Applications with Separable Equations (Differential Equations 14)

Using Separable Differential Equations to solve application problems involving Exponential Growth and Decay.

[AJ-hybj]

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.

[horizon]

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.

[minsungkim]

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

[NTWL]

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!

[basakatik]

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

[kylemunsami]

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

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!

[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.

[joeforshaw]

Hands down best math teacher on the internet!

[nta]

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.

[noorradi]

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

[martintejada]

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

[grace.venessa]

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

[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...

[ndelo]

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".

[LCT]

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.

[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.

[aibdraco]

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

[luckn.]

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.