Differential Equations: Lecture 4.4 Method of Undetermined Coefficients - Superposition Approach
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- Опубликовано: 30 сен 2024
- This is a classroom lecture on differential equations. I covered section 4.4 which is on the method of undetermined coefficients. I hope this is helpful. These lectures follow the book A First Course in Differential Equations by Dennis Zill. This is a great book for learning differential equations. Here is the book amzn.to/4ajOMyW (affiliate link).
For a moment I thought no one was gonna laugh at "ass. homo." at 6:30.
Then he Sorcerer laughed.
Then they all laughed XD
I tried to comment the same thing and it got insta-nuked by "algorithms". Apparently it's wrongthink if I say it.
Minuets later and I'm consumed by his energy. How he explains makes me feel like math isn't that hard after all
My current online professor has a thick accent, and all of his lecture notes are poorly scanned and hard to read. I was SOOO confused this section and you really presented the materials in a way that worked so well for me to understand. Thank you! I will subscribe for the rest of your videos to help me through the end of the semester.
Excellent!
If you are here with me studying how to identify Yp and etc. have a great day because we both put some efforts for our studies especially for those taking online class like me. It really is hard to study alone we must be grateful that we can easily access reliable sources to study such as this one. Have a great day I hope that someday our efforts will be rewarded!
I appreciate this video so much! I love how you explained things and didn’t expect that everyone already know what something meant. Most professors don’t understand that, yes it’s an advanced math class but we learn hard topics at such a fast rate it’s so hard to remember it all. YOUR EXPLAIN WAS AMAZING!!!
❤️
Thank you so much for this video! I have this exact section in my engineering differentials class for self study and I was struggling to understand it on my own, yet you made it so simple. I linked your channel to all my friends too :)
awesome thank you!!
ass. 🤣🤣 really much funny....i watched again and again....😁
👍
honestly this guy and prof leonard are the best at making hard stuff look easy
Hello sir. I want you to become my teacher honestly. Your teaching skill is amazing that anyone will understand what you're talking about. Thankyou you're the reason why i'm still in engineering. Can i have some request?? Would you give more example about that topic harder than before. Hihihi thankyou i'm from the philippines hope you noticed me😃
I'm still finishing the lecture, but thank you so much for breaking down the Yp's like that. Especially the last two. I have about 7 hw problems that are in that format, but we didn't go over anything like that and I have watched quite a few youtube videos with nobody doing examples like that. I'm going to finish the lecture then try to knock out the hw! The upcoming exam this week will determine if I drop the class or not...
You're very welcome!
and good luck!
@@TheMathSorcerer Thanks! I was able to do all the problems in this section! Now onto 4.6...
I feel like if you wrote a math book, it would be one of the best books. Tbh I love your explanations and I love how you can take very difficult topics and make them easy and accessible to understand! (Anyways, keep up the amazing work!)
That's a great idea! Maybe one day, I could definitely do it, it's just the amount of time:) Time spent writing math book vs time spent doing xyz, tough choice!
@@TheMathSorcerer Sir, I would definitely encourage you making a math book for these college courses. Like a study guide that they usually have for high school subjects. I feel it would garner more interest around math because your style of explanation is absolutely spot-on that even my friend in 12th grade who was studying with me could understand this.
Thank you for your time sir!
Thank you!
I've never seen a math professor hype up diff. eq. like this. My professor went through like three examples and then straight into a pop group quiz. Did not even teach us about the repeating terms. Math Sorcerer is AMAZING!!!!
You legitimately just saved my life! Way better than the other explanations out there!!
I loved the as* h*mo part, hilarious 😂😂
You're so passionate about this stuff. You made something that was absolutely brain numbing to me, and you made it fun. Thank you!
Thx man👍
He really did👊😍..
Thank You so much
Wish you’d teach elementary analysis 😭 is there a way to understand that????
Really your awesome!! I missed you as my professor in college but lucky to see in online. Thank you!!. Just awesome
You're very welcome!
Thank you! I understood the first part of the semester and got a 90 on my first test but now I'm so lost and my test is Wednesday on chapter 4 and 5 wish me luck time to watch all these videos! I like your style though
I have a question why is #9 not yp=(Ax^3+Bx^2+Cx+D)Ee^x I why does the e^x not get a number?
6:04 lmao
Math Sorcerer, even if your spelling is off, your spells are the best! Thanks:) 🐴
I hope these students appreciate what a great professor they have!
I am absolutely thankful for this video! It was explained in a great manner and I loved the energy. My professor used a different method that is very confusing ( t^s(Amt^m + ... A1t + Ao)e^(rt)...). I am forever grateful for your help!
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Great videos! I've been watching your proof based videos for a while now and decided to check out the diff eq stuff. I teach at a 2-year community college and will finally get the opportunity to teach this course. I tend to emulate 'pieces' from my favorite math professors and you sir are one of them even though I never had the opportunity to take your class. Keep up the good work!
Awesome! Have fun teaching the class👍❤️
oh man, I've been using "it's" wrong for 20 years.
Lol
please come teach at San Jose State in California. I wish you were my professor the one I have now. Just wants everyone to drop the class. He doesn't go over any pass calculus stuff. your really helping me pass
☺️☺️
@@TheMathSorcerer I wish i could show you his methods 😭. Do you offer help
Wow! You are entertaining. I really really wish I had you as a prof! great job. Thank you for sharing your passion!
THANK YOU VERY MUCH, finding Yp for me is the hardest at first since what I've studied is stating that when there are same roots, you multiply by x and I have no idea what roots they are talking about. Now it is clear that the roots of assumed Yp and the roots of the complementary function. Thanks a lot
Thank you so much for number 4! I have spent 2 whole days trying to figure this problem out! I wish my math teacher was like you!
Do you have any lectures on the annihilator approach? We covered the superposition in 4.4 and annihilator in 4.5. In the series you go from 4.4 to 4.6.
It's cool that all the sections line up besides that though! Must be using the same book.
holy bezos
This is just to let you know that, we appreciate you.
im glad you made this. I would be lost without you. youre a great teacher making sure everyone understand and being patience with everyone.
You're an amazing teacher. A true wizard
❤️
appreciate this lecture ,love from Pakistan
Great! I like your approach
Question: so if my g(x) was -18x^(2)e^(2x). Would my initial Y sub p be (Ax^2 +Bx +C) e^(2x)??
Ya then you would look at yc to see if there is repetition,if there is,multiply by x until it's gone
I owe you my diffy q grade my good sir 🤝
Thank you!
I have to admit that is what great teacher do often,you deserve more(winds frome Great Somalia)ilove much diffrential equations.
Thank you! 😃
You have good communication skills #yourfriendmathematics
thank you!
man why can't my diffy q's class be this :(
Hello sir! Which book are you following?
DIFFERENTIAL
EQUATIONS
with Boundary-Value Problems ?
Found a similar question, i got the answer from there, youre using Zill
Yup decent book👍
A great question for this is:
the fourth derivative of y wrt x = 3x - 1
d^4(y)/d(x)^4 = 3x - 1
The homogenous solution yields m1, m2, m3, m4 = 0.
I had to modify Yp = Ax + B four times, and I ended up getting the correct answer.
This is simply a matter of integrating it four times, rather than using the theories of differential equations.
You could also use the Laplace transform:
s^4*Y - u*s^3 - v*s^2 - w*s - p = 3/s^2 - 1/s
where u, v, w, and p are the initial conditions in increasing order of differentiation
Y = (3/s^2 - 1/s + u*s^3 + v*s^2 + w*s + p)/s^4
Y = 3/s^6 - 1/s^5 + u/s + v/s^2 + w/s^3 + p/s^4
y = 1/40*t^5 - 1/24*t^4 + u + v*t + 1/2*w*t^2 + 1/6*p*t^3
Thank You Sir!
Ops! in this course in my University they exclude 4.4 they instead explain and include 4.5. Unfortunately, I need to understand 4.5 by myself.
hey! I am from Bangladesh
wish you were my DE professor
I love the way you do math sir... From pakistan ♥️. Wish you live a peaceful life.
I love the confidence... you are just too much, can I come over to learn pure mathematics... attending lectures here is just almost a waste....
dear sweet baby math jesus. i always enjoyed watching your shorts (the videos, not the little trousers). I knew you sold udemy courses, so it was a huge shock to me when I saw you provided your diff eq course for free! so pleased to see you teach! youre lectures are awesome. All the work for the guesses was exactly what I was looking for. Thank you so much! love you camera bot too. very clever!
I believe there is an error in the yp of sin(2x). Its Axsin2x + Bxcos2x instead of Asin2x + Bcos2x. Please correct me if I'm wrong.
I took this course several years ago but watching this lecture, it allows me to remember this particular topic. Thanks.
Great explanation in a very structured way... Please also do a video on Cauchy Euler equation and factorization of operators... From Bangladesh,wish you good health... Thank you...
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I have a playlist for this I will find it
Cauchy Euler Differential Equations: ruclips.net/p/PLO1y6V1SXjjM0prvj_roxY-pHfy_GnL5d
Thanks a lot Sir for a kind reply... You really seem to be a good teacher with a good heart...
thank you
at 44:34 time was someone called brazil or a brazilian? I'm brazilian and I loved your videos this playlist saved me
This guy is trash....
Jk. Nice vid!
Lol
We doin some dif eq init?
Very nice lecture i watch again and again
thank you
Good videos wish the camera recorded the other side of the board though.
Very well taught sir! I'm a Chemical Engineering major studying for my first Diff eq test. Just subscribed, looking forward to seeing what you do next.
dude thank you so much! this was in-depth and easy to understand!!!
You are welcome👍
Happiest Teacher 😁
This guy, he’s awesome at explaining. Making it make sense, and very enthusiastic. Thanks for the upload!
Me está ayudando muchísimo sus clases, muchas gracias
:)
it helps me a lot. IS there any video on linear algebra?
Here is what I have so far, more will come, soon I hope:)
ruclips.net/p/PLO1y6V1SXjjN0auwro1YZEhhnM_yzsSzi
@@TheMathSorcerer thanks
Shout out my name on your next video. "John dave cusi"