Hey from 2022. It's been a decade since this was posted, but you've saved my buns at university. These lectures are brilliant. My Calc I prof acts like she doesn't even want to be there and makes all of these concepts so convoluted and unnecessarily difficult. I appreciate how you break everything down in easy to digest bites. It's amazing. I hope you're still teaching out there because mathematics sorely needs teachers who genuinely love helping others learn! Many thanks.

Basics: Limit(x->a) of f(x) = (a constant, c) 2:17 Limit(x->a) of f(x) = (x) 3:17 Limit(x->0) of f(x) = (1 / x) 5:24 Properties of limits 7:07 Finding Limits using their properties instead of tables 12:15 Limits of a Polynomial functions 18:34 Limits of a Rational functions 23:10 How to deal with domain issues 30:37 Can't simplify a domain issue ( Sign Analysis ) 40:45 Notes 47:35 Functions that are hard to factor 51:00 Rationalize out a square root with a conjugate 51:00 Limits of Piece-wise functions 1:01:12 Limits of Trigonometric functions 1:19:30 Using composition to solve 1:28:24 Squeeze Theorem 1:37:27 Tips When to write limit? 25:12 , 35:57 Difference between a hole and asymptote 31:35 Left off 53:56

how many of you are in 2024

I HAVE NEVER SEEN A MATHEMATICS TEACHER BETTER THAN HIM! I have been in this field for 40+ years. I am a maths teacher myself and, I must confess, he is a million times better than me. THREE REASONS WHY HE IS AT SUCH A HIGH POSITION OF EXCELLENCE: 1---------- Slow pace of progress 2----------Not skipping any step and Good explanation of all the necessary steps. 3---------- Making sure explicitly if everyone is on board.

Real talk. If this type of content would have been available when I went to college the first time, 25 years ago. I would not have failed and quit. Thanks to you and others, I am currently back in college as a 43 year old and thriving. You're the best man. Thank you.

See, TheOrganicChemistryTutor has been my jam since I started school but I just discovered Professor Leonard is equally good. If you are a science or a math major, pair these two youtube channels together and you really can't fail.

teachers like you is what makes mathematics a truly enjoyable creative experience..thank you!!

There are those who know what they teach, and there are those who can teach what they know.......Professor Leonard is the latter rarer breed. His enthusiasm is contagious.....long may he reign. A wonderful teacher.

Prof Leonard, you are a great teacher and a human being. from Australia a big thank you. you also bring a lot of respect to America, as you shaw that you are a representative of your culture to share knowledge and that not everything is money. THANK YOU. ALEX

this video was uploaded when I was in 1st grade in primary school now im a freshman in university! you've been teaching GENERATIONS thank you for that

Im sitting in school and paying attention in my calc 1 class and its like rocket science to me, and then I watch this videos and it all makes sense. thank you for explaining it so well

I have been in the University now for 2 weeks and I am learning MORE from Prof. Leonard.

As a calculus 1 students that haven't touch math in 2+ years. Professor Leonard, Khan Academy, blackpenredpen and Organic Tutor is the combo to go for pretty much anyone. I have a terrible calculus professor that is all about plug in numbers in formula and solve. Professor Leonard for lecture Khan Academy for simplify lecture/concepts Organic chemistry tutor for how to the work. blackpenredpen is great for reviewing everything. When do all that, go read your calculus book, you will understand what the book means. Then finally do as many questions as you can in the book Saving lives in 2023.

Late comment, but for anybody stuck or confused at 2:52:00 when Prof. Leonard says half angle identity and replaces cos(1/2pi -x) with sin(x) I believe he misspoke and meant to say Cofunction identity. Thanks to @Donovan Keating for pointing me in the right direction... To aid everyone else, I'll include the Cofunction Formulas here: sin(1/2pi -x) = cos(x) cos(1/2pi -x) = sin(x) csc(1/2pi -x) = sec(x) sec(1/2pi -x) = csc(x) tan(1/2pi -x) = cot(x) cot(1/2pi -x) = tan(x)

Its 2023 and you're still the best Professor!

Thank god for you, sir. My teacher refuses to explain the theory and just says, "accept that this is this, don't worry why,". Well if you don't know why, you really never understand what you're doing.

"Analysis is one of those things you can't abbreviate well" had me rolling lol

It has been a privilege to not only have the opportunity to learn calculus at my own pace (I typically catch on quickly and want to move on to the next part to understand the question "what's the point? or why are we doing this?") but to also learn from a good professor is amazing. There are a lot of people good at math and a lot of people good at spelling, but rarely do those skill join forces to create something as amazing as this course series. Thank you so much!

Am I the only that raises my hand when he asks if we understand. I feel like I'm watching Dora the Explorer...DO YOU SEE AN ASYMPTOTE..... DO YOU??? YAY! .....secants no swiping.

it’s been quite a while since you posted this video, but I wanted to let you know you’re still helping math students in 2018! :) thanks!

This video is of such high quality and standard that it has no dislikes or hate comments even after almost 2 entire years! That, professor, is a legendary achievement.

I pay $500 for a calculus course in university and these videos are way better and free, thank you.

I´ve donated a few hundred dollars to prf.Leonards patreon project in order for him to make more of these videos. Tbh I have never been able to grasp math as easy as when he´s explained it.

Thank you Superman! You saved my Math grade :)

He is an incredible teacher. I took calculus years ago before KZfaq. Seeing his videos make me realize what an incredible resource students have today.

Professor Leonard, THANK YOU I am Thukela Jaji a student from the South African university of Pretoria and I would like to extend my greatest gratitude to you. You have helped me a great deal and I am truly grateful without measure, you are really a superhero and I would like to ask you to continue to make a difference in other people's lives. I pray that God continues to bless you with many more years. You really make maths fun and exciting. THANK YOU ,BAIE DANKIE(AFRIKAANS), NGIYABONGA(ZULU) AND GOD BLESS THUKELA JAJI

Your videos are enjoyable to watch during this quarantine time, and doesn't feel like a 3-HOUR math lecture!

I think you singlehandedly got me through calc. I graduated in 2020 but felt like I should say thank you again 😀

I love this guy! My teacher doesn't explain things well, so I come here to learn the things I didn't understand in class. I was so nervous that I was gonna fail calculus this quarter, but now that I've subscribed to this channel I'm confident that I will do well in my class. THANK YOU THANK YOU THANK YOU!!!

if he were my teacher I would really enjoy every class. His lectures literally boost my self-esteem and confidence about study

I am so glad i found this chanel,I had already accepted that i was going to fail calculus but thank GOD ALMIGHTY I found this chanel,everything is starting to make sense.I might have a chance to save myself.I cant believe this was posted 10 years ago and its 2023 and its making absolute sense than my lecture ever does

You’re helping me to understand so much more. I wish you were my professor you’re so good at explaining things. God bless you and your family.

It has been 5 years since the video was uploaded and it is still greatly helping me with Calulus in 2017. Professor, you proved that you can withstand the test of time. Hats off!

suraj awal4 - For those of you who are seeking Lecture 1.3,you must understandably notice(If you watched the entire Lecture 1.2) that Lecture 1.3 was combined to Lecture 1.2 because the last solved problem in Lecture1.2 was on the board in the beginning of Lecture 1.4.Hope that answers your question guys This is suraf awal4's comment but I thought it would be more helpful on lesson 1.2

Haven’t taken a math class in 10 years. I’m a 27 year old freshman, this really gave me a lot of good input on what I can expect out of college level math. I really appreciate the effort he puts into making math fun and how the rules of calculus apply. 👏

2018 and he is still saving grades every day. Thank you Professor Leonard

Professor Leonard, I just want to thank you for creating such detailed lectures. I appreciate you and all the time you have taken to create examples and helpful hints enable for students to understand. My current professor in calc. 1 doesn't explain anything to the class and just writes problems on the board expecting us to magically grab hold of everything. This makes it overwhelmingly difficult especially for students near to the criteria. Your videos are allowing me to clearly understand. Without the use of your lectures, I would most likely fail. Thanks a million!

This is why i am a proponent of cloning

From 2024, I've been wishing I could have discovered Professor Leonard sooner. I binge-watched his tutorials on TPT, Precalculus, Differential Equations, and Statistics within just one month, and now I'm fully immersed in Calculus tutorial with him. Reflecting on his teaching style, I feel a twinge of regret that I hadn't found him earlier. His method of instruction made learning feel like watching a captivating movie, especially with his humorous interjections like "if that could go viral on youtube will be awesome 43:28" which i feel as if I am in his class. am in mid semester and I am very confidence A+ in calculas

If only all teachers were like you, the world would be a far better place.

He reminds me of my AP Calc AB and BC teacher from high school! Extremely smart, one of those muscly erudits, fun, and funny! If we had more teachers like that we would be a much smarter country!

Good lord why didn't I find you earlier! I struggled so much with my calculus teacher because he just could not teach. Marker board makes sense, drawing on that pad that gets projected onto the smart board doesn't. Kahn academy doesn't have anything on you good sir, well done!

WOw. I have learned more about calculus from ONE of your videos than from 2 tutors and my professor. Thank you!!!

slow and steady. no hurry at all. thumbs up!

calculus is so cool when taught by you professor

What an inspiring, passionate teacher. Thank you for helping students outside your own classroom!

This is all we need. We can repeat and watch it as many times as it takes. We can skip around. Then if we have a question, we save it for more KZfaq or maybe office hours.

I enjoyed this immensely. I did this exactly 40 years ago and am ever so pleased I still remember it all after all these years. Just proves that once you understand something, you'll never forget it. I will be looking out for other videos by Professor Leonard. I love the way he doesn't take any knowledge for granted and explains each and every step. Students are so lucky nowadays to be able to find such good stuff at the press of a button. Use it wisely!

Thank you Professor Leonard for all of your help. I like the way you teach because you explain the material clearly in a way I can understand. I have taken Calculus I and II but need a refresher for my upcoming job. You truly are the Superman of Math

Thanks so much for you're videos I go back to college in the fall and I'm watching you're videos to prepare and im really understanding calculus. My friends think I'm a dork for watching these videos everyday and it's like I'm actually in you're class I have my pencil and paper. I watch them every morning around 6 or at night. I like learning new things to keep my mind going 😊😊😊

You are a living proof of the phrase: "there are no difficult subjects, only bad teachers" Thank you for making me care about calculus

You are saving me, literally. This vid is a bit old, 2012, its 2019 now and its REALLY useful. I hope you are doing great prof.

Professor Leonard makes math easy to understand.

I also raise my hand when he asks "so who's okay with this one" , just to make sure i'm okay with that one lol

You are the best Professor ever! Jeez! Last time I studied mathematics was 10 years ago, now I am back to university, decided to study a different field, and it is so tough to manage going to classes, doing the assignments, getting ready for the midterms/exams...while also working. My exam is in 2 days and I feel like you are going to save my life! God bless you!

Thank you, thank you, thank you. I switched out of my first calculus class this semester because the professor didn't teach. He expected us to learn everything by reading a textbook. The professor in the class I switched into does teach, but not very well. He dove straight into solving limits without any of the explanation as to what it was or why it mattered. Your videos have given me the pre-cal/trig refresher that I didn't get from my first professor and the understanding of what a limit is that I have yet to receive from my current professor. You will be the reason I pass calculus this semester.

You deserve way more views for this quality of teaching

I have a really great teacher at my school, but sometimes, she doesn't show us why do we do the stuff we do. So I like how you constantly remind your students that this is heading to something bigger and show them how does the current piece help us to achieve it :)

Professor, i have just started watching your videos. I am a 45 yr old who is pursuing my bachelors degree in business. I have to say you have the best presentation skills I have ever seen in the mathematics field. I love the way you present the subject sections with extreme detail to explanation. I cant tell you how many classes i have taken in my adult pursuit of various degrees where the instructor was either terrible at presenting the subject or very vague and seemed to skip important steps that you would use as the key for the next section. Not saying they didnt know what they were doing, just that to me, the transfer of knowledge was not presented well. I have just finished watching 1.1 and 1.2 of calculus 1 and i understand more about limits than the entire semester class i took and failed taught me. Kudos to you sir!

2024 and we're still using your help. THANK YOU FROM THE BOTTOM OF MY HEART

Greatest teacher of all time! I'm doing well in Calc cause of you.

Wow thank you Professor Leonard am glad I was able to find your site ...this has given me a better understanding of the topic on Limits in my Calculus Class

I’ve been sleeping while my phone has been auto playing videos and woke up to this

Former math major college dropout here. This is fantastic! I'm brushing up on all the stuff that I thought I'd have to let go. Math was definitely a good choice for a major back when I was in school. By far the most interesting and engaging classes I took.

These videos are so legit! I wish i could just skip class and learn it from here and show up for tests, but my teacher takes attendance so i have to be there.. =(

I thank God for bringing you to me, I wish I could see you and give my voice of thanks to you professor for your helpfulness. I think you also thank the Almighty God for this Blessing. I have only 1 week at school but you have made everything very easy for me.I thank you Pro

I am in high school calculas and you make this class so much more understandable. Thanks and great job.

This guy is a really good teacher. He makes calculus seem easy. I've done teaching, and making a complicated subject accessible is not easy. It's a gift.

Sign analysis helped me on an exam today, thank you! So easy to do.

your class is so entertaining .I wish i were also there

I am currently taking business calculus and I am super thankful that you have taken the time to record your lectures. Much respect!!

you r the best professor i understand everything u teach u r better than my usless college teachers continue teaching mever stop plz make videos on straight lines and conic sections

I love this professor so much! Who knew you could actually crack up laughing and learn limits at the same time.. lol (At the "cross out both x's and get 'SIN'")

Thank you professor for sharing your knowledge. Invaluable stuff.

This is an example of someone who's truly passionate about their job. Which I appreciate because I love math myself, being into software and coding

I'm so unbelievably grateful for these videos. My professor spouts definitions and theorems at us, but does not go through the process of solving the problems or explain WHY these things matter or how they work together. Thank you so much.

your students are so lucky to have you as their prof.

Your videos are the best videos on college level mathematics tutorial! Could you please do a list of linear algebra videos? That would really help a lot

Yay distance learning now I’m self teaching calculus

so lucky that people like Prof. Leonard exist!!!! Thank you sir....!!!

the longest 3hrs of my life pheww good job

You're an incredible professor. Keep up the quality content.

Professor Leonard -- Saving one GPA at a time. I sincerely thank and appreciate you.

Calculus was difficult at first. But it gets easier and easier along the way.

Everybody Bow Down to the Calculus hero!

wooow.... that was the longest video I"ve ever watched on youtube. Thanks Professor

You are the absolute best at teaching. Calculus is a class that I hate with every fibre in my body but you make it really fun to do. I've never been on the same page let alone ahead of my professors because the work was always so foreign to me but watching your videos even once has made me enjoy going to class. Never stop with these videos!

you're so incredible, i've graduated highschool for over 5 years, hating math so much, but now i'm getting to like math more and more with your lecture

I really really thank you for these videos from the deepest of my heart i wouldn't know what to do do with out it cause i'm studying in turkey ''in Turkish of course '' and i can't understand a word from the teacher . you ARE awesome !!

+Professor Leonard Can you open the English subtitles automatically for this video ? I am not a native speaker, so it is difficult for me to understand the lecture without subtitles. By the way, thank you very much for posting those videos. It helps me learn math a lot.

I am so thankful I found this! I literally did not understand limits. I wish more MATH teachers would explain, show and engage students as he does. Thank you so much, Professor Leonard!

When I think of great professors I immediately think of Professor Leonard. Thank you for all that you do Professor H you are the best in the game and no one even comes close!

I wish Professor Leonard could give me homework. LOL.

It would be pretty scary if there was a sine analysis test

I was able to solve the tangent limit by my own, I'm loving this

These videos have literally saved my butt. The first week of calc 1 at the university and the teacher is really unorganized and I have learned nothing. These videos have taught me more than my professor has even said!! THANK YOU SO MUCH!

@ 2:51:55 that is a cofunction formula not a half angle identity, according to my trig identity sheet. Also thank you for your videos they amazing.

I praise you, Sir!

wow I am just starting Calc 1 in college and I am not math oriented at all.. this is so helpful I wish you were my teacher.. you need to teach math teachers how to teach bc you make it make sense.. thanks a ton

Differentiation made so easy and simple. Thanks Professor Leonard❤❤