deploy on realtime microcontroller?
