Calculus 1 Lecture 0.1: Lines, Angle of Inclination, and the Distance Formula

/ professorleonard
Calculus 1 Lecture 0.1: Lines, Angle of Inclination, and the Distance Formula

[@Liam_theX]

Bro, the fact that this video is 11 years old and yet I’m still watching it for help in calculus truly shows how helpful this man is and what a good, easy to understand teacher he is! Thank you so much Professor Leonard!

[@Hymandois]

I know exactly what you mean

[@CastledMallard]

big facts! taking calc rn and i would have died without this man. he is a blessing from God!

[@tribalpanda-ik7sp]

I have my calculus cat in two days time😂and truth be told he is really helping me out

[@chiensyang]

I just show these videos to my AP calculus students while I watch Netflix on my laptop. Therefore, the school winds up just paying me to give and grade homeworks, tests and finals. 🤫🤫🤫

[@pugsley201]

Math…math never changes

[@dadasut50]

in my religion they say when a man dies he has only three things left to be remembered by : 1) his good deeds . 2) a well raised child 3) the knowledge he left that continues to help others and you sir will live forever for every one you taught .thanks to you i have almost finished my engineering degree and no one ever taught me mathematics like you did .everything i will ever achieve in my life is because of you

[@Salehalanazi-7]

ahmed ibrahim KFUPM?

[@suhassamdeshi5691]

u better get down there and meet him in person to show ur gratitude and he will definitely be touched by that! we rarely have good teachers nowadays.

[@mr818toom]

what is your religion

[@imtjrao]

I believe he meant not to directly sound like a preacher but as a Muslim I believe it is Islam. The exact quote (translated into English) by Muhammad SAW is "When a man dies, his acts come to an end, but three, recurring charity, or knowledge (by which people) benefit, or a pious son, who prays for him (for the deceased)". In another source it is "When a man dies, his deeds come to an end, except for three: A continuous charity, knowledge by which people derive benefit, pious son who prays for him." Thanks.

[@imtjrao]

Where is this gentleman working? I would thank him personally too.

[@EagleLogic]

Not everyday you see a jacked calculus professor

[@paulmaybery7340]

EagleLogic w6

[@josephvanderhoven9967]

You beat me to the punch by two years.

[@RustlessPotato]

@Just-Passing-Through 11 you beat me by 3 weeks

[@BangMaster96]

@@RustlessPotato You beat me by being born

[@clintwestwood4545]

@@BangMaster96 my dad beat me as soon as i was born

[@cristhiangarcia5991]

As a 35-year-old going back to school, I want to thank you from the bottom of my heart.

[@irvlazaro7302]

35 isn't old, when your 50, you will look back and say damn good thing I started at 35.

[@brandonclay6572]

Yup. 48 here…

[@actj700]

I just turned 35 and starting my second Bachelors. I thought I was the only one!

[@bhorg9715]

You're gorgeous

[@kaylaprinsloo-steiner9437]

@@actj700 I'm 34 starting a second bachelors in chemical engineering!

[@forrestkennedy5458]

To everyone just starting their epic journey with prof Leonard: You are making a great decision by watching these videos. I started my journey with calculus almost 3 years ago, and prof. leonard's videos are beyond wonderful. I just received my final in calculus 3, and I got an A! When I started this series, I didn't know if I could do it, but Prof. Leonard proved to me that I could not only pass calculus but thrive in calculus. Now, I am just finishing up my freshman year of college having received Ain all three calculus classes and am pursuing my dream of becoming a physicist, and I have never been more confident in my life. If I can do it, so can you. Professor Leonard and I believe in you!

[@shetheyithe8894]

Either am I can do and understand it. I hope I make right decision,

[@OnePieceFan4765]

How’s college going?

[@baltai3123]

Thx mate. I hope, I can come back and write a comment like you

[@kronoxodusktc4011]

@@Tmacculate-zi2so what is bro yapping about?!

[@cubby091398]

I am reviewing. I took Calculus III a few years back and had an 89.6%. He rounded it to 90% so I got an A.

[@MandyDrex]

I don't know if you still check comments but I wanted to thank you for all of your videos. Since finding your channel my son's entire Calc. 3 class are watching your videos, I'm using your Calc 1 videos, and my 11 year old daughter watches your Algebra videos. I wish more math teachers taught with your enthusiasm and humor. Thank you so much for making these videos available to all!

[@ProfessorLeonard]

You're very welcome!! That's what its for :)

[@shetheyithe8894]

@@ProfessorLeonard Thanks you so much. Now I can understand all of those lectures that you've showed me In almost 50 mins. You was just teaching about 2 subject problems of math. Find 2 coordinators of (x1,x2) and (y1,y2) And second one is about (x1,y1) and an equation of the graph. Your videos are very helpful for me. You're explanations are very comfortable to me. It helped my brain can easily to collect it in the simply way.

[@alijoyce2169]

I love the way he teaches. He lets his students think and do it themselves. Our teacher just re-teaches himself...

[@Itsmyopinion3825968]

i think we have the same professor. man will stare at the board every 2 minutes for 30 seconds working out his own problems he wrote down already..

[@SourChips]

@@Itsmyopinion3825968 its like theyre learning with us

[@mwip57]

I have passed calculus at a major research university and knew that slope-intercept is y=mx+b but not why until I watched this video. Truly great teaching

[@yasarkar34]

I am watching you from Türkiye. As a engineer student I can easily work Math thanks to you. Your student proud of you Professor.

[@eraysona7916]

aynen

[@nurselinaktas]

same here

[@kennymetz187]

Professor Leonard, Hello, I am a senior at Temple University in the fox school of business. I sincerely want to thank you so much for making these videos and providing them for free to the public. My math professors here have all been incredibly intelligent, but i have really struggled with the material. I love math, but i'm just not very good at it, or so I thought. While watching your videos something just clicked and its all seems to be starting to fall into place. Now that's not to say that the material is easy by any means, but I now feel like I actually have a chance in learning it. You have a way of explaining things that makes me now able to visualize conceptually. Also, what I think really makes you stand out the most to me is how you actually give a background and explain the concepts of the theory. Many professors merely write a problem on the board and say," Here's how to solve. Any questions (three second pause) Good, moving on!" I have my first exam in seven days and thanks to you i now believe that i actually have a chance of not only passing, but might actually get a good grade. Please forgive the length, but the reason I am taking the time to write this to you is just to let you know how great of a teacher that you are.

[@ProfessorLeonard]

Best of luck on your first test Kenny!! I'm glad things are making sense :)

[@sleuth1521]

You wrote it as if it is a fckin letter

[@jerkpork4058]

@@sleuth1521 lol

[@HelluvaAnt]

@@sleuth1521 rofl XD

[@alanx4121]

@@sleuth1521 They should put back writing letters in the school curriculum.

[@ImDaRealBoi]

11 years later, and I have to say that this aged really well. Loved your teaching style and involvement with the class, you even got me answering out loud. Thank you Professor Leonard, I'm going to try to do calculus over the summer and I think this will definitely help.

[@plopsan]

Im gonna try for the second time (and last time, I only get two tries) to pass Calculus 1 next year, I failed the first time so wish me luck guys. This major is important to me, because it’s my life challenge, my “I can do it as well” moment, especially as someone who’s been struggling with math, dyslexia and attention my whole life. I’ve unfortunately always been one of the worst ones in math, and been extremely slow as well, when my friends finished an exercise, I was always three exercises behind... Even if I don’t pass, I want to thank Professor Leonard because thanks to you, I’ve understood key concepts that I would’ve never understood otherwise.

[@Helly04]

First of all, I wish you good luck for your math journey. All the best. You can . I will pray for you. ❤ Good luck man. At least you are trying. Keep trying and be consistent. Well my story is the same as yours . I am very weak at maths 😢😢 and l m just wandering here don't know why l want to learn but my basics are too poor. Anyhow trying to gather the strength to start and prove myself.😢❤

[@plopsan]

@@Helly04 Thanks man, I bet you can do it as well!! I've been watching the full 110 pre calculus videos from the Prof. Leonard and taking a ton of notes, if you have the time for it I would rly recommend you do the same because I'm finding it very useful to strengthen the basics. My objective is to watch the following videos from the professor: 120 videos of pre calculus, 30 videos of calc 1 and start the calc 2 videos before starting my semester in September (so in 2 months).

[@Otatoes]

How's ur prep going?

[@plopsan]

Slow. My objective was to make the best notes possible, so I wouldn't lose time during the semester. I produced 20 pages of very high quality notes, but I had not anticipated that it would take so long. Mostly, I try my best to understand the subject first, and then put it in words that I think will make me understand the subject right away when reading it. It takes me around 4-5x the length of a video to have good notes on it. It's extremely time consuming. I also often went back to previous notes to repage them, add or move content when reading them again and realizing they could be improved. Another thing I had not anticipated is how busy I would be even by having all my days free, because I ended up doing many things I didn't have the time to do during the year. I go to the gym most of the days of the week and that takes me around 2-3h per day because it's far away. And on top of that I'm on vacation for 2.5 weeks and can't work on my maths. I'm didn't give up, but I have my doubts on wherever that will be enough, but regardless I'll keep working on my notes during the semester as well.

[@mc9960]

I had to come back here to say thank you for my civil engineering degree. I couldn't have got it without your help!

[@shetheyithe8894]

I am learning about enigneering too.

[@jestfullgremblim8002]

Woah

[@alexjohnnythelumb7579]

IT student here, I'm gonna have a Calculus 1 exam tomorrow and I've watched your course to prepare myself. Whether it's going to be good or bad, thank you for everything you shared here, you're amazing!

[@damndudethatsawesome]

How did you do on your exam?

[@LFerrellMechEng]

This guy is a hell of a professor. I always found math extremely interesting, and originally wanted to make a career out of it. I've found throughout my life that I'm much better at applying complex mathematical concepts to real-world applications, so here I am, a mechanical engineer. As someone who's only watching these for a simple refresher. I really wish he would've been my Calc 1 instructor. Phenomenal teaching sir. you start simple with the basics and slowly work to the more complex problems. great pace, interactive with his students, and very knowledgeable.

[@gogos869]

I can’t believe I’m watching this! I’m 60 and always wanted to learn calculus. I was afraid of my math teachers in grade school and high school (had an overly critical father) He’s a good teacher. I understand so far!

[@2IITians]

When a Teacher becomes a performer he is adored by all students. Love from India. Also I will add that 9 years ago such a good videography was not easy!

[@shreyarora4739]

yep @2 IITians I am also an Indian and i admit the fact that he is really too good 😍😍😍😍

[@xoxocv889]

Hello, I am from an Arab country. I saw your account on Instagram and came immediately to KZbin to watch you. This is really great. I wish you success.

[@Itsmyopinion3825968]

This man got me an A on my Midterm. I had NOOO CLUE what had been going on the entire semester. i found these videos and 5 days of watching his videos up to the thirteenth video 2.5 I got an A. I was truly windblown. I hope this man is somewhere that truly deserves him doing what he loves.

[@N1tTROxUMP45]

I am finishing calc 3 at university. When i took calc 1, I NEVER went to a class. Taught myself the whole course through these calc 1 videos by prof leo and aced the final!!! Just finished his calc 3 videos with a week to spare before my final and I can vouch that all his videos from calc 1 to cal 3 are legit af

[@N1tTROxUMP45]

@@aalekhrasal4246 lol didn’t expect a reply 3 years later but from the textbook and hw. You can also prob try googling stuff like: ‘calculus practice test - integration by parts’ but replace integration by parts with whatever chapter u want help in

[@Alpha-Scythe23]

Which Engineering major did you take

[@shaunmike]

Inspiring me to relearn calculus and exercise, bravo.

[@getodog5894]

This comment made me laugh harder then I should of.

[@2nostromo]

I had this calibre of teachers all through school in the 60s-70s. Now many years later i understand how fortunate I was.

[@فستقعنتاب-د2ك]

Professor Leo, I am from Iraq. May God grant you success in your career. I understand you very well. Thank you from the bottom of my heart.🇮🇶🇮🇶🇮🇶🇮🇶

[@antik8867]

Professor, I cannot express how grateful I am towards you for uploading these lectures. I am 15 years old and have a huge obsession towards math. So, I thought that calculus was something that I should get a hang of from now on. That's when I had looked up on KZbin and found your channel. And I must say that you are one of a kind in teaching. Not only are your videos comprehensive, but they also make me feel like being in a classroom-like environment, which I've rarely experienced on other resources. I believe that throughout the help of your lectures, I can easily work my way through and gain sufficient experience in this complementary field. Thanks a lot!

[@juliancassidy3081]

I don't know if this would ever get seen, it's been 9 years after all. But I'd like to give my thanks to you, Prof. Leonard. I'm an international student trying to get a scholarship to go to the States, but sadly they don't offer any AP classes here and I think not having at least participated in a few would lower my odds tremendously. I found your classes, and they were all exceptionally put together. I got a 5 on AP Cal BC and I can't express enough gratitude towards you and your work. Sincerely, have an amazing day!

[@lavine1219]

wowowowo!!!! what tips do you have to get such high scores?

[@backtoafrica895]

Just wanted to say THANK YOU. Watch all your video and Clep CALCULUS , Intermediate algebra and am working now on statistic. just tell us How we can contribute to your work. Universities make us pay more and cannot even explain 1/4 of you explanation. THANK YOU

[@ProfessorLeonard]

Ben Ti Hello Ben! You are very welcome, and I am pleased that you find my explanations useful. If you so desire, you may contribute to the channel by visiting the channel home page and clicking on the support button on the right side of the screen. Thank you so much for your encouraging words!

[@mohamedalaa1669]

+Professor Leonard I just wanna say the same as Ben said ... thanks so much

[@mohamedalaa1669]

+Professor Leonard I just wanna say the same as Ben said ... thanks so much ..... you concentrate on basics and we all miss that important point and I like the way you teach ... so thanks

[@Kbaf4]

+Ben Ti How did Clep Calc go? Was it hard? I'm going to be taking it soon myself.

[@backtoafrica895]

+Kbaf4 the secret is do a lot of example. I had 1.23 min for each question. so you have to practice a lot so on the exam you don't have to think about what method to use. the exam by himself is not difficult. Proof Leonard explain every single example that will come on the test. I got A in statistic, and B in calculus.

[@briangale404]

Getting ready to take calculus again. First time was in 1991. These videos are the best review I could find on the internet. Very helpful and I am following along with the instructor and my old Thomas / Finney 8th edition Calculus book from the 90s. I would like to thank the professor for recording his lectures.

[@ademjaoski]

What I love about your videos is you teach everyone on the base level so everyone is on the same page before moving on while other teachers except you to already be on the same page which I mean I understand but when your in college there are people of different ages that might not be as familiar you never skip a step while other teachers do.

[@freddypelo]

Professor Leonard has all my respect and admiration for his clear, friendly, didactical and kind teaching style. Thanks to him I returned to maths, redeveloped my love of sciences and concluded my career with honours. I hope he is doing well wherever he is.

[@jacktaylor1516]

Man this is good stuff... When we get out of quarantine, we are gonna be some Calc BEASTS!!!! Who is with me?

[@vladislava8351]

I’m coming back to school to finish a degree I had tried to start almost 5 years ago. Calculus was one of the classes in addition to the other where I found my self far lost. Next week we start this class again. This time I’m starting to study before anything has started. This video is helping me see where I need to focus on the most in terms of preparation for this class. Thank you for making these. I plan to go over as many lectures & material before class starts.

[@issahmusenga1196]

To get maths help,reach me out

[@fitfuelplanner]

Love how you made this so understandable! I'm majoring in Computer Science and I'm coding and doing your classes online so I can be prepared. Thanks so much Professor! :)

[@richardpfeynman4526]

Steven Garcia Cryptography

[@منيمني-ي5س]

etiohpa

[@منيمني-ي5س]

etiohpa

[@iLoveTurtlesHaha]

I'm in the same boat as you. XD Came here because my Calculus prof can't teach and doesn't know English. I am scared to death right now because he only uses caveman English and no one understands what he is saying. I don't know how a university can take our money and hire people without the basic communication skills. I'm not even exaggerating, I'm able to understand people with heavy accents, but this dude is just like one worders and constant pointing.

[@tracegoskssmsmm7933]

if the uni is more research based they really don't care how well the prof teaches they care how well he can contribute to their research, and it sucks bc they don't care about finding a teacher that can teach like this guy

[@Dmccumsey]

I just want to say thank you for these videos, I just recently passed my calculus class in 2 months, without taking pre-calc or trig before. And these videos had a huge part in that, thank you again

[@ayee1457]

This gives me hope!!! I haven’t take pre calc or trig either and I start on Monday. Haven’t taken a math class in a while either. So scared.

[@gabesreality]

Just saw this pop up on my feed and haven’t watched any of this guy in years, but he helped me get through my stats and calculus classes in college so wanted to show some love!!! Thanks Professor Superman!!!

[@Rossbach2]

True genius in an educator is the ability to take a really abstruse subject (e.g., calculus) and make it accessible to the average student. Professor Leonard has that kind of genius.

[@baseernikzad7209]

i would never pass without his lessons! What a great man he is!! I think he should also give lessons to other calculus teachers, because they all sucks badly!!

[@khadijahmohammed2214]

yaaaaaaassssss !!!!

[@pangvang7572]

Wow.. He is teaching the very foundations of Calculus in less than an hour, when my university just skips it. It doesn't hurt to have this foundations review in one class bro ;-;

[@mateobalcorta9480]

Just wanted to say thank you! you carried me all the way through calculus 4 and differential equations. Couldn't have done as well as I did without you... you're impact is huge! thank you!!!

[@sergedaney3511]

Prof. Leonard you are an absolute hero. Thanks to people like you the internet is such a great place. I've named my cat after you.

[@ramirogonzalez8216]

www.ocf.berkeley.edu/~ramirogonzalez/courses/calculus1/0_1/0_1.html Lecture Notes www.ocf.berkeley.edu/~ramirogonzalez/courses/calculus1/

[@Forde3654Eire]

38:27 "Alright uh, let me re-cap... did you get that?" Oh for God's sake! Haha! Great introduction Leonard, great teacher! My efforts in Calculus I and II failed me miserably... planning on retaking them over the summer semester. Really glad to get a nice fresh clean start with your videos here! You're the man!

[@mnonymous8694]

I know I probably don't deserve to watch this lecture because of my IQ, but I didn't get the joke :(

[@TheVillagewearhouse]

this gonna get me addicted to calculus.. Professor Leonard teaching like a god. nice stuff

[@caspervandenberg8581]

I'm a 14 year old mathematics enthousiast, and this is just what I needed after I learnt algebra. You're amazing! 😀

[@unsalad]

Oh

[@kyawheinhtut3728]

This dude is still a legend after 12 years. Thank you so much for teaching clearly!!! You are a real LEGEND.

[@chrishogan4010]

Professor Leonard, It's been about 20 years since I've looked at calc. I'm just going to say this here and now, it's completely unfair that this man looks as good as he does AND is a master of calculus. Pick one dude, you can't have it all.

[@theucovers4325]

The way you started off by deriving the formula for the slope of straight line, I must say this....I have never been taught the same way. Math had always been a subject which for me sometimes "had" to make sense. Although now after having watched your videos....it does make sense. The education domain needs more talents like you to strengthen students' confidence and competence! Thank you sir!

[@rogerbodey9475]

I am English and sat mathematics O-level at thirteen (in 1967).. I was able to continue maths for another year before having to choose my three A-levels (in Modern Languages). I regret the fact that I was never taught calculus and, now that I have retired, I hope to make good this omission. Professor Leonard's lectures are just the thing I need, his teaching style is so extraordinarily good that they would be worth watching by any aspirant teacher of any discipline.

[@josha4969]

COMPLETE CALC 1 with 13-Day Guide. (4-8 hours a day) Day One 0.1 - 50 min (Lines, Angle of Inclination, and the Distance Formula) 0.2 - 1 hr 40 min (Calculus 1 Lecture 0.2: Introduction to Functions) 0.3 - 1 hr 20 min (Review of Trigonometry and Graphing Trigonometric Functions) 0.4 - 16 min (Combining and Composition of Functions) Day Two 1.1 - 1 hr 30 min (An Introduction to Limits) 1.2 - 3 hr (Properties of Limits. Techniques of Limit Computation) Day Three 1.4 - 1 hr 30 min (Continuity of Functions) 1.5 - 1 hr (Slope of a Curve, Velocity, and Rates of Change) Day Four 2.1 - 1hr 16 min (Introduction to the Derivative of a Function) 2.2 - 1hr 12 min (Techniques of Differentiation (Finding Derivatives of Functions Easily)) 2.3 - 1hr (The Product and Quotient Rules for Derivatives of Functions) Day Five 2.4 - 40 min (Applications of the Derivative) 2.5 - 50 min (Finding Derivatives of Trigonometric Functions) 2.6 - 1hr 35 min (Discussion of the Chain Rule for Derivatives of Functions) Day Six 2.7 - 1 hr 10 min (Implicit Differentiation) 2.8 - 55 min (Related Rates) 3.1 - 1hr 35 min (Increasing/Decreasing and Concavity of Functions) Day Seven 3.2 - 7 min (A BRIEF Discussion of Rolle's Theorem and Mean-Value Theorem.) 3.3 - 26 min (The First Derivative Test for Increasing and Decreasing) 3.4 - 37 min (The Second Derivative Test for Concavity of Functions) Day Eight 3.5 - 1hr 24 min (Limits of Functions at Infinity) 3.6 - 1hr 33 min (How to Sketch Graphs of Functions) 3.7 - 1hr 35 min (Optimization; Max/Min Application Problems) Day Nine 4.1 - 2hr 45 min (An Introduction to the Indefinite Integral) 4.2 - 1hr 34 min (Integration by Substitution) Day Ten 4.3 - 2hr 10 min (Area Under a Curve, Limit Approach, Riemann Sums) 4.4 - 30 min (The Evaluation of Definite Integrals) Day Eleven 4.5 - 2 hr 45 min (The Fundamental Theorem of Calculus) 5.1 - 1hr 34 min (Finding Area Between Two Curves) Day Twelve 5.2 - 2hr 50 min (Volume of Solids By Disks and Washers Method) Day Thirteen 5.3 - 55 min (Volume of Solids By Cylindrical Shells Method) 5.4 - 2hr 20 min (Finding the Length of a Curve on a Plane)

[@shayanali8771]

Thank you so much

[@TemplarX2001]

Legend

[@urmemlel8721]

I love you bro

[@spartacusche]

you did not do the exercises? or problem set?

[@josha4969]

@@spartacusche Recommended time is 4-8 hours a day, the lecture videos are only 3-4 hours long, the rest of the time would be practice problems. Good luck!

[@KrishJourney404]

You're the best math teacher I've ever had! I never thought I could enjoy learning these concepts, but you make it so fun. Thank you so much for your hard work and dedication. I admire how you stay fit and focused while teaching math. Maybe one day you'll even invent an equation as groundbreaking as Einstein's!

[@chadbrooks80]

Professor Leonard, I am learning calculus to become a data scientist. I will need to learn all the way up to multivariable calculus and have already watched just over 20 hours of your calculus 1 videos. I watch 2 hours of your videos per day without fail in order to reach my deadline. Then I go out and find problems where someone also solves them so i make sure I understand the concepts. Let me say that your courses on here are a goldmine and a true blessing. Hope you are doing well during these troublesome times!

[@mrborat2493]

Hi I'm in 11th grade, do you think I can take this course, if not, what do I need to know before starting Calculus 1, thank you

[@7rk.l]

شكلي راح اعتمد على شرحك مبين حلو مثلك

[@Dalalabdul-kareemAbdali]

شلون المواضيع نفسها 🙂

[@TikkyTakMoo]

22:16 - small error, you would get ¾ for x intercept, not four-thirds Really great review/lesson. I'm trying to scrutinize a new method of calculus comparing it to fundamental concepts and finding the crossovers. These are so useful. Thank you!!

[@TheManonCanon]

I love Leonard why cant all Calc teachers be this great??

[@rajshekhargupta8436]

I don't know why the students aren't discussing with enthusiasm! The lecture is too great man! Too simple that it even exceeds some professors of the greatest universities. Keep up sir! ☺

[@YoungEli9]

Your teaching style is the best, it only takes me to watch your videos once with complete focus to understand the topic, my school teacher's couldn't do this if their lives depended on it

[@arm9180]

I can only dream of a professor this good

[@standsour8916]

Josh A 1 year ago COMPLETE CALC 1 with 12-Day Guide. (4-8 hours a day) Day One 0.1 - 50 min (Lines, Angle of Inclination, and the Distance Formula) 0.2 - 1 hr 40 min (Calculus 1 Lecture 0.2: Introduction to Functions) 0.3 - 1 hr 20 min (Review of Trigonometry and Graphing Trigonometric Functions) 0.4 - 16 min (Combining and Composition of Functions) Day Two 1.1 - 1 hr 30 min (An Introduction to Limits) 1.2 - 3 hr (Properties of Limits. Techniques of Limit Computation) Day Three 1.4 - 1 hr 30 min (Continuity of Functions) 1.5 - 1 hr (Slope of a Curve, Velocity, and Rates of Change) 2.1 - 1hr 16 min (Introduction to the Derivative of a Function) Day Four 2.2 - 1hr 12 min (Techniques of Differentiation (Finding Derivatives of Functions Easily)) 2.3 - 1hr (The Product and Quotient Rules for Derivatives of Functions) 2.4 - 40 min (Applications of the Derivative) Day Five 2.5 - 50 min (Finding Derivatives of Trigonometric Functions) 2.6 - 1hr 35 min (Discussion of the Chain Rule for Derivatives of Functions) 2.7 - 1 hr 10 min (Implicit Differentiation) Day Six 2.8 - 55 min (Related Rates) 3.1 - 1hr 35 min (Increasing/Decreasing and Concavity of Functions) 3.2 - 7 min (A BRIEF Discussion of Rolle's Theorem and Mean-Value Theorem.) 3.3 - 26 min (The First Derivative Test for Increasing and Decreasing) Day Seven 3.4 - 37 min (The Second Derivative Test for Concavity of Functions) 3.5 - 1hr 24 min (Limits of Functions at Infinity) 3.6 - 1hr 33 min (How to Sketch Graphs of Functions) Day Eight 3.7 - 1hr 35 min (Optimization; Max/Min Application Problems) 4.1 - 2hr 45 min (An Introduction to the Indefinite Integral) Day Nine 4.2 - 1hr 34 min (Integration by Substitution) 4.3 - 2hr 10 min (Area Under a Curve, Limit Approach, Riemann Sums) Day Ten 4.4 - 30 min (The Evaluation of Definite Integrals) 4.5 - 2 hr 45 min (The Fundamental Theorem of Calculus) Day Eleven 5.1 - 1hr 34 min (Finding Area Between Two Curves) 5.2 - 2hr 50 min (Volume of Solids By Disks and Washers Method) Day 12 5.3 - 55 min (Volume of Solids By Cylindrical Shells Method) 5.4 - 2hr 20 min (Finding the Length of a Curve on a Plane)

[@Chad-yl9yy]

00:00 Calculus review: Section 0.1 - Lines and Slopes 06:29 Learn how to find the equation of a line using fixed points and slope formula. 12:39 Learned how to graph a line using slope-intercept form 18:24 Learned about graphing lines and slope-intercept form 24:29 Finding equations of parallel and perpendicular lines 31:56 Angle of inclination and slope are related through tangent. 38:08 Finding slopes and angles using trigonometry 43:34 Trigonometry is important for success in calculus.

[@AshishGupta-qu4zh]

"Let me recap" was hilarious. You teach logically from the basics in a great way. Appreciate it.

[@TidanOfc]

This man is the most generic-looking teacher ever, great fit, great haircut, muscles, everything a perfect teacher would have.

[@johnbush2556]

I enjoy Professor Leonard. Makes me see what I missed by going to class.

[@my-crazy-fantastic-fanatic]

Tbh, my teach covered the first 10 min. in 30 seconds flat, and _I didn't understand a thing._ It's been proved once again that KZbin saves our lives on any given day. 😉

[@vantx7]

استاذ كمل صح كلامك رغم ماافهم انكليزي بس اهم شي عضلاتك اقصد شرحك

[@توت-77]

😂😂😂😂😂😂😂😂😂😅

[@user-le9pu5nr6d]

😂😂😂😅

[@MarwaAhmed-ni3tw]

😂😂😂😂😂

[@richardsinclair7661]

What a fantastic introduction to Calculus. I'm taking Calculus II this coming semester and I'm reviewing for it. I felt lost in Calculus I, even though I got a B in the class, and I'm trying to avoid that this semester. I especially appreciate that this course is taught from the bottom, up, taking time to review fundamental concepts and establish relationships between them. This is a crucial step that many KZbin courses skip. This course also manages to teach concepts in a friendly way, whereas the MIT Online Course (while being a great resource) is too technical and abstract for first-time learners. Overall, a great start. I'm looking forward to binging this playlist.

[@shicrazy33]

I freaking love you, my Calculus AB teacher just says to use the point slope line formula for the function to a tangent line, but I never learn where it really comes from. None of my previous teachers taught me it, I don't think my Algebra teachers ever did.

[@maple_vanilla]

This brings me back to the joy of math class. Having severe ADHD math was the only class I liked because it was the only one that kept me occupied and not bored.

[@prim16]

I came for the Calculus. I stayed for the professor. 😍

[@vladusa]

Weirdo

[@iamsupriyo]

you naughty naughty

[@g0urra]

Thanks Leonard, you're the best.

[@abdullahinorisack1683]

Hi professor i am greeting from somalia i like the way you are teaching mathematics and i appriciate the work you are doing thanks

[@IbrahimMomar50]

While I reading the comments, I saw youf comment, and I am originally from Somalia, I am glad that Somali brothers are connected to this heroic man.

[@canman5060]

You are a excellent Maths teacher. I have learned all these stuffs some 40 plus years ago.Now I am recapping them at old age.

[@shjaaz4139]

maybe the best teacher i have ever seen in my life, thanks for everything. your teaching method is still the best for students like me. i hope you see my comment.

[@katielove1394]

He teaches so well that sometimes I forget I am watching a video and I feel really silly when he says "show of hands" and I raise my own or when he asks a question and I answer. lol

[@jayceinfinitealgharhythmns9814]

i do the exact same thing.... it shows that you're really engaged with the presentation!

[@savedbygrace8402]

This video helps me understand my college algebra class. YOU SIR, have an extraordinary teaching gift. Thank you so much for your videos and how they are free for anyone to access them. I have 2 kids, I work full time and paying for college out of pocket. I can’t afford a math tutor. Why can’t there be more professors like you in this world? THANK YOU!!!

[@agentsmidt3209]

Aha! now I get it...after 11 years lol! I've always wondered why they call it the point slope formula....great professor.

[@ufess1620]

I remember watching professor Leonard for pre calc. I can back to this old series for my new term in a difrent college for calc. Thank you professor Leonard, for having the ability to make math and approach teaching it in way that every student eagerly comes back for more. Wish there were more teachers like you,

[@mduduzinzuza7611]

I don't know if I'm 8 years to late but Thank you Professor Leonard, I was about to give up on Math abilities but now I aspire to get a PhD. People like you make us want to be better people you brilliant no lie. May God bless you

[@stephenfreeman2207]

Excellent instructor. Professor Leonard is so good at what he does that he transcends.

[@samae1Z]

31:48 Thanks Leonard you're the best!

[@FutureAIDev2015]

This professor is AWESOME!

[@ganymeade5151]

He is very smart. A good teacher. And looks very professional.

[@graceturnbull1379]

I'm going back to school after 5 years, nearly failed Cal 1 for the second time back then and about to start Cal 2. Thank you for making this much less overwhelming. I was terrified but you make this enjoyable. I'm literally sitting here laughing which is not something I thought I'd be doing relearning Calculus 1 for the third time.

[@StaticBlaster]

The best teacher on youtube. I already know calculus kind of but I'm here to brush up on my calc skills, then I'll brush up on my linear algebra, then learn statistics.

[@davidharford3873]

I leaped from Prealgebra #20 to this video just to see what it was like. Holy crap! I'm guessing im going to need the rest of prealgebra+Intermediate before tackling Calculus!

[@beitel21]

lol take out i'm guessing and you will be correct

[@FahimSleuth]

I suggest don't dare go to calculus without detailed pre calculus. i skipped pre- calculus and the university professor expected me to know everything and they didnt even give an intro to what they were gonna teach. I am nearly failing this semester.

[@TheSpasmer]

i watched all of prof.leonards videos before calculus 1. so yes, you´re right

[@russeldioneo5187]

do trigonometry as well, trust me i spent 2 months learning everything about it i never regretted it ever since

[@davidharford3873]

Update: Just finished Prealgebra and am up his 5th Intermediate Algebra video. Lets see how this goes!

[@ShomronDavidHawkTechDV]

Thank you, Professor Clark Kent, I like the way you explain.

[@chococat1313]

i already passed calc with a 97% but i watch anyway for those biceps

[@omarkyon1933]

+katie cook lol wth,

[@ArielVolovik]

I have calculus in 2 years, just readying up haha, did he help a lot?

[@omarkyon1933]

Ariel Volovik he's a great teacher but her comment made me laugh. I know women who watch baseball for the guy's butts but this..haha lol.

[@AlchemistOfNirnroot]

Random errors, they creep into calculations easier than you think.

[@hanisingh3369]

katie cook hye

[@Trenerdify]

Damn bro we are spoiled. I'm watching a 12 year old Calculus class with a fit ass male teacher inside of a technological box from the comfort of my own home. I'm about to take his whole damn class, this is mind blowing!

[@DaFireElf]

hi, professor leonard! i started my math journey using your videos to help me figure out math intuitively and easily. i absolutely love them.

[@ععقعقغرابابا]

اساذ انته ليش هيج حلو وصاااك ❤

[@helencreates]

When he said, "You guys are really quiet," it reminded me of my Trig teacher and my heart suddenly stopped. Scared the bejeezus out of me.

[@jasonandmonte]

Thanks Leonard, you're the best!

[@abisenaguna548]

He is the most calmest teacher i've ever seen

[@sameer8056]

I am so thankful to professor leonard. I completed his whole calculus playlist. He teaches in such a way that students find intresting to learn. It would have been wonderful if i got opportunity to attend his class.

[@7s7s-k]

ها خالي منُ اجه من الأنستا 🗿🗿

[@garrafromsand]

Hello Prof. Leonard, I am Gaurav from India. I must say, most helpful video on calculus lecture on earth and I really loved these video. I would like to request to you, Actually I am struggling with several variable(2 variable function) limit, continuity and differentiability, please make some video on this topic. It will be very helpful. Thanks Gaurav

[@ProfessorLeonard]

+Gaurav Singh This will be in a video next semester for Calculus III

[@garrafromsand]

Ohh so it is my bad luck, but I still request you the same Sir and anyways thanq very much Leonard Sir. You replied, it felt very good.

[@Light-w8z]

from Iraq? 👇

[@braa16-h7x]

Me😂😂

[@HejrNu]

أنا 🎀✨

[@ريَُٰٓحَُٰٓآنَُٰۿۿہ313]

شنوو عاد تفهمون لولا 😂 وهذا يا فصل

[@mohamedatef6514]

From Egypt Bro😂

[@tearson-c6b]

​@@ريَُٰٓحَُٰٓآنَُٰۿۿہ313He explains "calculus "

[@thezopelo]

I really like Prof. Leonard. Very charismatic, ensuring comfortability for his students, limiting the friction of the journey from ignorance to mastery.

[@AngelaMaeVillaroman]

In my 5th week of college calculus and I got a 47% on my first exam :,) I will update what I get at the end of the semester with Professor Leonard’s help!!

[@marcidah7302]

I wish I discovered this 8 years ago. I would have got better math grades😭😭

[@rxpoe]

at 42:10 shouldn't arctan (-1) = -π/4 in Quad 4 (not 3π/4 in Quad 2)? I was taught that y = arctan x has a Domain for all Real numbers, but a Range only between π/2 and -π/2 (i.e. either Quad 1 or Quad 4 only). I tried looking through old comments and didn't see any comments about this. NOTE: Really like your lecture style. I'm learning a lot from you.

[@ProfessorLeonard]

Sure, that's a great thought. Now, I want you to think of it this way; we are translating Slope into Angle of Inclination. That line is going to traverse both Quad 2 and Quad 4. So, the angle of -pi/4 is correct....depends on how you look at it. If we are trying to find a Positive angle of Inclination, then we have to have 3pi/4. Either one gives the same slope of the same line.

[@tstreetmusic]

Thanks, I had the same question and your answer helped!

[@ValueYourTimeOnEarth]

is there two answers 315 deg and 135? Or is only 135 correct?

[@killthem9669]

@@ValueYourTimeOnEarth, yeah, both are correct. Sorry for late response but maybe it will be usefull for someone else.

[@clinton15clinton15]

i swear if more math teachers looked like this guy i am certain more girls would take the class.

[@JasonWard79]

But boys aren't underrepresented in STEM so its not a 1:1 comparison.

[@JasonWard79]

I chose underrepresented on purpose, my friend. :)

[@ganymeade5151]

I would get an A grade for sure; and math is not my thing. LOL.

[@karmellammy4773]

and guys

[@migahigaofficial744]

@@karmellammy4773 u mean Gays

[@ganymeade5151]

This teacher is a straight arrow. This class is for math people. However, some can always watch and learn even if math is not best subject.

[@jamesdoctor8079]

best calculus professor on youtube.. i like the way that he assumes you no nothing and builds from the ground up