PLEASE NOTE MISTAKE: In the Second Example, I forgot two "NOT EQUAL" signs in the Set Builder form of the Domain. Please make sure to add those "NOT EQUAL" signs to both the "4" and the "-4" that I forgot to include. Sorry and thank you!
Ah my man, the Legend is still here! I finished my Applied Maths and Stats degree a couple of years ago and I owe so much of it to this man! A proper MONSTER tutor, I am eternally grateful! 😎
I really appreciate Prof Leonard’s explanations, including common confusions and why they’re incorrect. It’s obvious he understands why mistakes are made and isn’t condescending. Such great videos. I didn’t understand WHY domain was important and glossed over it in the past. Love it when he explains why as well as how. Back in my school days math teachers got to angry at my questions. Leonard obviously has a lot of experience with student questions and takes the time to help us understand.
I don't know what I would do without your videos. I am a student at ASU and I heavily rely on your detailed instruction to keep up in PreCalc. Thank you so much for taking the time to make these and post them. I hope you go all the way up to Calc 3 or I am in trouble lol.
Thank you, professor! I finished video 4 and I need to complete 69 more videos before I attended University this August. I will have to watch about three of your videos a day in order to achieve this. My current summer math teacher is very ineffective with his ability to teach the concepts. I really appreciate the time and effort you put into making this educational videos
@@toriel5695 Currently, I am in finals week for my college algebra class. My grade is an 81%. I have just been watching this video series and using khan academy for practice problems. These videos have substituted my teachers lectures and reading from the book provided in the class. This video series covers most of what you will need to know for pre calculus, but I would also encourage you to take the pre calculus course on khan academy www.khanacademy.org/math/precalculus
literally just started this in class today and found this vid. really really good explanations as to WHY the domain is written the way it is. thanks for the help!
It could be cool/ wonderful if you posted an older test/Exam to go with the units; I truly believe teaching is a scared profession, and as such you have that gift. I want to thank you for sharing your wisdom with the world.
Did 3 and 4 today, really appreciate the scaffolding in of the older stuff as I'm almost 40 and here from a master's in lit, wanting something... more math-y
Professor Leonard, this is a fantastic introduction on Finding the Domain of Functions in Precalculus and College Algebra. The examples are very helpful for all high school and college students.
Awesome shirt! I'm really happy to see that you're still on RUclips! I'm currently in the middle east with the military and had a huge break between Calc 1 and upcoming Calc 2. My days here have been filled with Prof. Leonard and I couldn't be happier. Thanks!
Literally studying pre calculus in preparation to my calculus 1 subject as a 1st year BS Math Student. I don't have any background about Calculus but watching these videos helps me a lot and I am amaze how easily I can understand this, his technique are really good!!!
Would this help me with pre-cal? I'm taking pre this fall, but I wanted to review algebra since it's been a while since I took it, and I had some trouble with trig.
@@anarchistsalute in my opinion, I think this series would really help you since it tackles different topics in pre cal but if you are focusing on algebra and trigonometry, I think it's much better to look for specific videos that focuses on what you need. Try to go back to basic then proceed with pre cal so that you won't struggle in understanding pre calculus.
You are the best professor in mathematics you can answer all the questions I can ask my self you can why I can do this Best professor I wish you always happy in your life my wish Is I can meet you in my life
I think you should choose a textbook of some kind, that we could all be on the same page with you. I think a good example would be maybe the free pre-Calc Book that is featured on open stacks, or another textbook of an earlier edition that you would follow faithfully and we could follow along. It’s nice to have videos on everything, but there’s not much organization this way. You have been a teacher for a long time, I’ve heard you say that you use three or four text books at a time, which would not be feasible for us. But your videos could reflect just going through one textbook of your choice. If it was an earlier version it would not cost much at all or you could resort to the free pre-Calc book I mentioned earlier. Thank you for what you are trying to do.
I just learned something here better than my profesor. U just explained why. Thats the important part of learning math, Why. Using the words not happy with ceros or roots dont like negatives, in that way I understand better.
I've watched some 66 videos from Prof. Leonard and he's an amazing teacher but his speeding up and slowing down, soft speaking and then loud speaking speech patterns makes for a hard time watching his videos. I just wish he would try to keep a constant voice volume and speech pattern just so that I could fully absorb the knowledge he's imparting in this amazing videos; either way thank you -Prof.- for putting up the time and effort of trying to make math fun and easy.
Hey professor, how many videos are there going to be for the whole precalculus section you're doing? I'm asking because I'm currently taking Calculus but I have a very weak algebra and trig base from my high school time, and I wonder if I could follow along your videos before my tests start or if I should go for something quicker.
Hi Professor - I love your videos! I wanted to make a gentle request - I know you give examples (which is wonderful), but is there anyway to condense the topics if your videos? In other words, I would like to see specific topics in shorter 10-15 min videos. If you can't, I understand and others have probably asked, I just have a time crunch so I am trying to learn as quickly as humanly possible. Thank you kindly.
Great videos but I'm a bit confuse Professor L. - In the example 3x-15/x-4 under the radical- couldn't you get a negative in the denominator and a negative in the numerator which would turn it into a positive and therefore OK to be under the radical? What am I missing here? Am I over thinking this?
Thank you so much for your clear and informative explanations. One question, in the last example at the end of the video, there is a square root in the denominator. shouldn't square roots be eliminated from the denominator?
![Yeat & Quavo - 5BRAZY [Official Music Video]](http://i.ytimg.com/vi/4XxnTAwyxus/mqdefault.jpg)
PLEASE NOTE MISTAKE: In the Second Example, I forgot two "NOT EQUAL" signs in the Set Builder form of the Domain. Please make sure to add those "NOT EQUAL" signs to both the "4" and the "-4" that I forgot to include. Sorry and thank you!
Sir
Expect t=0, t=-4, t=4
I thing, this is correct.
Am I right?
Sir please make a video on real analysis...
Hi prof. plz make Videos on techniques for Higher order differential equations
It's ok. We all make mistakes.
Ah my man, the Legend is still here! I finished my Applied Maths and Stats degree a couple of years ago and I owe so much of it to this man! A proper MONSTER tutor, I am eternally grateful! 😎
Who freaking asked.
@@jesus5508 That was meant to be a joke just forgot to inform him I appreciate the comment, though.
@@jesus5508 I'm a bit older than that, 13 to be exact. Nice guess, though
@@johnbiluke8406 🤡
Someone give this man a nobel prize! I was almost rushed to the ER after having an Navier-stroke trying to figure this out on my own lol.
I really appreciate Prof Leonard’s explanations, including common confusions and why they’re incorrect. It’s obvious he understands why mistakes are made and isn’t condescending. Such great videos. I didn’t understand WHY domain was important and glossed over it in the past. Love it when he explains why as well as how.
Back in my school days math teachers got to angry at my questions. Leonard obviously has a lot of experience with student questions and takes the time to help us understand.
I'm gonna try to watch and understand all pre-calc, and calc 1-3 videos in two weeks. wish me luck
how'd it go?
Could you do it? if yes how did you plan? Please share your plan. if not , what was the reason to fail
I'm sorry but I'm gonna call it impossible lol...to fully understand them too? lol
Just 3 weeks for calculus u kidding..
@@phenomadit1821 I did it in less time easy.
You've saved our lives, we're eternally grateful.
I don't know what I would do without your videos. I am a student at ASU and I heavily rely on your detailed instruction to keep up in PreCalc. Thank you so much for taking the time to make these and post them. I hope you go all the way up to Calc 3 or I am in trouble lol.
There are already Calc 1, 2, 3 videos present in his channel. You can watch them after completing preCalc.
I died at the MC Hammer thing, I love this guy!
He uses the MC Hammer joke a lot.
I think I have heard him use it on 3-4 different occasions, lol.
M.C. Hammer is a pastor today.
Thank you, professor! I finished video 4 and I need to complete 69 more videos before I attended University this August. I will have to watch about three of your videos a day in order to achieve this. My current summer math teacher is very ineffective with his ability to teach the concepts. I really appreciate the time and effort you put into making this educational videos
How is your progress? I’m curious cause I’m trying to prepare for a Calculus 1 course which will start in the end of September
@@toriel5695 Currently, I am in finals week for my college algebra class. My grade is an 81%. I have just been watching this video series and using khan academy for practice problems. These videos have substituted my teachers lectures and reading from the book provided in the class. This video series covers most of what you will need to know for pre calculus, but I would also encourage you to take the pre calculus course on khan academy www.khanacademy.org/math/precalculus
Just come here to say thank you. THANK YOU PROF. LEONARD!
literally just started this in class today and found this vid. really really good explanations as to WHY the domain is written the way it is. thanks for the help!
BEST TEACHER IN RUclips. STILL WATCHING YOU SIR
It could be cool/ wonderful if you posted an older test/Exam to go with the units; I truly believe teaching is a scared profession, and as such you have that gift. I want to thank you for sharing your wisdom with the world.
This guy is funny and good at explaining math. Such a gifted/skilled/tactful man! Thanks for helping me
I have never understood these concepts more clearly! Great Job, Professor!
Did 3 and 4 today, really appreciate the scaffolding in of the older stuff as I'm almost 40 and here from a master's in lit, wanting something... more math-y
I swear I love this guy especially with covid19 going around I can play catch up on all my work and come in strong.
Who asked
lets gooooooooooo! did you come in strong mate?
@@Stashdaddy69 Yo
@@johnbiluke8406 Jesus, what the heck is your problem, mate?
i don't what to say you save my life thank you professor .......... from Ethiopia
Professor Lenard you are best - you have all the qualities of a humble teacher ♡ ♥💕❤
Professor Leonard, this is a fantastic introduction on Finding the Domain of Functions in Precalculus and College Algebra. The examples are very helpful for all high school and college students.
Awesome lesson, many thanks for uploading all this material for free!!
You're literally developing my math skills by the minute of watching your videos.
God sent, TY prof Leonard you are far more important than Einstein, Even Einstein didnt explain maths like this!!!
Awesome shirt! I'm really happy to see that you're still on RUclips! I'm currently in the middle east with the military and had a huge break between Calc 1 and upcoming Calc 2. My days here have been filled with Prof. Leonard and I couldn't be happier. Thanks!
Literally studying pre calculus in preparation to my calculus 1 subject as a 1st year BS Math Student. I don't have any background about Calculus but watching these videos helps me a lot and I am amaze how easily I can understand this, his technique are really good!!!
Would this help me with pre-cal? I'm taking pre this fall, but I wanted to review algebra since it's been a while since I took it, and I had some trouble with trig.
@@anarchistsalute in my opinion, I think this series would really help you since it tackles different topics in pre cal but if you are focusing on algebra and trigonometry, I think it's much better to look for specific videos that focuses on what you need. Try to go back to basic then proceed with pre cal so that you won't struggle in understanding pre calculus.
The best videos for learning math. He should start his own school.
Thanks Prof Leonard, you have Math so enjoyable!
wow man, learning more than any other teachers attempt in my 12 years of school
i have been stumped and literally exploding my brain trying to understand precalculus thank you so much omfg everything start making sense!!!
HOW? Just how a math teacher can make an educational video to be hilarious? Lol i lost it after square root wants to be "POSITIVE".
You are the best professor in mathematics you can answer all the questions I can ask my self you can why I can do this
Best professor
I wish you always happy in your life my wish Is I can meet you in my life
I think you should choose a textbook of some kind, that we could all be on the same page with you. I think a good example would be maybe the free pre-Calc Book that is featured on open stacks, or another textbook of an earlier edition that you would follow faithfully and we could follow along. It’s nice to have videos on everything, but there’s not much organization this way. You have been a teacher for a long time, I’ve heard you say that you use three or four text books at a time, which would not be feasible for us. But your videos could reflect just going through one textbook of your choice. If it was an earlier version it would not cost much at all or you could resort to the free pre-Calc book I mentioned earlier. Thank you for what you are trying to do.
if you want to see some free books , go to (OpenStax.org)
Professor Leonard.. you are what I wish all of my math teachers were. Thank you :)
Lifesaverrrr I literally can’t thank you enough I’ve been struggling with the whole concept but you cleared everything up
had to pause because I was laughing so hard at the MC Hammer reference - I love these videos!
This content is incredibly good. Thank you SIR!
makes a lot of sense and these videos are clearing up a lot about fucntions for me
Just thanks for all the good stuff! I was never great at math and you will make it finally years after college !
Love these lectures, but just wondering does anyone else miss the class set up where it made you feel like you were in class?😁
I just learned something here better than my profesor. U just explained why. Thats the important part of learning math, Why. Using the words not happy with ceros or roots dont like negatives, in that way I understand better.
Wow! I wish my teachers EXPLAINED exactly like this guys does. I understand now.
Thank you for the explanation, Professor Leonard; it was super helpful.
You are just the best tutor ever
Keep up with the good work
I don't understand it in my first language and here I get it omg thanks man
not all heroes wear capes, thanks professor leonard!!!
thanks prof your the best
Best teacher for calculus 😍
brilliant videos mate helped a lot keep it up
He is a great professor. thank you very much.
I've watched some 66 videos from Prof. Leonard and he's an amazing teacher but his speeding up and slowing down, soft speaking and then loud speaking speech patterns makes for a hard time watching his videos. I just wish he would try to keep a constant voice volume and speech pattern just so that I could fully absorb the knowledge he's imparting in this amazing videos; either way thank you -Prof.- for putting up the time and effort of trying to make math fun and easy.
Amazing professor 👏Thank you👍
That's a nice shirt prof!
You cant touch this!! i am dead! Absolute Legend !
this man is a saint
The superb mathematician!!!
Hey professor, how many videos are there going to be for the whole precalculus section you're doing? I'm asking because I'm currently taking Calculus but I have a very weak algebra and trig base from my high school time, and I wonder if I could follow along your videos before my tests start or if I should go for something quicker.
He is doing an excellent job, however you can watch mine videos two and I am positive they will also help you a lot.
anon _ go with michel van bizen
Good job Professor! Can you please post your workout routine? =)
Great job brother
14:04 is what a aunt says a thanksgiving lol
You're the superman of my grades
you are a legend Prop
You are like magic
Lex Luthor is the teacher in the next room telling his students that math is not important.
I never understood why the domain is so important ! WOW ! thank you Lenard.
Hello there, I think in square roots, you should have instead written, "Inside must be non negative". Inside must be positive excludes zero you see...
THANK YOUUUUU
You saved my life
amazing video!
Hey Professor... Nice shirt.
:) Thanks again!
Absolute legend🎉 subscribed
Big thank superman
Prof Leonard: I'll come back in a little bit with two examples.
*ad starts*
Me: It's magic!
Thank you so much.
Still following the playlist
Sir plz make a video on finding the range and domain of log and exponential functions..
Please what the text book you are using for the course so that I can follow
Hi Professor - I love your videos! I wanted to make a gentle request - I know you give examples (which is wonderful), but is there anyway to condense the topics if your videos? In other words, I would like to see specific topics in shorter 10-15 min videos. If you can't, I understand and others have probably asked, I just have a time crunch so I am trying to learn as quickly as humanly possible. Thank you kindly.
you the man
I love you man
Thanks professor :)
Professor i love you
Great videos but I'm a bit confuse Professor L. - In the example 3x-15/x-4 under the radical- couldn't you get a negative in the denominator and a negative in the numerator which would turn it into a positive and therefore OK to be under the radical? What am I missing here? Am I over thinking this?
please make a video for ranges as well
do all of the videos go over what we will learn in a pre-calculus class?
There’s a 100 vids so I’d assume so
thanks sensei😇😇😇
Today is sunday, 11:16pm Malaysia time, waiting for video #5...
yes!
thank you
2nd example 5t over (t3-16t); why not cross out t from b nominator and denominator to 5 over (t2-16) ?
lovin it
Sir please make video on real analysis
dew dew dew dew do do do...can't touch this
Thanks! :)
18:58 Still doing the Mc Hammer references :D
He really saidd "dooo du du dooo, dooo du du dooo. Can't touch thiss" XD
Love the duddeeee.
following a different series atm, but just stopping by as couldnt let a new video go unliked
Thank you so much for your clear and informative explanations. One question, in the last example at the end of the video, there is a square root in the denominator. shouldn't square roots be eliminated from the denominator?
its like MC hammer, laughed outloud in the library 😂
anybody watch this for fun
Dear sir I would like to know for which class you teaach i mean 10.11.12