hey leonard, i like coming back to your videos to watch you teach. seeing that youre doing precalc/college alg makes me happy. to help understand the higher math stuff, a strong base in the early stuff is extraordinarily helpful. youre becoming a huge thing in the undergrad stem world. i hear people say watch your videos all the time in calc 1-3. your teaching style resonates so much that youre pretty much teaching a new generation of scientists, mathematicians, engineers, etc. thanks for everything you do.
Just bought a bunch of your decals from your store! I got the red and gold ones since I'm an ISU Cyclone. Just wanted to say thanks for everything you do. You have helped me tremendously in my journey to becoming an engineer.
The more I get my hands dirty with advanced material in college the more I realise how much important it is to have strong foundations. Unfortunately i have not grasped intuitivally many concepts from pre-calc and calc 1 like derivatives and integrals and math has a way to humble you when you are reading up on Machine learning or cryptography on a slightly deeper level and you feel like the dumbest person in the world. I like teachers with passion like prof leonard that make the video come to life. Ty for the free content you are providing to us all
Studying ML & Cryptography and have been struggling with the math as i never paid attention during high school. Going back right now to relearn linear algebra and calculus.
These are must have things before calculus class and algebra based physics class. I remember when I relearn physics, the difficulties come from mathematics. Nice.
Thank you so much Sir. I am an international student who is going to attend college in the US.I am really lack of maths knowledge since I didn't understand most of the maths lessons that I was taught in my country government school. But by watching your videos, I can recall most of the things that I forgot and I really love the way you teaches which includes jokes and perspectives from the student that help me easy to understand your lessons. Right now, I am confident enough to take maths courses at the college that are waiting ahead.
In highschool I was always wanting to know the "whys" in math and I had great teachers but they wouldn't always be able to or willing to delve into the "whys". I'm really grateful for how much you emphasize understanding why we need the "whys" to feel concrete about following the have tos.
Hello Prof Leonard, thank you for such beautifully explained videos. I wish I had a teacher like you when I was in school. I am trying to learn Calculus to advance my career in Deep Learning. Since I have never had any formal education in this subject I am basing my efforts fully on your videos. I was feeling that I am lacking some practice to I decided to buy a copy of Precalc by Stitz and Zeager. Thank you for your brilliant lectures, you truly are an angel born as a human. Loads of love and respect from India.
Thank you! I spent hours/days/months finding you. You are really helping me understand everything. It is so hard to remember every step and the way you are doing these videos has really helped me. I was so stressed. So my biggest thanks to you! you are saving so many people with the way you do these videos!! THANK YOU, THANK YOU, THANK YOOOOU!!
Hey leonard. Hope you will be doing well. I am writing this for you that 2-3 months ago I didnt know anything clearly about math. One of my friends suggest you're channel so i started watching you're vedios. I completed your intermediate algebra playlist and doing pre calculus. And now i can do most of the problems just b/c of your. Love from Pakistan.❤
Professor Leonard, thank you for a solid explanation and smooth analysis on the Operations of Functions in classic Precalculus and College Algebra. I am currently reviewing Precalculus, Trigonometry, Calculus, Linear Algebra and Differential Equations.
For those who don't understand why we keep the domain of previous functions even though the domain seems to be cancelled out, I think I've figured out what the problem is. In the division we're assuming that denominators are not equal to zero, because if you put 2/3 instead of x you get ((4/3 + 3)/0) / (8/3/0) which is nonsense. So when we're doing the division we're assuming that previous denominators still cannot be 0, and this carries to the new function even though it seems like there is no problem anymore. If this was independent function then yeah there would be no problem, but since we got it by dividing two other function we have to consider the domains of those functions. I hope I got it right
Hi! I am just in love with your classes, thank you so much for being so didatic and doing all that for free! Do you have any exercise lists to recommend to me? I feel like if i do not practice i will just forget! Thank you so much!
Hi Professor Leonard, Is there a book that you use that we might follow along with. I ask because I'd like to be able to have more problems to practice with from each video and check them. Thanks in advance for your help. And thanks for what you're doing for us.
when i graph (x sqrt(x+3))/5) it looks like x can equal zero but i thought x can not equal zero from the original function? thats what im confused about. does the new function not have the same domain issues as the original functions? because from your lesson the main point was that the domain issues carry over to the new function.
I am currently going through the statistics playlist and I am loving it....you are the best teacher@👍...any topics becomes so easy when you explain it. Thank you for helping us learn the right way.
One question I have is when adding or subtracting two different functions as you did in your first two examples, what would happen if their domains were not the same as each other in their own individual forms?
oh man im sad this wasn't around when I was in college algebra, i know it would have saved me a ton of time and struggling! I'm glad it is here now for everyone though, on the off chance you see this Professor Leonard, thank you so much for your calculus series, it is saving me a lot of time!
Hi Professor Leonard, thanks for these wonderful videos. At 5:40 you talk about order of operations with fractions. It's been a while since I've picked up math and I was hazy on that, do you cover that in a video?
I feel a little sad that as this series progresses there are fewer views. I wonder if the earlier viewers gave up or are they now doing well on their own
;D ;D ;D same. For that maybe try EdX? MIT does have videos similar to that. Also I have seen courses from all over the world on EdX, so maybe check that out.
Hi Professor, I have a question about the last problem in lesson 5 (f/g)(x). Don't we distribute the x/5 to the square root of x+3, and this will equal x the square root of 3x all over 5? Please correct me, if I am mistaken.
hmm... this is really confusing because if i simplify -2x-3 all divided by 4x i will get a -3x divided by 4 - 0.5 and then i wont have any problem can anyone explain please
Sir,please make videos on matrices and determinants....I looked through many videos on them but all of them just tell us to memorise the steps and solve.. Only you can make us understand them ..so please sir
I wish I found his videos while I was taking pre-calc and calc 1. I am watching those two classes as refreshers since I go back to school in January and I have to take calc 2. I really wish he taught PHYSICS. Due to a previous professor I ended up dropping that class and I even switched majors. If anyone knows any real good playlist for college physics calc base I would greatly appreciate it ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Wonderful series on pre calc. I would like to know how the prof produces this and then posts it to you tube? Does Google charge him? Are the videos screened by the Google censor? Who ensures the information is accurate? He is very articulate.
Got another question for you: You made it very clear that when you divide functions the old domain issues carry over and I can take your word for it, but I don't see how myself. For instance, when I plug in 2/3 into 2X+3/4X, that looks solvable to me. It looks like I get 4 1/3 divided by 2 2/3. I don't see what's wrong with that? Or is this just one of those "you'll see later" things?
Yep, I understand the confusion... it happens a lot. When we start looking at combining functions, we always have to consider where they came from, or perhaps what they're 'made-of'. Here's an example: Let's say a person is allergic to peanuts. If they eat peanuts, they have a bad reaction. So, I make a cookie with lot's of other stuff, but one of the ingredients is ground peanuts. In the cookie, can you see the peanuts? No. Can you taste the peanuts? Maybe not. Are you still going to be all messed up because I put peanuts in there? Yep! Because of what the cookie is made of. It had a history. It has a piece that doesn't play nicely if we misbehave with it. I hope this is a good analogy.
@@ProfessorLeonard, I got a doubt. the example seems to be good but sir in example after eating cookie he will be allergic but in our case, after applying function operation we are not facing any problem it is fine completely. please explain sir
I was confused by this as well. Professor Leonard does it have something to with dividing the two functions and plugging in real numbers for values of x. If you plug in f(2/3) / g(2/3) and calculate each function first before dividing. Then the previous domain still counts?
@@andrewparcell3861 @Professor Leonard By looking at the un-factored combination of the two functions: [(2x+3)*(3x-2)] / [(3x-2)*(4x)], you will notice that you can not have x = 2/3 because that will make the resulting combination [(2x+3)*(3x-2)] / [0*(4x)] which if we simplify the denominator further, it will equal zero. I hope this explanation helped.
@@ProfessorLeonard its not, you didnt provided a intuitive explanation by doing a problem or something, because plugging 2/3 to x doesnt equal to zero in the denominator
when applied to the vector. (square root of 3,1,1) a counterclockwise rotation of angle theta with respect to the Z axis, followed by a dilation of factor K, the vector is obtained (-12,0,6). Find the values of K and theta.please make a video solving these problem.
He has said in the video "Professor Leonard's Important Announcement 2019 " that he is working on Differential Equations, Pre-Calculus, Statistics and Linear Algebra, and that it would take a while, but that he was definitely going to finish them as long as people kept watching him.
Yh let's get into more advanced topic. Personally I would go for intro topology, diff geometry and I guess for complex for people who havent done it yet.
You mean english subtitles? There are already english subtitles. Maybe you can try to request subtitles for other language in the facebook group. Perhaps you can make them with people that are interested as well
hey leonard, i like coming back to your videos to watch you teach. seeing that youre doing precalc/college alg makes me happy. to help understand the higher math stuff, a strong base in the early stuff is extraordinarily helpful. youre becoming a huge thing in the undergrad stem world. i hear people say watch your videos all the time in calc 1-3. your teaching style resonates so much that youre pretty much teaching a new generation of scientists, mathematicians, engineers, etc. thanks for everything you do.
Just bought a bunch of your decals from your store! I got the red and gold ones since I'm an ISU Cyclone. Just wanted to say thanks for everything you do. You have helped me tremendously in my journey to becoming an engineer.
Sweet! I am shipping those out today. I hope you love them :)
GL
The more I get my hands dirty with advanced material in college the more I realise how much important it is to have strong foundations. Unfortunately i have not grasped intuitivally many concepts from pre-calc and calc 1 like derivatives and integrals and math has a way to humble you when you are reading up on Machine learning or cryptography on a slightly deeper level and you feel like the dumbest person in the world.
I like teachers with passion like prof leonard that make the video come to life. Ty for the free content you are providing to us all
Studying ML & Cryptography and have been struggling with the math as i never paid attention during high school. Going back right now to relearn linear algebra and calculus.
2024/9/15 and these videos are really teaching me , i will try to put comment once in a while to show my progress , and man you are saving my ass
he's saving mine as well
I watched and took notes of your videos from 1 to 5 within a day. Everything is explained in a fairly easy way. Thank you
When it comes to learning calculus, the quality of the teacher is paramount. Professor Leanard is the best math teacher.
These are must have things before calculus class and algebra based physics class. I remember when I relearn physics, the difficulties come from mathematics. Nice.
Thank you so much Sir. I am an international student who is going to attend college in the US.I am really lack of maths knowledge since I didn't understand most of the maths lessons that I was taught in my country government school. But by watching your videos, I can recall most of the things that I forgot and I really love the way you teaches which includes jokes and perspectives from the student that help me easy to understand your lessons. Right now, I am confident enough to take maths courses at the college that are waiting ahead.
In highschool I was always wanting to know the "whys" in math and I had great teachers but they wouldn't always be able to or willing to delve into the "whys". I'm really grateful for how much you emphasize understanding why we need the "whys" to feel concrete about following the have tos.
Your content is critical for me doing well in my math courses! Thank you professor! You make math very intriguing!
Hello Prof Leonard, thank you for such beautifully explained videos. I wish I had a teacher like you when I was in school. I am trying to learn Calculus to advance my career in Deep Learning. Since I have never had any formal education in this subject I am basing my efforts fully on your videos. I was feeling that I am lacking some practice to I decided to buy a copy of Precalc by Stitz and Zeager. Thank you for your brilliant lectures, you truly are an angel born as a human. Loads of love and respect from India.
Thankyou for helping me get ready for Computer science.
Thank you! I spent hours/days/months finding you. You are really helping me understand everything. It is so hard to remember every step and the way you are doing these videos has really helped me. I was so stressed. So my biggest thanks to you! you are saving so many people with the way you do these videos!! THANK YOU, THANK YOU, THANK YOOOOU!!
Hey leonard. Hope you will be doing well. I am writing this for you that 2-3 months ago I didnt know anything clearly about math. One of my friends suggest you're channel so i started watching you're vedios. I completed your intermediate algebra playlist and doing pre calculus. And now i can do most of the problems just b/c of your. Love from Pakistan.❤
Professor Leonard, thank you for a solid explanation and smooth analysis on the Operations of Functions in classic Precalculus and College Algebra. I am currently reviewing Precalculus, Trigonometry, Calculus, Linear Algebra and Differential Equations.
your work can help me become a pilot engineer. thank you so much.
For those who don't understand why we keep the domain of previous functions even though the domain seems to be cancelled out, I think I've figured out what the problem is. In the division we're assuming that denominators are not equal to zero, because if you put 2/3 instead of x you get ((4/3 + 3)/0) / (8/3/0) which is nonsense. So when we're doing the division we're assuming that previous denominators still cannot be 0, and this carries to the new function even though it seems like there is no problem anymore. If this was independent function then yeah there would be no problem, but since we got it by dividing two other function we have to consider the domains of those functions. I hope I got it right
yes ...you absolutely nailed it right
Thankyouuu
I had mistakingly glossed over domains in the past. Love these videos!
you are the best professor, thanks you for saving me
no doubt
This man is a genius , I only wish I found this in High school
Hi! I am just in love with your classes, thank you so much for being so didatic and doing all that for free! Do you have any exercise lists to recommend to me? I feel like if i do not practice i will just forget! Thank you so much!
Calculus in a week.
I'm really confused about the division example. If you graph the resulting function y=(2x+3)/4x you can clearly see that 2/3 is now in the domain.
Thank you for the explanation, Professor Leonard; it was super helpful.
Hi Professor Leonard, Is there a book that you use that we might follow along with. I ask because I'd like to be able to have more problems to practice with from each video and check them. Thanks in advance for your help. And thanks for what you're doing for us.
You’re a National Treasure!
Great upload, sir! Thanks for the help learning math.
love the simplicity; :)
OMG, my hand was shaking when writing out all your important notes (even though I know i always can replay your video), my goodness!!! Thanks.
when i graph (x sqrt(x+3))/5) it looks like x can equal zero but i thought x can not equal zero from the original function? thats what im confused about. does the new function not have the same domain issues as the original functions? because from your lesson the main point was that the domain issues carry over to the new function.
Thank you for taking the time to make these
I am currently going through the statistics playlist and I am loving it....you are the best teacher@👍...any topics becomes so easy when you explain it. Thank you for helping us learn the right way.
One question I have is when adding or subtracting two different functions as you did in your first two examples, what would happen if their domains were not the same as each other in their own individual forms?
it would be the same, but because the domain is the same number, you just write it down once. if there is two different, you write them both down.
Resultant function 3:12
Best way of teaching... Thanks a lot..
Awsome.Thanks alot u saved my semester mid.
uhm maybe if you could, teach physics as well? You literally made maths so approachable for me, I was wishing for the same in physics as well
Sir, you are a beast!
Thank you so much.
For people who are looking to practice what they are learning here - can you point us toward a textbook or something like that with practice problems?
oh man im sad this wasn't around when I was in college algebra, i know it would have saved me a ton of time and struggling! I'm glad it is here now for everyone though, on the off chance you see this Professor Leonard, thank you so much for your calculus series, it is saving me a lot of time!
Hi Professor Leonard, thanks for these wonderful videos. At 5:40 you talk about order of operations with fractions. It's been a while since I've picked up math and I was hazy on that, do you cover that in a video?
Sir could you please make video on abstract algebra(modern algebra) also
Thank you ❤
Thank you sir✊🏿
I feel a little sad that as this series progresses there are fewer views. I wonder if the earlier viewers gave up or are they now doing well on their own
I didn't know functions had parental issues too!!!
Help, is there any Engineering lessons online just like this but about Machine Design and Powerplant Design that's not Indian.
Check out skill share
No promises tho.....
;D ;D ;D same. For that maybe try EdX? MIT does have videos similar to that. Also I have seen courses from all over the world on EdX, so maybe check that out.
thank you
Hi Professor, I have a question about the last problem in lesson 5 (f/g)(x). Don't we distribute the x/5 to the square root of x+3, and this will equal x the square root of 3x all over 5? Please correct me, if I am mistaken.
well done my boy............
Why in the last example the domain `x != 0` is still valid?
god bless you
hmm... this is really confusing because if i simplify -2x-3 all divided by 4x i will get a -3x divided by 4 - 0.5 and then i wont have any problem
can anyone explain please
Sir,please make videos on matrices and determinants....I looked through many videos on them but all of them just tell us to memorise the steps and solve..
Only you can make us understand them ..so please sir
Just use calculator techniques on Matrices its easy. Use Casio 991-Es plus
Hey, did you find any resources for matrices and determinants (linear algebra)? I hate memorization, too.
If f(x)=x(x+3)^1/2 , what will the domain be?
set the inside >0 and use a sign analysis test to determine positive intervals. I'll cover that in an upcoming video.
@@ProfessorLeonard Will the domain be different from what you showed in the video with the functions of f(x) and g(x)?
I wish I found his videos while I was taking pre-calc and calc 1. I am watching those two classes as refreshers since I go back to school in January and I have to take calc 2. I really wish he taught PHYSICS. Due to a previous professor I ended up dropping that class and I even switched majors. If anyone knows any real good playlist for college physics calc base I would greatly appreciate it ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
If you’re still looking, try the Yale Physics class with Ramamurti Shankar, it’s calculus based and excellent
Love from Pakistan ❤
By any chance are you working on a trigonometry series?
Thanks so much
Thanks!
Wonderful series on pre calc. I would like to know how the prof produces this and then posts it to you tube? Does Google charge him? Are the videos screened by the Google censor? Who ensures the information is accurate? He is very articulate.
What book does he teach from?
15:12
complete
Didn't understand how you got, "x does not equal 2/3," and I did watch the last video.
@Yavor P Thanks.
Got another question for you: You made it very clear that when you divide functions the old domain issues carry over and I can take your word for it, but I don't see how myself. For instance, when I plug in 2/3 into 2X+3/4X, that looks solvable to me. It looks like I get 4 1/3 divided by 2 2/3. I don't see what's wrong with that? Or is this just one of those "you'll see later" things?
Yep, I understand the confusion... it happens a lot. When we start looking at combining functions, we always have to consider where they came from, or perhaps what they're 'made-of'. Here's an example: Let's say a person is allergic to peanuts. If they eat peanuts, they have a bad reaction. So, I make a cookie with lot's of other stuff, but one of the ingredients is ground peanuts. In the cookie, can you see the peanuts? No. Can you taste the peanuts? Maybe not. Are you still going to be all messed up because I put peanuts in there? Yep! Because of what the cookie is made of. It had a history. It has a piece that doesn't play nicely if we misbehave with it. I hope this is a good analogy.
@@ProfessorLeonard, I got a doubt. the example seems to be good but sir in example after eating cookie he will be allergic but in our case, after applying function operation we are not facing any problem it is fine completely. please explain sir
I was confused by this as well. Professor Leonard does it have something to with dividing the two functions and plugging in real numbers for values of x. If you plug in f(2/3) / g(2/3) and calculate each function first before dividing. Then the previous domain still counts?
@@andrewparcell3861 @Professor Leonard By looking at the un-factored combination of the two functions: [(2x+3)*(3x-2)] / [(3x-2)*(4x)], you will notice that you can not have x = 2/3 because that will make the resulting combination [(2x+3)*(3x-2)] / [0*(4x)] which if we simplify the denominator further, it will equal zero. I hope this explanation helped.
@@ProfessorLeonard its not, you didnt provided a intuitive explanation by doing a problem or something, because plugging 2/3 to x doesnt equal to zero in the denominator
Complete
It would be cool u added some practice exercises.
at the part one already mentions not gonna go to details, you have to work on your own
Love you Leonard. Take a like!
The boss!👍✌
when applied to the vector. (square root of 3,1,1) a counterclockwise rotation of angle theta with respect to the Z axis, followed by a dilation of factor K, the vector is obtained (-12,0,6). Find the values of K and theta.please make a video solving these problem.
day 1
Thank you legendard
Please finish differential equations!
He has said in the video "Professor Leonard's Important Announcement 2019
" that he is working on Differential Equations, Pre-Calculus, Statistics and Linear Algebra, and that it would take a while, but that he was definitely going to finish them as long as people kept watching him.
day 2
nice shirt! representing nasa AND new mexico!
🎩
Professor, Plz make a videos on Differential geometry, Complex Anaylysis , Real Anaylysis and linear algebra..!!
Thanks in advance..
Yh let's get into more advanced topic. Personally I would go for intro topology, diff geometry and I guess for complex for people who havent done it yet.
GODSPEED
I am mathematics student and I want to hear from you
daddy
whys he kinda...
My teacher please add english I am translating to understand You and it is difficult to understand the Course
You mean english subtitles? There are already english subtitles. Maybe you can try to request subtitles for other language in the facebook group. Perhaps you can make them with people that are interested as well
What book does he teach from?