You're telling me I spent almost 2 months trying to understand variation of parameters when this was here the whole time and actually helped me understand and remember the steps? With a difficult problem no less? Kicking myself for not watching this sooner, thank you so much!

@jugglingnumbers

2 ай бұрын

I don't get why teachers can't just give a succinct summary of the steps before explaining any technicalities. Honestly, I feel like math is just a bunch of gatekeeping.

our prof doesn't finish the lectures for DE, thanks to your videos i can learn them during my free time. you're a life saver

The best thing about this prof. is his genuine excitement for doing math. It is how I taught AP calculus for 32+ years. I thought everything was cool to do!

I really like the way you go about explaining the reasoning for each move you make, almost making it fun, like you're walking me through something you find cool, knowing that this is the first time I've seen this.

@TheMathSorcerer

3 жыл бұрын

👍

You are THE BEST! Your D.E lecture videos are what got me through this semester. Your passion and enthusiasm is absolutely one of a kind, and you made learning this class not only possible but enjoyable. You are an absolute gem of a teacher and please never stop doing what you do. I'm not even one of your "students" but you are the best math teacher I've ever had! Thanks for these lecture videos, the fact that they are free is absolutely amazing.

After weeks of struggling with this concept, I finally find a good video two days before my exam. Math can be great if the teacher is able to explain as well as you are. Your students are in good hands, and so are we. Thanks!

@anypenanybook2001

Жыл бұрын

Same here. Test in two days. It's a great video.

I've been following the entire series thus far. Having taken a fair share of university math courses I can confidently say you are a true gem in math education. Thank you for your well prepared lessons, student engagement, and overall positive attitude towards the subjects you teach. Most of all thank you for posting these lessons free of charge!

Isnt it crazy how easy math can be when someone actually takes the time to explain it properly? Ive been trying to learn differential equations for a couple of months as well. As soon as I came across these videos it gave me hope that I will be able to finish my math and engineering degree

Man you are amazing. My current professor is awful at conveying a clear process to solve problems and this one made it super easy. Thank you so much!

You explain very well. I wish I could be live in your class over there: my maths life will then be a great one. 🎯 Kudos to you, Prof.

Hi Math Sorcerer, your knowledge of integration techniques just blows my mind! I guess teaching calculus helps a little bit:) Enjoy your day 🐴

I hope this channel booms exponentially. Ps really wanted to listen to the discussion about the test in the end xD.

@TheMathSorcerer

4 жыл бұрын

Hahahaha thx man

Keep up the good work man ,, Africa appreciates u ,,, Giaolem Pre-eminent signing out

I didn’t think I’d sit through this but omg… it helped so much thank you

@TheMathSorcerer

2 жыл бұрын

awesome:)

all the way from SOUTH AFRICA, I enjoy your lessons wish they were contact. YOU'RE THE BEST!!!

@TheMathSorcerer

3 жыл бұрын

👍

im really impressed by the way you teach and make difficult concepts seem quite simple and fun to understand god bless you !

Came here for the VofP and got a bonus mnemonic for the Hyperbolic functions. Memorized in 30 seconds what an entire unit of Calculus couldn't get to stick...

Absolute legend thank you - I love your humble approach to teaching maths

really enjoyed your teaching sir!. We want you to upload more of your lectures. May God bless you.

@TheMathSorcerer

4 жыл бұрын

Thank you!

I found myself laughing harder than I should at your C4 joke. I really appreciate all that you're doing for students. Keep up the great work!

@TheMathSorcerer

3 жыл бұрын

Hahah c4 yeah I remember that,

You are a genius and an amazing teacher. This is so much better than the wy I was taught and gives me less if a headache omg!! Thank you! aNd thanks to your students for their willingness to allow filming + thanks to your cameraperson!!

@TheMathSorcerer

Жыл бұрын

You are so welcome!

Lol I would I admit I love watching these videos. You’re really engaging that’s honestly a talent

literally dark magic thank you, you make learning a tad more fun

This video helps for my next test! Thanks!

I love your channel!! I really hope you keep making videos. your videos help me in my differential equations class 💜 and best of all it is entertaining while learning because I feel like I am in your class

@TheMathSorcerer

2 жыл бұрын

I'm so glad!

wow! what an explanation wish i could subscribe twice

You're actually amazing

Thank you very much! Came in handy during the pandemic. 🙂👏

@TheMathSorcerer

3 жыл бұрын

You're very welcome!

You're really helpful, thank you very much!

@TheMathSorcerer

4 жыл бұрын

You are very welcome thank you for your comment ❤️

I think I just saw you sniff a marker at 3:20. That's how you're so excited lol

@TheMathSorcerer

3 жыл бұрын

ROFL!!!!!!!

Dude you are awesome

Is there a formal name for the simplification technique used with the (e^x+7)/(e^x+7)-7/(e^x+7)? I use it all the time but when I teach the technique to students, I am not sure what to call it. It has to have a name right?

@eigentheory

2 жыл бұрын

Just following up, does anyone know if there is a formal name for this technique?

@carultch

9 ай бұрын

@@eigentheory I call it adding zero in a fancy way. I don't know if there is a formal name for it.

When stating a solution, does 'simplify' in this context usually mean 'fully factorised'? Sometimes I can pull a GCF out of everything like an e^(-x) out of all terms.

@TheMathSorcerer

3 жыл бұрын

your question is actually a common one, and the answer is, no it does not:) so like say you had e^x ln(x) + e^x * sin(x), you could just leave it like that

@TheMathSorcerer

3 жыл бұрын

this is what simplify means in this context, say we had c_1e^x + c_2e^(2x) + 3e^x + 5e^(2x), which you could write as (c_1 + 3)e^x + (c_2 + 5)e^(2x), then rename things c_3e^x + c_4 e^(2x), where c_3 = c_1 + 3 and c_4 + c_2 + 5 so basically one can make this jump, c_1e^x + c_2e^(2x) + 3e^x + 5e^(2x) = c_3e^x + c_4 e^(2x) I usually tell my class they can do this since it's understood what was done, but yeah, use with caution. If it was me and I was taking a class I'd show that middle step:)

Question, so in order to use the variation of parameters and undetermined coefficients, you can not have functions of x Infront of the y double prime and y prime? like you cant have (X^2)Y'' +(X)Y' = 3X^2. would you only be able to solve those with Cauchy Euler method or annihilator method?

@carultch

9 ай бұрын

You can, as long as you know the two fundamental solutions to the homogeneous part, which is the challenging part to solve. You can use the Laplace transform for DE's with x in front of either of the derivatives. There is a property that relates derivatives in the s-world, to t-multiplying in the t-world. It's tradition to replace s with p, when we use x. For your example, I'd reduce the order of the DE. Let v = y', and rewrite in terms of v: x^2*v' + x*v = 3*x^2 Divide thru by x^2: v' + v/x = 3 This we can solve with first order methods: v(x) = C1/x + (3*x)/2 Integrate to find y(x): y(x) = C1*ln(|x|) + 3/4*x^2 + C2

I'm pausing the video or working ahead of it to check my work. I find that helps me remember mistakes that are my favorites and not to do them on the test 🤣🎉

Say you're panicked on an exam and you didn't even think of going that elegant route at 28:00, could you just work through a uv-int(vdu) for the successful integration of U2?

You saved me sir.🙏🙏

@TheMathSorcerer

3 жыл бұрын

👍

You rock!

Studying before my exam tomorrow and my class has been entirely online (meaning we're basically teaching ourselves at this point). Thank you for providing these lecture and going through enough examples. And thanks for making it light-hearted!

Solving Systems of Linear DEs by Elimination Is this lecture Recorded?

I witnessed dark magic at play at 29:23, and had to fast forward to 31:34 to see it all come crashing down. xD

@TheMathSorcerer

3 жыл бұрын

Haha

Gorgeous !

@TheMathSorcerer

3 жыл бұрын

👍

Was there a mistake on 29:23? I thought you would integrate just e^x moving the Constant (-1) out of the integration and then bringing it back in resulting in -e^x. Am I tripping?

@lollypop0328

3 ай бұрын

Nevermind at 31:39 the mistake gets caught lol

Why does he stop at 4.6 and doesn’t continue this for the rest of differential equations I was watching his videos and they are suddenly over I really enjoyed this series

You make math so much fun. I wish you were my math teacher. In a way you are, just liked and subscribed to your channel :-)

@TheMathSorcerer

3 жыл бұрын

Cool thx man👍

Thank you so much ..👌👌

@TheMathSorcerer

3 жыл бұрын

👍

34:47 "you can't distribute there" Remembering students like me:)😁

This professor reminds me of my teacher when I was taking this course except my teacher would make the board a bit more organized and colorful as if we are in kindergarten XD. Did anyone figure something wrong! In 26:08 integrating u2 the numerator should be - e^(-4x) because you filp the e and becomes negative exponent then add it to the other e if you know what I mean.

Dark Magic!

@TheMathSorcerer

4 жыл бұрын

hehe

❤❤❤

can you also factor e^(-x) from ln(7+e^x) and C3 as well and make it e^(-x)*[C3 + ln(7+e^x)]

@TheMathSorcerer

3 жыл бұрын

yes you can yup

We love u2

THANK YOU

Thank you for this Sir!

@TheMathSorcerer

3 жыл бұрын

Nice

sir can you solved y"+2y'+10y = 17sinx-37sin3x in variation parameters?

@Learnhifz

2 жыл бұрын

Lol they will say that "do yourself they're pretty easy when a difficult question comes"😃😃😅🤣🤣😂😂

@carultch

9 ай бұрын

You can, but there's really no need to do so, since the forcing function only consists of sine functions. Given: y" + 2*y' + 10*y = 17*sin(x) - 37*sin(3*x) Find the homogeneous solution: yh" + 2*yh' + 10*yh = 0 yh = e^(r*x) (r^2 + 2*r + 10)*e^(r*x) = 0 (r^2 + 2*r + 10) = 0 r = -1 +/- sqrt(1 - 10) r = -1 +/- 3*i This means: yh = A*cos(3*x)*e^(-x) + B*sin(3*x)*e^(-x) For the particular solution, since both homogeneous solutions are independent of the right side, we can use RHS terms directly. Thus: yp = C*cos(x) + D*sin(x) + E*cos(3*x) + F*sin(3*x) Take derivatives of yp, and gather like terms: yp' = -C*sin(x) + D*cos(x) - 3*E*sin(3*x) + 3*F*cos(3*x) yp" = -C*cos(x) - D*sin(x) - 9*E*cos(3 x) - 9*F*sin(3*x) Apply to diffEQ: yp" + 2*yp' + 10*yp = 17*sin(x) - 37*sin(3*x) Set up equations to match coefficients: cos(x): -C + 2*D + 10*C = 0 sin(x): -D - 2*C + 10*D = 17 cos(3*x): -9*E + 6*F + 10*E = 0 sin(3*x): -9*F - 6*E + 10*F = -37 Solutions: C = -2/5, D = 9/5, E = 6, F = -1 Using y = yh + yp, the general solution is: y = A*cos(3*x)*e^(-x) + B*sin(3*x)*e^(-x) - 2/5*cos(x) + 9/5*sin(x) + 6*cos(3*x) - sin(3*x)

thank you sir so much for this video 🤎🤎 can you please make a pdf or something for the worksheet to solve so that i can fully understand variation of parameters

I hated the algebra of the superposition method. I understand integrating is harder for most people, but I think that this is easier method since I get lost plugging things in often times.

Can anyone confirm this is correct: @26:25 i used the U sub and "reverse engineered" it and was left with the same solution except i had a -7 constant in the solution for U2. Which, at the end of the final solution of y, left me with an additional -7e^(-2x) in the solution.

@heleni5946

3 жыл бұрын

agreed, I did the same thing and was wondering if I made some mistake. Then I put it in an integral calculator and it was the same answer as mine. -7-e^x+7\ln(7+e^x), I checked his calculations but it also seems to be correct. It's really weird, i thought of it like maybe -7 is just absorbed by C, but I'll still ask our diff professor

@asadcake6375

3 жыл бұрын

@@heleni5946 I also did the same thing, but if you factorize your solution by e^-x and e^-2x you will notice that you can transform C2-7 into an other constant C3 and basically end up with the solution in the video.

@heleni5946

3 жыл бұрын

@@asadcake6375 Oh yes exactly, i figured that after a while

Sir please solve all the questions of 4.6 dg zill for mechanical engineering students 🙏

when you spend 20minutes trying to figure out why your answer is slightly different; passing over your steps, then mine, then yours, then mine, until i finally see a mistake, only to let the video play 30 more seconds and have you realise it. rip.

@TheMathSorcerer

3 жыл бұрын

hehe

@AC-wf6pd

3 жыл бұрын

haha i read this comment before I got to the part, and it still had me so confused until i just keep playing the vid

thanks dad

13:30 best part

If our prof. had real balls he would have checked his solution!!!! That would have made for a 4-hour video. Moreover, imagine if something went wrong with the checking! You don't know if your solution was wrong or you made a mistake in the checking of the solution. THAT'S what sucks the most about Diff. EQs.

honestly easier to remeber then bernoulli for some reason

Course book Or Reference book

Here are you using green function

Thare is no 4.5? Am i missing something? Pls get back to me i have exam in 4 days

I think u messed up your U2. that is the wrong reciprocal of W

I wish i took your exams

here cuz my school shut down .-.

@TheMathSorcerer

4 жыл бұрын

Aww yeah ours shut down too😟

Yo I totally remember that u2 album. Totally annoying

Hehe. His hair looks like a mop.

@MagnusonX

3 жыл бұрын

...a nice, curly mop

@TheMathSorcerer

3 жыл бұрын

❤️

@somerandomperson467

3 жыл бұрын

Guys It was just a joke

is this dude sniffing markers as hes teaching or what? lol