I am currently taking honors calculus in senior year of high school. I do not think I will be able to go over this before the end of the year with our curriculum’s pacing. That said, I wanted to get a leg up on my classmates and better myself even if it is only for a moment. This explanation was extremely understandable, interesting, and engaging for someone like me and I have ADHD! Thank you so much!
I deal with hydraulics/fluid dynamics. What must be done BEFORE DOING ANYTHING is finding a model of the system that can generate the positions, velocities and accelerations as a function of time. System identification is key. Then one can generate positions, velocities and accelerations as function of a control signal. This is the FIRST step. Now Euler's method can be used. What wasn't pointed out in the video is that a better approximation of the derivative or slope can be found by using the current slow and the slope at the next step and then averaging the two to provide a better slope. This increase the accuracy significantly but it requires twice as many steps. BUT WAIT! There's more!. There is a method called Runge-Kutta, RK4, that makes 4 evaluations per step but it increase the accuracy even more. There is even a RK45. Although RK4 takes 4 times evaluations per step the steps can be 10 time bigger and still have the same accuracy so the reduction in the number of evaluation drops by about 40%. In German eu is pronounced like oy. Von Steuben has his name butchered all the time.
I’m only in eighth grade and I’m only 13 and I really don’t understand this. I also do regular math for 8th grade which is only pre algebra. However I wish to be as smart and even smarter than gifted minds like Katherine Johnson. I honesty watch these videos and I’m heavily inspired by these videos even though I don’t understand mostly anything in this video. Honestly most intelligently gifted people would be able to understand this by my age but I really don’t. Anyways my real question is would you have any advice on how to learn stuff like this but ahead of time? I really wish I was as smart as people like you at the age I am Now because the ability to learn is a great gift by god and it shall not be wasted. And I don’t expect to be anywhere near as smart as you are right now I’d just like to hear any advice you’d may have for young people like me who are inspired to learn and how to learn ahead of their age if you understand what I mean
I recommend you to study basic calculus (understanding the basic meaning of differentiation, basic differentiation, basic integration and etc.) first before attempting to understand the contents of this video. This video is about Euler's method which is one of the methods used to solve differential equations. To understand the differential equation and Euler's method well, it is essential to have a firm understanding of basic calculus. Of course, you first need to have a firm understanding of algebra to understand calculus well. I understand that you are eagerly wanting to get ahead of your classmates in mathematics and you are passionate about it too, but you need to understand that the set curriculum is there for a reason. Following the curriculum step by step will be the best and hopefully the fastest way to get you a firm base for mathematics. Don't skip steps, but try to follow the steps one by one. If you are passionate about it and find it interesting, I am sure that you will be able to follow these steps faster than all your classmates, and master mathematics. I hope this helps, Good luck! -From random G12 highschooler
Math is extremely linear. Keep learning math and don’t try and be a math genius at 13. If you really love mathematics and are interested, just keep going and you’ll enjoy learning. People like Katherine Johnson and Terrence Tao are very gifted but also had to work hard. You can’t learn algebra without knowing pre algebra, and you can’t know calc without knowing trig and basic geometry/math. Also, studying some physics is cool too. It’s basically applied math and calculus was literally invented to solve physics problems
Daniel, I really appreciate the time and effort and care that you put into this. But that said, I disagree with your principal recommendation. Calculus is absolutely NOT necessary for the understanding of these videos. The whole strategy of our class, and our book "Modeling Life", is that you can understand differential equations without calculus!! I know that can sound crazy, but it's true. Many many fine young minds are lost to science because they never could master the pet tricks, the procedure-based approach that is the standard calculus class. I suspect luvyz might be one of those.
If you're interested in calculus, this series on the fundamentals of calculus is a great place to start! ruclips.net/p/PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
After scavenging RUclips for anyone who was able to dumb-down Euler’s method for me to understand, I have finally found it. Thank you!
hah hah, that's a huge compliment! thanks!
man he is such as brilliant professor..I now remember why I loved calculus 1,2 and advanced at University of Padua and miss these classes
I am currently taking honors calculus in senior year of high school. I do not think I will be able to go over this before the end of the year with our curriculum’s pacing. That said, I wanted to get a leg up on my classmates and better myself even if it is only for a moment. This explanation was extremely understandable, interesting, and engaging for someone like me and I have ADHD! Thank you so much!
thank YOU so much, kiser!
Thank you for sharing this information, very well explained!!
What a beautiful explanation. Thank you Prof.
🙏Nicely explained...Had heared EULERS METHOD in Movie HIDDEN FIGURES and now I was able to understand in detail
Very good explanation, thank you Professor.
I have no doubt that Euler is one among the gods in heaven as he keeps blessing us until this day.
Well…Madhavan of Kerala School on Mathematics (India)… did work on infinite series in 14th century… long before Euler
If we don't know the formula for the red curve, how do the spacecraft know it?
they don't know the *formula* for the trajectory, but they can calculate the trajectory to ANY desired approximation by Euler's method
I deal with hydraulics/fluid dynamics. What must be done BEFORE DOING ANYTHING is finding a model of the system that can generate the positions, velocities and accelerations as a function of time. System identification is key. Then one can generate positions, velocities and accelerations as function of a control signal. This is the FIRST step. Now Euler's method can be used. What wasn't pointed out in the video is that a better approximation of the derivative or slope can be found by using the current slow and the slope at the next step and then averaging the two to provide a better slope. This increase the accuracy significantly but it requires twice as many steps. BUT WAIT! There's more!. There is a method called Runge-Kutta, RK4, that makes 4 evaluations per step but it increase the accuracy even more. There is even a RK45. Although RK4 takes 4 times evaluations per step the steps can be 10 time bigger and still have the same accuracy so the reduction in the number of evaluation drops by about 40%.
In German eu is pronounced like oy. Von Steuben has his name butchered all the time.
I’m only in eighth grade and I’m only 13 and I really don’t understand this. I also do regular math for 8th grade which is only pre algebra. However I wish to be as smart and even smarter than gifted minds like Katherine Johnson. I honesty watch these videos and I’m heavily inspired by these videos even though I don’t understand mostly anything in this video. Honestly most intelligently gifted people would be able to understand this by my age but I really don’t. Anyways my real question is would you have any advice on how to learn stuff like this but ahead of time? I really wish I was as smart as people like you at the age I am Now because the ability to learn is a great gift by god and it shall not be wasted. And I don’t expect to be anywhere near as smart as you are right now I’d just like to hear any advice you’d may have for young people like me who are inspired to learn and how to learn ahead of their age if you understand what I mean
I recommend you to study basic calculus (understanding the basic meaning of differentiation, basic differentiation, basic integration and etc.) first before attempting to understand the contents of this video. This video is about Euler's method which is one of the methods used to solve differential equations. To understand the differential equation and Euler's method well, it is essential to have a firm understanding of basic calculus. Of course, you first need to have a firm understanding of algebra to understand calculus well.
I understand that you are eagerly wanting to get ahead of your classmates in mathematics and you are passionate about it too, but you need to understand that the set curriculum is there for a reason. Following the curriculum step by step will be the best and hopefully the fastest way to get you a firm base for mathematics. Don't skip steps, but try to follow the steps one by one. If you are passionate about it and find it interesting, I am sure that you will be able to follow these steps faster than all your classmates, and master mathematics.
I hope this helps, Good luck!
-From random G12 highschooler
Math is extremely linear. Keep learning math and don’t try and be a math genius at 13. If you really love mathematics and are interested, just keep going and you’ll enjoy learning. People like Katherine Johnson and Terrence Tao are very gifted but also had to work hard. You can’t learn algebra without knowing pre algebra, and you can’t know calc without knowing trig and basic geometry/math. Also, studying some physics is cool too. It’s basically applied math and calculus was literally invented to solve physics problems
Daniel, I really appreciate the time and effort and care that you put into this. But that said, I disagree with your principal recommendation. Calculus is absolutely NOT necessary for the understanding of these videos. The whole strategy of our class, and our book "Modeling Life", is that you can understand differential equations without calculus!! I know that can sound crazy, but it's true.
Many many fine young minds are lost to science because they never could master the pet tricks, the procedure-based approach that is the standard calculus class. I suspect luvyz might be one of those.
Ability to learn isn't god gift but Evolution gift: try to understand and accept this truth and you'll achieve a lot .
If you're interested in calculus, this series on the fundamentals of calculus is a great place to start! ruclips.net/p/PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
I ❤ math / comp 🎉 from UPR.
Thankyou.
somehow i understand this and didn't understand it at the same time lol
I'm really just sitting here 👁👄👁
"what's a girl to do?"
lol yes. I paused the video and had myself a hearty laugh.
“Form - u - lar”