Differential Equations: Lecture 2.2 Separable Equations

[@Lawton407]

Imma owe my degree to professors like you, Leonard, and the organic chemistry tutor. Words can't describe how helpful you've been to me, Thank you!

[@High_Priest_Jonko]

Students are lucky to have such a funny and open lecturer

[@ggcruise]

Okay ... I am learning so much using this guy's videos. I pause constantly and try to do the steps myself, then press play to see if I'm right or learn something I forgot from earlier calc classes. AND he is so likable as a person so it is totally making learning fun. Wish I could take a class from him in person!!! Thank you for posting these videos x1000!!!

[@jfeast5469]

I love the way this dude connects with his students. That's a mark of a good teacher!

[@JohnFL]

The relationships you develop with these students makes the lecture feel so much more enjoyable and personal than if it were just a formal presentation. As always, thank you for sharing your gifts with us! 🐴

[@xavierbuck7179]

Great Lecture. At 37:05 partial fractions is not necessary to use. You can multiply all terms by P^-2 then pick the denominator as a u substitution and solve.

[@حلفانكوارقينوكي]

As enjoyable to follow as listening to a concert of superb music! Well done!

[@avibank]

I went through my entire math major degree without coming across the tabular method. Really enjoying this playlist!

[@avibank]

ditto for Heaviside cover-up method

[@kavishchattoor1729]

Dude is amazing how he nice is. I would love to have him as my teacher.

[@alexh.4514]

THANK YOU SO MUCH! Also learning Tabular just blew my mind. So much friendlier than IbP.

[@franciscorolotti3569]

your classes are great! you motivate me for studying for my undergraduate in economics in Argentina

[@TheMathSorcerer]

Thank you !

[@franciscorolotti3569]

@@TheMathSorcerer You're welcome. Do you have any lectures about Concavity/Cuasiconcavity, Method of succesive aproximations, Contraction Mapping, Metric spaces and vector normed spaces, Cauchy sequences?

[@TheMathSorcerer]

I have an advanced calculus playlist on the main page that covers some of those topics

[@emanuelfeldman8182]

You’re a saviour.. thank you so much for your help to students everywhere

[@zanib9854]

Thank you, professor! The examples were beneficial, and now I know a quicker way to do partial fractions, thanks to you 😊

[@14_21r]

I cannot get bored while watching you. Thank you ❤❤❤ you are the best 😊😊

[@hhaze2020]

mayne you da best, thanks to this video i was able to crush DEs in college, didnt know about tabular but its super effective ,Love from Pakistan

[@JulianVara-xm7kc]

Thank you so much for making my review for my exam way easier!!!

[@benschwer]

You definitely make math fun.

[@asjidahmed2581]

You are such an angel. My Savior from these monsters. Really a great demonstration. Love from Pak

[@TheMathSorcerer]

👍👍

[@mc_comn6484]

Thanks a loooot professor! The lesson was really helpful! I have never heard about tabular method, i regretcnot using it. I wish I had a teacher like you!Best wishes!

[@TheMathSorcerer]

You're very welcome!

[@A.Hisham86]

Interesting! I'm happy watching your course.

[@L33L4ND]

Watching you do the problems is like when I sing to my favorite song. It makes me feel like I can sing, but when the music stops and I hear my voice I get reminded that I sound terrible.

[@saidfarid6382]

Hello Professor Thank you so much for your interesting lessons,i do appreciate your job.I wish you peace and happness under the sky of prosperity. Take care and have a good time. All the best. Your Student from Algeria

[@rudyj8948]

You are so fun to watch lmao, hopefully this preps me for ODE next semester

[@TheMathSorcerer]

Ya it totally will!

[@johndorsey931]

Thank you. Never heard of either tabular integration or the Heaviside Cover Up method.

[@akifcolak5033]

for the paritcular soln in 18:00 of video, what is the interval of defn? it seems like [0, inf.) but if x=0 then y=0, and if we look at the diff equation, if y=0, then the d.e. become meaningless because of y=0. Now, the int.of defn should be (0,inf.) or something else?

[@wsar7669]

Wow I've never heard of tabular ! Very cool

[@noamyakar249]

Fueling my passion for mathematics!!

[@nontokozoprincess3771]

thank you sir, in the chemical engineering field from South Africa😃😃

[@lucascorey3475]

How have I never even heard of tabular integration? It would have saved me so much pain to know this like 3 years ago.

[@squarerootofpi]

I want to see that student's proposed method in close to 39:00.

[@jonathansanchez2854]

So I just took my first exam in my differential equations class and I felt confident but I absolutely bombed it because I could not identify them as the correct DE. In one of your lectures you said for a review for the test you were going to put a bunch of DE'S on the board to see if they could identify them. Do you happen to have that lecture recorded to post it? Or if possible can you please make a video like that please.

[@lukeolfert9010]

32:36 the bravery of this lad

[@TheMathSorcerer]

haha I know exactly who that was, love that guy, great student:)

[@iremiposiajayi122]

Hi! Thank you for this! Do you have a playlist with only videos from your class lectures? I'm trying to compile all the DE class lectures, so I can learn in sync. Thank you so much for the work and effort you've put into these!

[@VndNvwYvvSvv]

Another great lecture. Flag is backwards though. Blue field in the upper left, unless reversed for the right side of a uniform. Tabular is also great for IBP where you need to obtain the original expression again to get 2(stuff) on one side.

[@ShinXiao]

Does the cover up method work for all partial fraction problems?

[@TheMathSorcerer]

No only those with distinct linear factors

[@ShinXiao]

@@TheMathSorcerer like simple factors as such (x-n)^2 and (x-n)(x+m) along with (x+m)^2 as the denominator?

[@carultch]

@@ShinXiao When there's repeated roots, like (x+m)^2, that is when it doesn't work, and you have to find another term to plug in to try it. Usually x=0 or x=1 are easy values to use, if they aren't already spoken-for. The Heaviside coverup method makes it so you can significantly simplify the system of equations you need to solve, to generate partial fractions.

[@akifcolak5033]

For the last d.e., P=1 and P=0 are singular solns? These provides the equation if they are imposed into it. Besides, it cannot be obtained from one parameter fmily soln because we know that the constant C cannot be equal zero and in 51:30 as you made that we multplied both sides with 1-P so it is valid for P not equal 1. Actually we can^t get it P=1 from one p.f.soln. Thus, they are singular solns. Am I right?

[@akifcolak5033]

Lastly, the interval of defn is whole real numbers?

[@ebramsaif3999]

excellent teacher thanks alot man

[@angelreyes-xd8zu]

Amazing class ❤🎉

[@uzairmehmood4620]

which textbook is being used?

[@TheMathSorcerer]

Zill's textbook

[@uzairmehmood4620]

@@TheMathSorcerer thanks for such a quick response, i just finished 1st lecture and wanted to solve hw problems

[@fayeduddin3229]

Does anyone know what school this professor teaches at?

[@eryarer]

It is funny in a bad way to see my teacher going to the "easy ones" because we need to know the hard ones and putting on the homework extrahard ones that he knows hot to solve because it has years of experience giving the same course on the same way, and it is a sad an a boring class with a lot of teori, not much practice it getss pretty confusing cuase it fills the board with a lot of things at the same time... i hate it and this is much better

[@cristofuscolombus1175]

What did you say about arbitrary constant in video when occurring had of letter on C? I can't figure out the pronunciation. Just like "Siktir le" in Turkish. What does it mean italianistica word?

[@cristofuscolombus1175]

ha okey "C tail" sounds like anti-militarist Italian language

[@cristofuscolombus1175]

oh nope it's tildé okey ı learned in next video xd

[@John-ny3ig]

In the last problem, if I take (-) out from (1-P) factor and Integrate it as -ln|P-1|, the final answer becomes P= Ce^t/(Ce^t - 1). Am I doing somthing wrong there? How is it possible to have different answers when I take (-) out from (1-P) ?

[@cristofuscolombus1175]

I did same mistakes, you forgot the - sign in substation part of the (1/1-p) as u=1-p, in the continuation:dp=-du. John, maybe you miss that "-" sign in "-du"

[@kewalmohapatra8340]

Which rule is being used to find the integral of x^3*cos(2x)?

[@glenmatthes8839]

He's using what's called Tabular Integration. It's really just a shortcut way to do integration by parts that works well for certain types of integrals.

[@carultch]

@@glenmatthes8839 It can be used a lot more than you think. Just about anything where integration by parts works, tabular integration also works. You simply need to know the three kinds of stops to look for: 1. You differentiate the D-column to zero 2. You can spot the original integral in the I-column, or across the final row. The kind that The Math Sorcerer calls a looper. Common when you have trig and exponentials in the integrand together. 3. You can construct an integral you can solve by another method, across your final row. Common when you have logs and inverse trig.

[@BigDaddyGuagg]

Can we get the homework prolems/solutions as well or does the university impose some restrictions on that?

[@heyysan9860]

Students sitting in this legends class have no idea have lucky they are!!!

[@MathewGlenn]

Pulling out big P in front of the whole class... brave

[@leonardobranco8829]

Whenever it is "easy" to derive the two functions can I use tabular?

[@TheMathSorcerer]

whenever one of the functions after repeated differentiation is zero, and whenever you can integrate the other, then tabular:) so like the integrals of x^3sinx x^4e^(2x) x^2cos(5x) are all classic examples of tabular

[@leonardobranco8829]

@@TheMathSorcerer That's great!🤩

[@neilsmith2585]

I was never taught tabular in high school or the first two years of college at a pretty decent math and engineering college. I don’t understand the ideology of making thing more difficult than necessary.

[@komalpandya5785]

Heyyy i really loved your teaching.Can we also get the homework questions for practice? 😃

[@TheMathSorcerer]

We just did problems from zills book on DE, so the section s follow that book. If you get an old copy should be roughly the same stuff

[@komalpandya5785]

@@TheMathSorcerer okay thanks alot !!

[@p0intblAnkwaziT]

@@TheMathSorcerer thank you!

[@saymyname5942]

have you ever heard of the DI method?

[@isurigunatilake2910]

Thank god these videos exist

[@akifcolak5033]

thanks for efforts, you are really amazing and motivating. There is a small detail about 7.25 of the video. You were saying taking derivatives of x. (And u^2). However, it could be more correct like this: We take the differentials of u^2 and x. As you know, differentials and derivaties are not same. Am I wrong? f'(x)=dy/dx then f'(x).dx=dy and left handside called the differential of f(x) or as well as y.

[@georgettebeulah4427]

Okay very good nice but how to get that board I really wish to get some materials but not sure how so I will wait. Thank you . Sure.🤣😔🌹🌷💕

[@justinclark9258]

Eat your heart out professor Leonard... lol

[@TheMathSorcerer]

lol

[@ashleyscavuzzo2708]

Why has this teacher taught me more in an hour than my professor has in 2 months????

[@thomasjefferson6225]

You're integration by parts on problem 5 is the tabular method. You can see that this goes on forever, and you go until a product is integrable. It's great you support the d i method through ❤

[@mikkithemeche]

Never woulda guessed young Rob Halford was a math wiz with a full head of hair. \ ^.^ / Thanks for saving my neck this semester!!!

[@TheMathSorcerer]

you are welcome!

[@bensengil8635]

I really wish the camera didn't move so much, otherwise great video!

[@liftsu9943]

Are you a full time teacher?

[@TheMathSorcerer]

Yup😄

[@liftsu9943]

@@TheMathSorcerer how you manage to make college classes seem so personal is a unique skill LOL

[@TheMathSorcerer]

​@@liftsu9943 haha thanks man:)

[@rishiraj6140]

Awesome

[@joshuabermea2869]

👍

[@TheMathSorcerer]

:)

[@ZeusCaboose]

I kind of feel like he was disappointed nobody asked for a pizza party

[@anjanbhattacharjeesir]

❤❤❤

[@kingx822]

♥️♥️♥️♥️

[@TheMathSorcerer]

:)

[@ronaldjorgensen6839]

here is where i skip class boss, thanks all is theoretic physics now i just remembered my quantum tunneling incryption !@ auto second remember if you ever mathematics collapse the plank unit to quantum aware bandwidth beyond theory you still have logarithmic scaler as a flash unit of differentiating and doing geometry tripping i guess sorry mr hand

[@lokeshverma5902]

LMAO. i am confused. "Big P" was that intentional or what?

[@zuchotheghost]

teacher i think there's a mistake in number 5, when solving the integration by part, vdu is not correct

[@wsar7669]

34:49 random politics mention lol

[@donutspeanuts6370]

pushing P

[@eglaff492]

Sub!!!

[@TheMathSorcerer]

Thx man😀

[@cristofuscolombus1175]

Olm herkes son soruda varoluşsal sorular soruyor? Son soruda içinize ne kaçtı olm? Yorumlara patladım ya adam 50. dakikaya kadar her şeyi anlayıp son soruda burada niye eksi işareti var diyor? Olm geç kaldın, ilkokulda dahi olmadan önceki hype moment'da söyleyecektin onu sdıoghsdolgıkshjgsdgpsdoşj

[@anthonypo2718]

Anna getting triggered over the smallest things.. ah yes modern women are so fun