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Two Squared
Philippines
Приєднався 25 вер 2023
DIFFERENTIAL EQUATIONS explained in 21 Minutes
This video aims to provide what I think are the most important details that are usually discussed in an elementary ordinary differential equations (ODE) course, in just about 21 minutes. Simple examples are also provided (I, as an applied physics major, yearn for examples.).
This video is divided into five chapters.
CHAPTER 1: INTRODUCTION
0:00 1.1: Definition
0:30 1.2: Ordinary vs. Partial Differential Equations
1:24 1.3: Solutions to ODEs
2:49 1.4: Applications and Examples
CHAPTER 2: FIRST ORDER DIFFERENTIAL EQUATIONS
3:14 2.1: Separable Differential Equations
4:10 2.2: Exact Differential Equations
6:01 2.3: Linear Differential Equations and the Integrating Factor
CHAPTER 3: HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
7:57 3.1: Theory of Higher Order Differential Equations
10:43 3.2: Homogeneous Equations with Constant Coefficients
13:04 3.3: Method of Undetermined Coefficients
14:44 3.4: Variation of Parameters
CHAPTER 4: LAPLACE TRANSFORM
16:18 4.1: Laplace and Inverse Laplace Transforms
17:41 4.2: Solving Differential Equations using Laplace Transform
CHAPTER 5: SUMMARY
19:15 5.1: Overview of Advanced Topics
20:28 5.2: Conclusion
This video is designed to be beginner-friendly and focuses on finding analytical solutions to ODEs, since ngl these are the topics that my ODE class covered and the ones that I can explain confidently. 3Blue1Brown's video on ODEs offers a more intuitive and geometric approach to the topic.
This video is animated using Manim, a Python math animation engine developed by 3Blue1Brown. Voice-overs are provided by me.
Feel free to suggest improvements, and point out the possible mistakes I have made in this video. I hope this video is helpful for understanding at least the basic concepts in ODEs. Please subscribe and support this small channel for more uploads!
This video is divided into five chapters.
CHAPTER 1: INTRODUCTION
0:00 1.1: Definition
0:30 1.2: Ordinary vs. Partial Differential Equations
1:24 1.3: Solutions to ODEs
2:49 1.4: Applications and Examples
CHAPTER 2: FIRST ORDER DIFFERENTIAL EQUATIONS
3:14 2.1: Separable Differential Equations
4:10 2.2: Exact Differential Equations
6:01 2.3: Linear Differential Equations and the Integrating Factor
CHAPTER 3: HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
7:57 3.1: Theory of Higher Order Differential Equations
10:43 3.2: Homogeneous Equations with Constant Coefficients
13:04 3.3: Method of Undetermined Coefficients
14:44 3.4: Variation of Parameters
CHAPTER 4: LAPLACE TRANSFORM
16:18 4.1: Laplace and Inverse Laplace Transforms
17:41 4.2: Solving Differential Equations using Laplace Transform
CHAPTER 5: SUMMARY
19:15 5.1: Overview of Advanced Topics
20:28 5.2: Conclusion
This video is designed to be beginner-friendly and focuses on finding analytical solutions to ODEs, since ngl these are the topics that my ODE class covered and the ones that I can explain confidently. 3Blue1Brown's video on ODEs offers a more intuitive and geometric approach to the topic.
This video is animated using Manim, a Python math animation engine developed by 3Blue1Brown. Voice-overs are provided by me.
Feel free to suggest improvements, and point out the possible mistakes I have made in this video. I hope this video is helpful for understanding at least the basic concepts in ODEs. Please subscribe and support this small channel for more uploads!
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Dam, nice work but now time for calculus 2 😶🌫🥲
Thank you i will always use this to revise differential Equations
Amazing content, however it whould be nice if you added some background music
Nice
I didn’t know that guy before and he is SEVERELY underrated
This video seems to be getting picked up by the UA-cam algorithm (which puts a smile in my face ngl ❤). Thanks for all the feedback and topic suggestions! Just some notes with this video. I was inspired to make this video by 3Blue1Brown's comment on his tour to differential equations video: "I hope you enjoy the tour, but at the same time know that it is, by design, very different from taking courses on the subject." I intended to make this video to be a simple guide / overview for those who will take an ODE course or to those who just want to learn ODEs from scratch. It is almost always the case that when you take an ODE course, you first learn the methods on how to solve them even if they might be considered useless in practical situations (since you can just let the computer do all the solving). However, taking an ODE course can be tough, since in my university, quite a number of students struggle a lot and fail. I recommend you watch this video for the purpose of improving your problem-solving skills, and then you watch 3Blue1Brown's video to capture the essence of ODEs visually. For future topics, I can consider other math disciplines such as linear algebra, complex analysis (after taking this course), PDEs, or even vector analysis, but no guarantees for now since I did this video with my free time and I am about to enter another gruesome semester in my university 💀 but always stay tuned and subscribe to support this side hustle of mine!! :))
I just wanted to say at 3:53 it's important to note that because of the absolute value sign, the 2nd C is actually equal to +/- e^C, just a small not, but the video is great!
hey brother, will you consider posting source code for the video like 3b1b does, as there are enthusiast people like me waiting for something to implement our knowledge on 🙂
Absolutely amazing. I've never seen someone cover this topic in such a clear, concise, and understandable way. Could you please consider doing a simular video to this one about topics covered in vector calculus or linear algebra?
i feel like the style is completely ripped off from 3b1b 🫤
I wish ODE course was one third of its total time. A little too easy for undergrads. But adding intuitive sude would be fascinating
If the focus is more on pure math, there should be more geometric content and stuff about dynamical systems. The techniques used to solve ODEs analytically are useless in the wild.
Differential equations explained in 21 minutes, now that’s efficiency! This video made me feel like I could tackle anything. It’s amazing how much you can achieve with the right examples and tools like SolutionInn for extra support.
Absolutely amazing. Waiting for a similar video for PDEs ❤
Waiting for when he'll reach topology
Just read the manga.
@imnimbusy2885 the WHAT
There's a manga guide to topology?
Fun fact: I made a video (link: ua-cam.com/video/DuM9teNNsys/v-deo.html) for my math project in my university that mentioned the very basic concepts of topology. But I'm majoring in applied physics (and topology classes are not offered at my uni), so it is unlikely that I will be able to have the rigor needed to properly explain the topic in-depth :< But maybe quantum mechanics instead? Who knows!
@TwoSquaredYT yayyyuy quantum mechanics!!
Nice!
Let's when this channel will boom
I can feel it in 3 months after this
idk rn
Very cool video about some advanced math Im just starting on
You did not even gave a geometric proof for lim x to 0 of sinx/x? This is covered in every book of anal
And that's is just a university project. Envy and blessings to you. Like + subscribe!
No, This is Patrick
1000th subsciber!
Loved the video!! I have a suggestion, make a few videos on Discrete mathematics or combinatorics.
no this is a donut
I subbed just off the thumbnail 👍🏼. Love the video, awesome animations.
Topology mentioned 🔥🔥🔥🗣️🗣️🗣️🗣️📢📢📢📢📢💯💯💯💯💯💯
Cool
This video could have been much shorter and started off more user-friendly at the beginning. The transitions could have been much smoother rather than jumping onto "here is the squeeze theorem" or "here is the mean value theorem".
Man I can’t appreciate you enough this vid helped my enormously thx from the bottom of my heart
Excellent video
Algo bien.
skibidi toilt
Best video
0:16 the function has variable n but in the table, values of x are being taken
Nerd
Consider it as lim(n->x) and it works haha
blinks eye* teacher :
There is one minute left for the midterm, I hope this will help.
question, in @0:22, isn't the derivative of x^3+1 equal to 3x^2? why does it have 1 as a numerator? pls correctly me if I'm wrong
It's just getting the dx from du: du = 3x^2 dx, then you find dx by equating dx = du/3x^2, then dx = 1/3x^2 du
Multiply by 1 in a fancy way, to make 3*x^2 appear as your outside function, so the derivative of the inside function, appears multiplied out in front of the outer function. Given: integral x^2*(x^3 + 1)^100 dx The inner function is x^3 + 1, and its derivative is 3*x^2. We *almost* have 3*x^2 appearing out in front, so we multiply by 1/3*3, which is equivalent to 1, to make it appear. This gives us integral 1/3*3*x^2*(x^3 + 1)^100 dx The 1/3 is just a constant, so it can be pulled out in front. 1/3*integral 3*x^2 * (x^3 + 1)^100 dx Letting u=x^3 + 1, we get u^100, with the 3*x^2 dx becoming du.