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While searching the internet for some books on ordinary differential equations, I came across a link that I believe is very useful for all math students and not only. If you are interested in ODEs, it's worth taking the time to study it.
A First Look at Ordinary Differential Equations by Timothy S. Judson is an excellent resource for anyone looking to understand ODEs better. Here's a brief overview of the main topics covered:
- Introduction to ODEs: Basic concepts, definitions, and initial differential equations.
- Methods of Solution:
- Separable equations
- First-order linear equations
- Exact equations
- Transcendental functions
- Applications of ODEs: Practical examples and applications in various scientific fields.
- Systems of ODEs: Analysis and solutions of systems of differential equations.
- Series and Numerical Methods: Use of series and numerical methods for solving ODEs.
This book provides a clear and comprehensive introduction to ODEs, making it suitable for students and new researchers in mathematics. If you're interested, you can explore the book in more detail here: A First Look at Ordinary Differential Equations.
Many MATLAB enthusiasts come Cody to sharpen their skills, face new challenges, and engage in friendly competition. We firmly believe that learning from peers is one of the most effective ways to grow.
With this in mind, the Cody team is thrilled to unveil a new feature aimed at enriching your learning journey: the Cody Discussion Channel. This space is designed for sharing expertise, acquiring new skills, and fostering connections within our community.
On the Cody homepage, you'll now notice a Discussions section, prominently displaying the four most recent posts. For those eager to contribute, we encourage you to familiarize yourself with our posting guidelines before creating a new post. This will help maintain a constructive and valuable exchange of ideas for everyone involved.
Together, let's create an environment where every member feels empowered to share, learn, and connect.
There are a host of problems on Cody that require manipulation of the digits of a number. Examples include summing the digits of a number, separating the number into its powers, and adding very large numbers together.
If you haven't come across this trick yet, you might want to write it down (or save it electronically):
digits = num2str(4207) - '0'
That code results in the following:
digits =
4 2 0 7
Now, summing the digits of the number is easy:
sum(digits)
ans =
13
Hello and a warm welcome to everyone! We're excited to have you in the Cody Discussion Channel. To ensure the best possible experience for everyone, it's important to understand the types of content that are most suitable for this channel.
Content that belongs in the Cody Discussion Channel:
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- General discussions: Anything else related to Cody that doesn't fit into the above categories.
Content that does not belong in the Cody Discussion Channel:
- Comments on specific Cody problems: Examples include unclear problem descriptions or incorrect testing suites.
- Comments on specific Cody solutions: For example, you find a solution creative or helpful.
Please direct such comments to the Comments section on the problem or solution page itself.
We hope the Cody discussion channel becomes a vibrant space for sharing expertise, learning new skills, and connecting with others.
Spring is here in Natick and the tulips are blooming! While tulips appear only briefly here in Massachusetts, they provide a lot of bright and diverse colors and shapes. To celebrate this cheerful flower, here's some code to create your own tulip!
Hello MATLAB Community!
We've had an exciting few weeks filled with insightful discussions, innovative tools, and engaging blog posts from our vibrant community. Here's a highlight of some noteworthy contributions that have sparked interest and inspired us all. Let's dive in!
Interesting Questions
Cindyawati explores the intriguing concept of interrupting continuous data in differential equations to study the effects of drug interventions in disease models. A thought-provoking question that bridges mathematics and medical research.
Pedro delves into the application of Linear Quadratic Regulator (LQR) for error dynamics and setpoint tracking, offering insights into control systems and their real-world implications.
Popular Discussions
Chen Lin shares an engaging interview with Zhaoxu Liu, shedding light on the creative processes behind some of the most innovative MATLAB contest entries of 2023. A must-read for anyone looking for inspiration!
Zhaoxu Liu, also known as slanderer, updates the community with the latest version of the MATLAB Plot Cheat Sheet. This resource is invaluable for anyone looking to enhance their data visualization skills.
From File Exchange
Giorgio introduces a toolbox for frequency estimation, making it simpler for users to import signals directly from the MATLAB workspace. A significant contribution for signal processing enthusiasts.
From the Blogs
Cleve Moler revisits a classic program for predicting future trends based on census data, offering a fascinating glimpse into the evolution of computational forecasting.
Boost Your App Design Efficiency – Effortless Component Swapping & Labeling in App Designer by Adam Danz
With contributions from Dinesh Kavalakuntla, Adam presents an insightful guide on improving app design workflows in MATLAB App Designer, focusing on component swapping and labeling.
We're incredibly proud of the diverse and innovative contributions our community members make every day. Each post, discussion, and tool not only enriches our knowledge but also inspires others to explore and create. Let's continue to support and learn from each other as we advance in our MATLAB journey.
Happy Coding!
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Drumlin Farm has welcomed MATLAMB, named in honor of MathWorks, among ten adorable new lambs this season!
📚 New Book Announcement: "Image Processing Recipes in MATLAB" 📚
I am delighted to share the release of my latest book, "Image Processing Recipes in MATLAB," co-authored by my dear friend and colleague Gustavo Benvenutti Borba.
This 'cookbook' contains 30 practical recipes for image processing, ranging from foundational techniques to recently published algorithms. It serves as a concise and readable reference for quickly and efficiently deploying image processing pipelines in MATLAB.
Gustavo and I are immensely grateful to the MathWorks Book Program for their support. We also want to thank Randi Slack and her fantastic team at CRC Press for their patience, expertise, and professionalism throughout the process.
___________
I found this plot of words said by different characters on the US version of The Office sitcom. There's a sparkline for each character from pilot to finale episode.
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A high school student called for help with this physics problem:
- Car A moves with constant velocity v.
- Car B starts to move when Car A passes through the point P.
- Car B undergoes...
- uniform acc. motion from P to Q.
- uniform velocity motion from Q to R.
- uniform acc. motion from R to S.
- Car A and B pass through the point R simultaneously.
- Car A and B arrive at the point S simultaneously.
Q1. When car A passes the point Q, which is moving faster?
Q2. Solve the time duration for car B to move from P to Q using L and v.
Q3. Magnitude of acc. of car B from P to Q, and from R to S: which is bigger?
Well, it can be solved with a series of tedious equations. But... how about this?
Code below:
%% get images and prepare stuffs
figure(WindowStyle="docked"),
ax1 = subplot(2,1,1);
hold on, box on
ax1.XTick = [];
ax1.YTick = [];
A = plot(0, 1, 'ro', MarkerSize=10, MarkerFaceColor='r');
B = plot(0, 0, 'bo', MarkerSize=10, MarkerFaceColor='b');
[carA, ~, alphaA] = imread('https://cdn.pixabay.com/photo/2013/07/12/11/58/car-145008_960_720.png');
[carB, ~, alphaB] = imread('https://cdn.pixabay.com/photo/2014/04/03/10/54/car-311712_960_720.png');
carA = imrotate(imresize(carA, 0.1), -90);
carB = imrotate(imresize(carB, 0.1), 180);
alphaA = imrotate(imresize(alphaA, 0.1), -90);
alphaB = imrotate(imresize(alphaB, 0.1), 180);
carA = imagesc(carA, AlphaData=alphaA, XData=[-0.1, 0.1], YData=[0.9, 1.1]);
carB = imagesc(carB, AlphaData=alphaB, XData=[-0.1, 0.1], YData=[-0.1, 0.1]);
txtA = text(0, 0.85, 'A', FontSize=12);
txtB = text(0, 0.17, 'B', FontSize=12);
yline(1, 'r--')
yline(0, 'b--')
xline(1, 'k--')
xline(2, 'k--')
text(1, -0.2, 'Q', FontSize=20, HorizontalAlignment='center')
text(2, -0.2, 'R', FontSize=20, HorizontalAlignment='center')
% legend('A', 'B') % this make the animation slow. why?
xlim([0, 3])
ylim([-.3, 1.3])
%% axes2: plots velocity graph
ax2 = subplot(2,1,2);
box on, hold on
xlabel('t'), ylabel('v')
vA = plot(0, 1, 'r.-');
vB = plot(0, 0, 'b.-');
xline(1, 'k--')
xline(2, 'k--')
xlim([0, 3])
ylim([-.3, 1.8])
p1 = patch([0, 0, 0, 0], [0, 1, 1, 0], [248, 209, 188]/255, ...
EdgeColor = 'none', ...
FaceAlpha = 0.3);
%% solution
v = 1; % car A moves with constant speed.
L = 1; % distances of P-Q, Q-R, R-S
% acc. of car B for three intervals
a(1) = 9*v^2/8/L;
a(2) = 0;
a(3) = -1;
t_BatQ = sqrt(2*L/a(1)); % time when car B arrives at Q
v_B2 = a(1) * t_BatQ; % speed of car B between Q-R
%% patches for velocity graph
p2 = patch([t_BatQ, t_BatQ, t_BatQ, t_BatQ], [1, 1, v_B2, v_B2], ...
[248, 209, 188]/255, ...
EdgeColor = 'none', ...
FaceAlpha = 0.3);
p3 = patch([2, 2, 2, 2], [1, v_B2, v_B2, 1], [194, 234, 179]/255, ...
EdgeColor = 'none', ...
FaceAlpha = 0.3);
%% animation
tt = linspace(0, 3, 2000);
for t = tt
A.XData = v * t;
vA.XData = [vA.XData, t];
vA.YData = [vA.YData, 1];
if t < t_BatQ
B.XData = 1/2 * a(1) * t^2;
vB.XData = [vB.XData, t];
vB.YData = [vB.YData, a(1) * t];
p1.XData = [0, t, t, 0];
p1.YData = [0, vB.YData(end), 1, 1];
elseif t >= t_BatQ && t < 2
B.XData = L + (t - t_BatQ) * v_B2;
vB.XData = [vB.XData, t];
vB.YData = [vB.YData, v_B2];
p2.XData = [t_BatQ, t, t, t_BatQ];
p2.YData = [1, 1, vB.YData(end), vB.YData(end)];
else
B.XData = 2*L + v_B2 * (t - 2) + 1/2 * a(3) * (t-2)^2;
vB.XData = [vB.XData, t];
vB.YData = [vB.YData, v_B2 + a(3) * (t - 2)];
p3.XData = [2, t, t, 2];
p3.YData = [1, 1, vB.YData(end), v_B2];
end
txtA.Position(1) = A.XData(end);
txtB.Position(1) = B.XData(end);
carA.XData = A.XData(end) + [-.1, .1];
carB.XData = B.XData(end) + [-.1, .1];
drawnow
end
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Hey MATLAB Community! 🌟
In the vibrant landscape of our online community, the past few weeks have been particularly exciting. We've seen a plethora of contributions that not only enrich our collective knowledge but also foster a spirit of collaboration and innovation. Here are some of the noteworthy contributions from our members.
Interesting Questions
Victor encountered a puzzling error while trying to publish his script to PDF. His post sparked a helpful discussion on troubleshooting this issue, proving invaluable for anyone facing similar challenges.
Devendra's inquiry into interpolating and smoothing NDVI time series using MATLAB has opened up a dialogue on various techniques to manage noisy data, benefiting researchers and enthusiasts in the field of remote sensing.
Popular Discussions
Adam Danz's AMA session has been a treasure trove of insights into the workings behind the MATLAB Answers forum, offering a unique perspective from a staff contributor's viewpoint.
The User Following feature marks a significant enhancement in how community members can stay connected with the contributions of their peers, fostering a more interconnected MATLAB Central.
From File Exchange
Robert Haaring's submission is a standout contribution, providing a sophisticated model for CO2 electrolysis, a topic of great relevance to researchers in environmental technology and chemical engineering.
From the Blogs
Verification and Validation for AI: From model implementation to requirements validation by Sivylla Paraskevopoulou
Sivylla's comprehensive post delves into the critical stages of AI model development, from implementation to validation, offering invaluable guidance for professionals navigating the complexities of AI verification.
In this engaging Q&A, Ned Gulley introduces us to Zhaoxu Liu, a remarkable community member whose innovative contributions and active engagement have left a significant impact on the MATLAB community.
Each of these contributions highlights the diverse and rich expertise within our community. From solving complex technical issues to introducing new features and sharing in-depth knowledge on specialized topics, our members continue to make MATLAB Central a vibrant and invaluable resource.
Let's continue to support, inspire, and learn from one another
Don't use / What are Projects?
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Updating some of my educational Livescripts to 2024a, really love the new "define a function anywhere" feature, and have a "new" idea for improving Livescripts -- support "hidden" code blocks similar to the Jupyter Notebooks functionality.
For example, I often create "complicated" plots with a bunch of ancillary items and I don't want this code exposed to the reader by default, as it might confuse the reader. For example, consider a Livescript that might read like this:
-----
Noting the similar structure of these two mappings, let's now write a function that simply maps from some domain to some other domain using change of variable.
function x = ChangeOfVariable( x, from_domain, to_domain )
x = x - from_domain(1);
x = x * ( ( to_domain(2) - to_domain(1) ) / ( from_domain(2) - from_domain(1) ) );
x = x + to_domain(1);
end
Let's see this function in action
% HIDE CELL
clear
close all
from_domain = [-1, 1];
to_domain = [2, 7];
from_values = [-1, -0.5, 0, 0.5, 1];
to_values = ChangeOfVariable( from_values, from_domain, to_domain )
to_values = 1×5
2.0000 3.2500 4.5000 5.7500 7.0000
We can plot the values of from_values and to_values, showing how they're connected to each other:
% HIDE CELL
figure
hold on
for n = 1 : 5
plot( [from_values(n) to_values(n)], [1 0], Color="k", LineWidth=1 )
end
ax = gca;
ax.YTick = [];
ax.XLim = [ min( [from_domain, to_domain] ) - 1, max( [from_domain, to_domain] ) + 1 ];
ax.YLim = [-0.5, 1.5];
ax.XGrid = "on";
scatter( from_values, ones( 5, 1 ), Marker="s", MarkerFaceColor="flat", MarkerEdgeColor="k", SizeData=120, LineWidth=1, SeriesIndex=1 )
text( mean( from_domain ), 1.25, "$\xi$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
scatter( to_values, zeros( 5, 1 ), Marker="o", MarkerFaceColor="flat", MarkerEdgeColor="k", SizeData=120, LineWidth=1, SeriesIndex=2 )
text( mean( to_domain ), -0.25, "$x$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
scaled_arrow( ax, [mean( [from_domain(1), to_domain(1) ] ) - 1, 0.5], ( 1 - 0 ) / ( from_domain(1) - to_domain(1) ), 1 )
scaled_arrow( ax, [mean( [from_domain(end), to_domain(end)] ) + 1, 0.5], ( 1 - 0 ) / ( from_domain(end) - to_domain(end) ), -1 )
text( mean( [from_domain(1), to_domain(1) ] ) - 1.5, 0.5, "$x(\xi)$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
text( mean( [from_domain(end), to_domain(end)] ) + 1.5, 0.5, "$\xi(x)$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
-----
Where scaled_arrow is some utility function I've defined elsewhere... See how a majority of the code is simply "drivel" to create the plot, clear and close? I'd like to be able to hide those cells so that it would look more like this:
-----
Noting the similar structure of these two mappings, let's now write a function that simply maps from some domain to some other domain using change of variable.
function x = ChangeOfVariable( x, from_domain, to_domain )
x = x - from_domain(1);
x = x * ( ( to_domain(2) - to_domain(1) ) / ( from_domain(2) - from_domain(1) ) );
x = x + to_domain(1);
end
Let's see this function in action
▶ Show code cell
from_domain = [-1, 1];
to_domain = [2, 7];
from_values = [-1, -0.5, 0, 0.5, 1];
to_values = ChangeOfVariable( from_values, from_domain, to_domain )
to_values = 1×5
2.0000 3.2500 4.5000 5.7500 7.0000
We can plot the values of from_values and to_values, showing how they're connected to each other:
▶ Show code cell
-----
Thoughts?
I recently had issues with code folding seeming to disappear and it turns out that I had unknowingly disabled the "show code folding margin" option by accident. Despite using MATLAB for several years, I had no idea this was an option, especially since there seemed to be no references to it in the code folding part of the "Preferences" menu.
It would be great if in the future, there was a warning that told you about this when you try enable/disable folding in the Preferences.
I am using 2023b by the way.
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In the MATLAB editor, when clicking on a variable name, all the other instances of the variable name will be highlighted.
But this does not work for structure fields, which is a pity. Such feature would be quite often useful for me.
I show an illustration below, and compare it with Visual Studio Code that does it. ;-)
I am using MATLAB R2023a, sorry if it has been added to newer versions, but I didn't see it in the release notes.
Welcome to MATLAB Central's first Ask Me Anything (AMA) session! Over the next few weeks, I look forward to addressing any questions or curiosities you might have about MATLAB, the forum, sasquatches, or whatever's on your mind. Having volunteered as a contributor to this community before joining MathWorks, I'm excited to act as a bridge between these two worlds. Let's kick things off by sharing a little-known fact about the forum’s staff contributors!
A couple of years ago, before I joined MathWorks as a developer on the Graphics and Charting team, I often wondered who were the MathWorkers with the [staff] moniker answering questions in the Answers forum. Is their MATLAB Central activity part of their day-to-day job expectations? Do they serve specific roles on some kind of community outreach team? Is their work in the forum voluntary in the same way that non-staff contributors volunteer their time?
Now that I'm on the inside, I'd like to share a secret with my fellow MATLAB users and MATLAB Central enthusiasts: with the exception of the MathWorks Support Team, staff participation in the Answers forum is completely voluntary! The staff contributions you see in the forum arise from pure intrinsic motivation to connect with users, help people out of ruts, and spread the word about our product!
For example, Steven Lord has contributed 20-150 answers per month for 9 years! Steven is a quality engineer for core MATLAB numerical functions. Cris LaPierre develops training material and has been a faithful contributor in the forum for almost 6 years! Kojiro Saito and Akira Agata have been tackling Japanese content for more than 7 years! There are many others who have inspired me as a user, and I am honored to now call colleagues: Peter Perkins, Michio, Joss Knight, Alan Weiss, Jiro Doke, Edric Ellis, and many others who deserve appreciation.
The forum's success hinges on the invaluable contributions from the majority of non-staff volunteers, whose dedication and expertise fuel our community. But I know I wasn't alone in wondering about these staff contributors, so now you're in on the secret!
I'm curious to know what other topics you're interested in learning about. Ask me anything!
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