Applications with Separable Equations (Differential Equations 14)

[@AJ-hy5bj]

Its 2024, and this man is still helping me with learning this stuff. Wherever you are in this world professor, I hope you are doing well and blessed in life for the amount of help you've given to us struggling students. Leaving this comment for someone in the future to find.

[@actualBIAS]

You are tired here and you still go on and teaching complete strangers on the internet how to solve DE. Man, your heart is even bigger than these arms of yours. I respect you in a way that can't be described by words. Huge thanks for sticking around and doing what you do. I hope you have a nice life.

[@horizon210]

Professor Leonard, it is virtually impossible to convey the depth of gratitude one has for the expertise you so generously share. The application problems bring it all to life and provide real-world purpose and context to the mathematics, making it all the more enjoyable and useful. It has been said by virtually everyone commenting that you are an extraordinary teacher, but so simple a statement hardly does justice to one who makes so vast a difference in the lives of so many. Thanks to you, and the understanding you convey, many career hopes and goals that would otherwise lie shattered are able to come to fruition. You are more than an extraordinary teacher. You are an extraordinary person.

[@minsungkim6792]

It really puts my mind at ease whenever I can find Professor Leonard's videos on the topic that I am stuck in.

[@kylemunsami6039]

a century from now...people are going to discover this channel and be like...our generation was fortunate to meet the Einstein of our time who had his work recorded! What a great time to be alive to see a character enhancing the education of a learner to an extraordinary extent. Its what we South Africans call LEGENDARY! "Education is the most powerful weapon which you can use to change the world"-Nelson Mandela Prof.....may you continue to expand greater than infinity and may your lessons be unlimited under the topic of mathematics. Hoping to see other courses from you soon!

[@N7TWL]

Professor Leonard is rare! He has the brain and mindset of a world-class mathematician, and he is one, but he also has the innate ability to shift the focus away from theory, proofs, and rigor that so commonly cloud the important concepts in our textbooks, and put it back on those important concepts. That is pretty good all by itself, but then he has the ability to explain the details in language that we non mathematicians can understand, and most importantly, using logic and examples that the rest of us can follow. Professor, your technique and style of teaching math is far beyond outstanding! Thank you! Add-on: Professor, in answer to your questions about the value of your videos. Absolutely yes to being worth while. I think it is clear from everyone's comments that we greatly appreciate the time and effort you have put into your tutorials. The following is why they are of value to me: I am 77 years-old and teaching myself differential equations. I am a bit of a slow learner when it comes to math. I have to roll around in it for awhile before I get a gut-understanding of it. I have 3 or 4 textbooks on beginning ODEs, but as I said in my first paragraph, the authors do not write for clarity; they write for rigor. I do not believe that these authors have any idea as to the struggle many of us have in learning the concepts when those concepts are buried between the lines so to speak. I have watched this video twice and worked all the problems each time. Now, I can go to a text and sort of work my way through their rigor-speak in the sections on separable equations. I can't wait to get to your next video!!

[@cbcomer]

I love these videos with lots of examples. Working them out on my own and then watching you get the same answer is the best!

[@basakatik4770]

thanks for being so explicit! You have the clearest style I have ever seen. thanks to you, math is more attractive and explicit. As a prospective mathematician I would like to say you are the one who has the biggest impact on me and you will be! I am sincereley grateful to you. I hope you will continue to enlighten us. Too much distance is not a barrier for you to grow us. I want to thank you again and again can not stop speakig! Okay, I stop otherwise I will start crying

[@ProfessorLeonard]

Thanks very much for you kind words!!

[@joeforshaw8362]

Hands down best math teacher on the internet!

[@nta699]

I enjoy your videos. I'm 75 and can still recall my days at the university. I can honestly say I wish I had math professors like you. Math would have been more enjoyable. Keep up the good work.

[@noorradi6975]

you're the reason I passed my calculus 1 and 2 class. and now on to differential equations! THANK YOU!!!!

[@BalancingChaos]

Professor Leonard, I have always loathed word problems and as I've been following every single example you've used, it's finally starting to click. Thank you SO much for all of your time you've dedicated for us.

[@martintejada9042]

wow It has taken me a little bit over a year and a half to watch every video starting from pre algebra to diff equations, and not once have I been disappointed by your lectures. Now I just need calc 3. I just wanted to take a moment to thank you. I came from graduating h.s without understanding basic algebra to making math my favorite subject and now being a couple of semesters away from getting an EE degree. Thank you so much for your hard work and dedication towards your viewers.

[@elijahachiri]

You are literally saving my life right now! I am learning more here than I have spending days going to class. YOU'RE THE BEST

[@astinuspalanthas]

What this guys does shows how a teacher should teach. He uses numbers to identify the proportions (half the c14, 6 times the population...) instead of letters. He has clearly identified that students have problems working with letters and he explains it a way the students can easyly understand. I wish every teacher would be like this...

[@grace.venessa2025]

I thought I wasn't good in math till I took your lessons. Thank you because now I'm really doing well in math!

[@ndelo4947]

Thank you for your time and your effort. Some of us could never have the privilege of sitting in your lecture halls, but the level of deliberateness and detail in which you broach each topic is confidence-inducing. Please don't stop... I can't wait until you do "REAL ANALYSIS".

[@aibdraco01]

You are the best teacher in the world! Other teachers should follow you! God bless you!

[@LC35T]

I started watching this video series in early January because I knew my differential equations professor for the Spring semester was going to suck. A terrific job so far I love the teaching style and examples. Even with this lengthy video, it was engaging and I am so glad to have Professor Leonard teaching differential equations like a boss. I'm looking forward to the rest of the series.

[@gangadharvenkataramanap7651]

Awesome applications, I realized the meaning of so many questions I have encountered so far. Thank you so much.

[@adhiamboalali]

Your lecture videos have really helped me through online learning during this pandemic and I just wanted to say thank you very much

[@adhiamboalali]

From South Africa❤❤❤

[@MikeyBro5728]

To answer your question about whether this is helping..... the answer is YES!, every single video you have made is helping (I have watched every single video you have made up to this point in my math education), I really feel like I can math now because of you Professor Leonard.

[@michelcretier5382]

Professor Leonard what a talented pedagogue you are! I am enjoying every second of your videos. I am rediscovering Physics and you are giving me the mathematical tools for it. A million thanks to you

[@RobertComeaux-xq9wi]

I'm preparing to teach this content to my high school Calculus class, so the wealth of great examples is extremely helpful!

[@AlexJZ]

Professor Leonard, because of you, I'm literally feeling sensational when studying math rn lol, been watching this series for about 15 vids so far, absolutely helpful, Thank you so much!!!

[@steph_dreams]

this is my first time watching one of ur videos and I’m already convinced that ur the real life version of clark Kent

[@luckn.3371]

Very helpful! My teacher doesn't put in as much effort into her class and its a great change of pace doing it alongside you! I try to do all the problems and then check how you ended up solving them to compare and contrast my techniques with yours, and its enlightening especially with online learning and a teacher who only puts me and other kids in her class down by giving random hard problems on the test that she never even taught us. Have a quiz soon but after this I feel like I can nail it! I thank you from the bottom of my heart.

[@dogfooddevin5538]

I know I'm 2 years too late, but with the pandemic happening (and my professors deciding to literally not teach at all over the web) these videos have saved my life! I've used your Calc 2 series before so now I'm onto using this one and Calc 3! I have no idea how I'm going to survive the other classes without your videos :(

[@darstking2044]

These are amazing. It is people like yourself that are the real heroes. Thank you so much for everything you've done.

[@AMLennon]

Getting application questions in my first test for Ordinary Differential Equations. Your examples are really helpful in preparing.

[@lofijedi]

this video seriously did not feel like an hour and 50mins at all! thank you so much for all your help

[@tiaanjansevanrensburg2762]

Thank you, so much! I don't even watch my university's lectures only his.

[@nazifataha8868]

Thank you for your effort in making these videos and helping us learn math the way we all should. Wish there were more professors like you.

[@kesjerdna]

Definitely, of course. I was studying mathematics and computer science at Faculty of Education at University of Ljubljana, but Professor Leonard really explains very well and actually some mathematics covers are new for me too and I love it when I learn new stuff...

[@gulnazshalgumbayeva8655]

Wow! I also studied criminal law, I got my BA in criminal law then got BS and MS in math. In both cases we investigate:) glad to hear that I am not the only one who are interested in both. ( Watching this to brush up my stuff for my research ;)

[@dfc543]

Felt great to watch these examples get done and start to understand and apply the processes. Thanks!

[@silkysixx]

This was my favourite video so far. So many examples and with the Prof pointing out the important parts of each step, I feel like his voice will be in the back of my head whenever I'm looking at one of these in the future. Also the best thumbnail so far. DJ ProLen on the 1s and 2s m-m-m-meoooooooooo!

[@Eren-he5dt]

That last question man, i was so done after 1.5 hrs in here but that question was so interesting I stopped to solve it and compare. Im really satisfied now, you really found a fun one.

[@vhutalimakatu2339]

thank you prof for dropping the differential eqs playlist. it is helpful

[@notRaphaelI]

These lectures and practice problems are amazing, explaining every single step is very helpful.

[@aubreeswart2206]

I really appreciate the respect and appreciation you have for and the understanding you have of mathematics as made evident in your pedantic wordings on things like pure mathematics and modeling nature. That’s wonderful!

[@AMLennon]

Enjoying your videos so far. The following subtopics of Differential Equations I would love for you to cover soon: 1. Method of Undetermined Coefficients for non-homogeneous equations 2. Variation of Parameter method for non-homogeneous equations 3. Second order homogeneous and non-homogeneous Cauchy-Euler differential equations 4. Power Series: Taylor and Maclaurin Series 5. Laplace Transform 6. Numerical Methods (Runge-Kutta method)

[@EKhan89]

Just throwing a comment up like Prof asked. Super long video but it does help drill in the practice so thank you. I really appreciate it!

[@SakeKaama]

The application problems are some of my favorite. I love seeing where/how this stuff can be applied while I am considering a future career.

[@MechanicalEI]

Professor Leonard, Great Video. The illustration and example were perfectly supported by your explanation. Your soothing voice helps to focus on the lecture too. Thanks for uploading!

[@ketofitforlife2917]

Thank you for this! This is going to help me tutor my students tomorrow, and I'll also share this vid with them!

[@rwharrington87]

These applications do help. It's nice to have something concrete to tie everything back to. When you get around to finishing this course, I'd love to see some electric circuit applications.

[@aubreeswart2206]

How could we not stick with you? You the man for math! Thank you so much for these!

[@colinmartin9797]

Jesus christ Leonard when I asked you to hurry up with this series you really took it to heart! That means I get partial credit, right? When I finish Calc 4 (get on it next!) I'm sending you a present.

[@1adrq]

The problems were perfect and perfectly explained Professor Leonard. Thank you sooo much!! (: 🙂🙂🙂

[@spanishlanguageeducational3737]

Your videos are awesome. I went through the entire video, but I had to pause so many times... it took me about 3 days.

[@jonirolle650]

I like the way of teaching and I find the videos very helpful. Thank you!

[@theoendre6484]

Applications show how math is connected to real world. So, of course we're enjoying them :) thanks professor, really great video, especially the last application.

[@frankfrimpong7959]

Prof. your videos have been very helpful to me.... I really appreciate your efforts and sacrifices. Thank you

[@sirawesomehat8814]

In the "population increase x fold" or "radioactive material halves" kind of problems, I usually just set them up as "x times P(0) = P(0)e^kt", then divide out by P(0). Obviously this is the same thing as you're doing, but you don't even need to pick an easy number, you can algebraically represent that the initial values cancel out. P.S., I adore your videos, I'm getting prepped for PDEs in the fall and am enjoying your lecture series as review. Thank you so much for these!

[@violethill4454]

may I ask why are they both P(0)? Isn't it P(t) = P(0) e*kt

[@AdnanKhan-mm6bo]

I just complete that video & I'm here to say, your videos really help us, Professor Leonard..!!

[@أبوفيصل-ع5ط8ج]

Thank you for the videos series Sir . leonardo I am from Saudi Arabia and I have learned from your videos a lot 😘

[@abdelrahmanelbatran1164]

thank you very much for your great effort. I really appreciate the amount of effort and time put into these precious videos 😊♥

[@AvinashKumar-jc3ng]

These are very profitable.....keep posting such long videos with tonnes of examples...

[@taekwondotime]

Examples are great! Just like in my textbook. I had no idea differential equations played such a large role in so many real world problems. :)

[@jurgenkoopman9091]

Great lecture, I learnd much about setting up the differential equation. You truly made me think about it. See you at #15!

[@Pete1711]

Thanks for your work on these videos! These and the Calc series have been great. The examples here were certainly helpful. Personally I found the last lecture - simply solving the equations without any real world context - was quite easy, and imagined before actually watching this video that I'd be able to easily translate the process to actual word problems. I was very wrong! Without these examples I would likely have been completely stuck when later trying to apply these ideas to exercise found online/in textbooks, etc. Definitely worthwhile to have watched them all. Thanks once again.

[@barryhughes9764]

Thank you Professor for another exceptional video. Always a pleasure to watch them.

[@MelissaRudden]

Your videos are so helpful!!! I'm "taking" your ODE class this summer in preparation of the graded ODE class I'll take in fall so fall will be easier! Thank you!!!!

[@Flaystray]

The only reason I come to the internet for math help is for applications. If you made only applications videos, I would watch them on repeat

[@muawiyahhaq8488]

VERY HELPFUL LIKE ALWAYS, THANK YOU MR GAINZZZ

[@henkoegema6390]

Thanks for interesting lesson. Even after 4 years of publishing it is of much interest.

[@gunterrebing1556]

Problem in Differential Equations Video 14 at 29:25 Professor Leonard jumps here from ln(6) = 10k to k = (ln(6))/10 and gets 0.179 as a result. I come to a different result by way of the following steps: (1) ln (6) = 10k In order to convert k from an exponential to a factor I apply ln to both sides: (2) ln (ln(6)) = k times ln (10) In order to solve for k I divide both sides by ln (10) (3) (ln(ln(6))/ln (10) = k Since ln is not a factor but a description of or a command what is to be done with the number in brackets ("Take the natural log of six") I think it is not possible to cancel out the ln in the numerator against the ln in the denominator. It seems to me that Professor Leonard has just done that by writing (ln(6))/10 in the next line. I prefer to proceed like follows: (4) ln (6) = 1.792 ln (1.792) = 0.583 (5) 0.583/ln(10) = 0.253 Whose solution is the correct one? (G.R., Bonn, Germany, a great fan of Professor Leonard)

[@jacobdavis5691]

"I'm not gonna go into the birds and the bees with you" 😂😂😂

[@dg-gaming942]

the funniest part was watching professor leonard get flustered while trying to explain baromatric pressure. to be honest, i did not see it coming and it caught me off-guard

[@kamalmakhloufi6707]

Thank you so much professor for all the lessons .they are highly useful

[@daverd6434]

Thank you very much Professor Leonard

[@mayhaz126]

these examples really help...Thank you for your effort

[@oximas-oe9vf]

Hi professor Leonard I hope you are doing great. these problems are really helpful.... I Would suggest you add a PDF or some sort of attachment in the description of the problems you solve so we can Solve them prior to watching the video, that helps with saving time and as always thanks for the great work

[@kenkreis2924]

Excellent application set. Presented in great detail.

[@alekslyubenov348]

Thank you for all of your hard work, you really do help a lot!

[@nikolozperadze4887]

Great work on the examples killed it.😎

[@spcverger]

These are fantastic. Really helps solidify.

[@ryanduncan2525]

I'm at a calculus 2 level, so I'll follow along with this series for as long as I can xD

[@williammendez5209]

But you will need Calc 3 for PDE's!

[@williammendez5209]

Yeah I know, but Prof. Leonard said that he'll be covering PDE's later on. Also, idk why u mentioned Mech. Engineer; that's kind of random. If you're referring to me, I'm not a Mech. Engineer.

[@robertbrandywine]

Calculus 2 should be followed directly by differential equations. Calculus 3 is more about sequences and series.

[@williammendez5209]

Robert Brandywine No. Calculus 3 is just calculus 1 and 2 in R^3. It mainly focuses on partial derivatives and multiples integrals. It also covers vector calculus like vector fields, divergence, curl, line integrals, etc.

[@robertbrandywine]

@@williammendez5209 - not where/when I took it. Perhaps it varies.

[@catherinebopp9469]

King, I would never leave you

[@tanvirtscientist608]

it was awesome to learn from a genius teacher like you sir! i wish you a very happy life! go ahead and do some more math videos sir!

[@ansahfrank4850]

extremely helpful video, thank you Professor Leonard

[@Illu0ne]

Professor Leonard I know there is a special seat for you in heaven

[@Sonofapoop02]

This video helped a TON!! Thanks, Professor!

[@minkim2576]

Thank you so much Prof. Leonard!!!!

[@hellmuth26]

26:55 He should do a separate series of videos where he DOES go into the birds and the bees for us.

[@nuzhatazim8194]

I'd watch it although I would cringe the whole time lmao

[@Tzone02]

Made it through all of them. Taking a diff eq & linear algebra course in my first upcoming semester of college. Hopefully I’ll be ready.

[@amiteshshekhar601]

professor leonard it was just awesome

[@jstadler417]

Great lecture as always!

[@Dave-dt9ss]

Who said maths are not useful for everyday life. I can now estimate time of death! :) Awesome work from Prof Leonard

[@heitorlopes9816]

the one with the cooling the soda and the other with the crime scene were really funny to do

[@ephraimcabiliza317]

thank you so much professor leonard

[@davidxguitar]

Rock solid video. Really enjoyed the models.

[@sorinpanciuc5712]

thanks for those exercices !

[@wawaT100]

legend Prof Leonard.

[@thevegg3275]

At 12:24 you say that P(t)=P0e^kt because C=P0. That seems incorrect because C=P0 ONLY when t=0, not at any time t. If P(t)=P0, then also P(4)=P0 and P(any positive integer) =P0. That cannot be true.

[@marq6325]

Really an erudite professor, thanksss

[@damuddohonson2282]

Of course imma still watch education for free. I'm planning to finish all of your classes too.

[@maesab2104]

Thank you so much to this video ❤️ 10/13/20

[@pipertripp]

Definitely helpful. The reps are good!

[@mozamelahmadi5693]

I trust this guy's biceps.