Can someone clarify at 30:28 does it mean by factoring out the x-1 we are not making q=p and not making x=1.What does sir mean when he says "are we letting x=1 and p=q"
@@tyrenluke95 he meant we are getting really really close but not reaching there so we can cancel out the two (x-1)s but if we got to 1 we couldn't do the cancelling out
I think I was in grade 2 when you uploaded these videos, and now 2022 I am a 1st year engineering student at university who uses these videos to pass my calculus course. You are giving education to generations sir, thank you very much!
Attention Everyone!!! PLEASE Forward quickly to 25:18 and take this ONE very important advise from Professor Leonard - watch it multiple times and embed it in your minds. It is very, very true that you can be successful in Calculus by just memorizing formulas and limits/differentiation/integration rules. For those of you who are serious about studying Math, Science, Physics, Engineering, it is essential that you understand "why you are doing what you're doing," simply memorizing formulas WILL NOT make you successful as it may have had in your lower level maths. I've used the concepts of Calculus in virtually every higher level classes. Since this is the first official lecture in Calculus 1, I thought this would be the best place to post this comment so everyone starting off will have the right mindset. Lastly, I would like to thank Professor Leonard for all his time and effort he put in these excellent videos - I don't know wth I would do without it.
students wont get what u are saying till they are deep in a fluid mechanics book and trying to read it, lost as hell but know how to find sinks and sources. Learn what a derivative is, what it MEANS, same with intergral, surface intergrals, etc. You will have a much richer and deeper understanding everytime you take an advanced course in engineering.
This is VERY true. In my engineering courses we say that we are measuring 'x' with an infinite sum and of course, it implies an integral and everyone is expected to know it. The unit circle is utilized quite often if not in every engineering course that I've taken. I started calc 1 not knowing why I'm using any of this and didn't understand, but just memorized. When I got into calc 3 I had to go back to calc 1 and truly understand what I was doing in order to grasp engineering and physics concepts. THIS IS THE BEST ADVICE. LISTEN TO THIS ADVICE!!
Even when I was in engineering school, students in calculus would still ask "why are we doing this?" Like... you don't get it by now? You've taken years worth of mathematics and witnessed the progression of needing more tools to handle increasingly complex situations? Calculus is all about change. Algebra provides the basis for handling variables and mathematically understanding the 2D and 3D environments. But, how do you mathematically express changes occurring in these environments? Calculus hammers all of it home. Pair it up with its companion physics and, damn, it doesn't get much clearer than that.
George Olagov. Precisely. Well said. Anyone can learn the rules...but knowing why and how those rules are derived is difference between true learning and just learning by rote. This man cares that you understand where it all comes from, and this is what makes him a great teacher. There are those who know what they teach and those who can " teach" what they know, and there is a world of difference between the two.
I rarely respond to comments but do appreciate them greatly. You have my thanks for that. However, a comment by Can B. made me feel a response is warranted. A secant is by no means the same as a tangent, nor do I believe that I ever mentioned that was so. If you are under the assumption that a secant IS the same as a tangent, please read about limits, or carefully watch the video again. It should be clear that as the distance between the two points of a secant approaches zero (the idea of a limit), the secant so closely approximates a tangent that there is no difference and we can treat the slope of the secant to be the SAME as the tangent. Hopefully this clears up any confusion. God bless you all.
here's a question, though an answer isn't exactly required. can you use two secants to get the exact slope of a tangent? if the two secants are of equal distance from p, wouldn't you be able to predict the slope of the tangent of P by using the curve? on a perfect curve (such as the edge of a circle) i imagine the tangent would be in the middle but if the curve curves more unpredictably i imagine you could still get it if you know by how much the curve is curving.
I am extremely happy that I have come across your channel. I am 70 years old and I want to refresh my calculus and you are gifted to make complex concepts simple, thank you Professor Leonard
Best Calculus professor ever. This man helped me get an A in my calc class. I was sending out emails of all his videos to students to help them as well and they love him. You made me fall in LOVE with calculus. Thank you so much.
I wish I had him during my college days. He is extremely good in teaching this course and explains things very easily. We need more people like Prof. Leonard in colleges!
To anyone wondering if the time commitment to these videos is worth it, *I promise they are.* I go to UT Austin and my professor was atrocious at teaching calculus. I skipped virtually every lecture he gave after the first exam (when I confirmed they were genuinely unhelpful) and, before the curves were applied, averaged a 93.25 between our 3 midterms and final. For reference, the class average on the midterms and final ended up being a 61. Prior to Leonard's lectures, I was subpar at best at math. At this point, I'm very confident in my abilities and Leonard's lectures are why I'm able to say that. Sincerely, Leonard, your lessons are a gift and I'm SO thankful to have watched your videos.
I'm almost in the exact same boat as you, though it took me a bit longer to realize that my professor was not great (3 failed exams). Hopefully, I can turn things around. I'll use his videos to review during this spring break and maybe get ahead :3
DEAR PROFESSOR LEONARD, IM IN CALC RN. HOMEWORK DUE TODAY. MY PROFESSOR IS AN OLD RUSSIAN GUY AND NO ONE CAN HEAR HIM AND NO ONE UNDERSTANDS ANYTHING. BUT IM DOING THE HOMEWORK NOW !!! AT 8 PM. WHY? BECAUSE OF YOUUU. I LOVE YOUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU SOOOOOOO MUCH PROFESSOR LEONARD WISH I COULD GIVE U A BOX OF CHOCOLATES OR SOMETHING AMAZING UR SO BLESSED BY PEOPLE EVERYWHERE FOR THIS GIFT TO THE WORLD I LOVE YOU !!!! AND I WISH FOR NOTHING BUT THE BEST FOR U AND UR FAMILY
Certainly wish we had the internet and videos like this in the 80's. This professor seriously makes calculus as simple as possible. He knows the pitfalls where people get lost and bridges that gap. Great work Professor, you'll succeed as a teacher with just your approach.
Came here to learn about Calc, and noticed the following: A) He is very good looking. B) Has a friendly demeanor. C) Is obviously very intelligent and talented at teaching. D) He is not wearing a wedding ring. E) He calls himself a professor, indicating he teaches at the college level. Therefore, practically all students are 18+. Conclusion: This dude might be the first man in the history of man to successfully use Calculus as a means of getting showered in fresh, young ladies just dying to find a good looking *and* intelligent guy. Thug level: Off the charts.
16:40 was THE MOMENT I learned something. THE MOMENT something went click in my head, took a bunch of new information, and suddenly SNAPPED it into correlation. Sir you are a FANTASTIC teacher, your excitement for the subject is palpable, and you gave m something I can really latch onto... I always had a vague idea of what limit is - but now I KNOW. And that knowing happend RIGHT HERE, RIGHT NOW, thanks to you.
To any of you guys who are just starting your journey into calculus and have come across this video. DO NOT STOP. I am a senior in college and just finished differential equations recently. I struggled when this all started until I came across professor Leonard. This legend is everything anyone could ever ask for in a math professor and deserves everything and more. I know the videos may seem long, but you can always speed them up a little. It got to the point where I didn't even attend my lectures for calc classes except on exam days because I wasn't learning anything and quite frankly it was a waste of time when I was learning everything so much better through these videos. I'm not saying skip like I did. But Professor Leonard will get you to the places you wanna be. I owe my degree to this guy.
high school sophomore here (currently in precalc and taking calc 1 and 2 next year), i've heard that a lot of professers also grade based on attendance. if i get a professor like that who's also bad at teaching calc, should i just watch these videos while at the lectures? i'm asking because both of my older siblings have had some very bad professors in college. thanks!
Professor Leonard, I hope you understand and never forget that you have a great gift. I have come upon your videos looking for review as a 35 year old returning to school for an engineering degree in a couple weeks. Through your videos I actually understand these concepts better now than I ever did before. You will surely receive recognition for your approach if you haven't already. You are thorough, positive, and enthusiastic, without being condescending to the students in the classroom. Superb job professor.
I am here for the same! Almost 30 and getting ready to start a Civil Engineering degree. Need some refreshers and I'm understanding it better now than I did in high school.
Do you get to study at such an old age in your country!...... What are the job prospects?. Will a company be willing to recruit you after you earn your degree? Or are you just doing it for knowledge enhancement?.....I have passed my graduation and have renewed interest in physics and mathematics. But this wont be of much use in my country India, apart from teaching kids and helping them with their study
@@anwesaroy6998 it doesnt matter in fact it's not uncommon for alot of older people to be in college I'm 26 and currently going towards my engineering degree and so are alot of people I'm rarely in class with anyone below the age of 21
If my teacher was this good at explaining things, I would not have dropped out of calculus 30 years ago. Learning it again at age 52 and having a much more enjoyable experience. Thank goodness for teachers like this.
I'm preparing to go back to grad school at 56... i have five months to ramp up to linear algebra.... i think this prof is going to be a great asset. Thanku prof if you happen to read this. you're an amazing teacher!
@@luisavelar9883 Gonna assume you're a kid/teenager. I'm just about to hit 25 and I already can tell you that the years go by faster as you age and before you know it, kids are gonna be calling you old. Even so, I personally consider up to 13 a kid, 13-19 a teenager, 20-29 a young adult, 30-64 an adult and then 65+ is finally what I would consider "old".
Your students are so fortunate to have you as their Calc professor. Colleges should hire you to teach their teachers how to teach. You're a legend dog!
He is the only teacher that I've seen that has actually thoroughly explained what limits are and why they are used! My professor just sort of brushed through the conceptual part of this lesson and just told us the rules on limits. Thank you, sir!
I know this video was made long ago, but I must say, you are THE BEST teacher I have ever had the pleasure to learn from. If even half of my teachers had the passion for what they do, the teaching style, and the reinforcement of taught concepts that you do, I would have graduated college with a Masters at 18. I'm currently Majoring in Computer Science and Minoring in Mathematics at Texas Tech University, and you alone have taught me more than any math professor I've had. A very sincere thank you, Professor Leonard
Hash Tag. Professor Leonard was there for me when no one else was. Much love to you always. So amazing to see your videos has hit millions. Teaching Calculus around the world. I hope your house in Costa Rica is all done and built.
Hi! So glad that you found the videos helpful :) And yes, the house is done! It took 4 days with a group of us working nonstop. It was for a local Costa Rican family near San Jose.
Seriously, you are the best Math professor I had so far. You exactly know what questions students has in their minds while understanding the different concepts of math. That's is a talent in itself. Proud of you. Keep up the good work for all of us.
I needed this guy as my Math teacher in High School where I failed miserably in 1985...You are truly a fantastic teacher, I understood a part of Calculus for the first time......:)
I am a teacher in Thailand university, I always watch this video to adapt with my class. I like how you teach fundamental or the concept idea. And it make me to improve my work
So I go to school , learn , take my notes , get back home and keep them then log onto RUclips to learn from Prof Leonard. Better explained than the classes I pay for. smh.
Yes..he...does know the subject matter clearly.....that's why he doesn't need big words..just plain and simple.... Like what Einstien said: If you can't explain something to a child....you really don't know the subject matter.....
You're a better teacher than my college calculus professor. I always watch you vids after a lecture to understand a subject better. Thank you so much for your work!
Haha wow, I haven’t seen one of these lectures in years.. i dropped out of my sophomore year of college and worked odd jobs for nearly a decade. However, i was offered the chance to enroll into my university with the condition that i pass calculus 2. At this point i had forgotten even the basics of algebra and was terrified of the prospect of relearning all of math just to pass a calc 2 class to reenroll into my university. Thanks to these lectures and these lectures alone, now i am a first year medical student. Your lectures were the best resource i found online so sincerely thank you!
On a side note, it really is nice when math teachers have good penmanship. I had a professor who drew the most beautiful integral symbols you've ever seen.
Imagine a very complicated crime which has hunted many people over many years. But suddenly an investigator solves that crime by putting together all the pieces of information he has collected. By making logical connections between those pieces of information he will explain it to the public in a way that no doubt remains about the case. The same is true for math. Professor Leonard is a great Mathematics detective.
Next year I start calculus at San Antonio College. I'm a bit nervous about this, but will give it my best shot. Just like I do all my classes. Oh BTW, I'm 63-years-old and a disabled veteran.
+The Pinnacle here in the states, precalculus and calculus are taught in the last two years of High School. However, initial calculus classes are usually only single-var calc. College classes cover far more in depth subjects and topics in calculus, they're usually more oriented to study fields. For example, a calc class for engineering is VASTLY different from a calc class for theoretical physics.
Thanks so much for you lecture(s)! I'm a 38yr old guy who graduated high-school a pretty long time ago but never took Calculus courses. Never understood what it was until I watched your videos. In some ways, you remind me of my high-school Algebra teacher who was very good at explaining the whys and hows of the math and where and how it could be used. Because of that, I got an A+ but then was assigned another teacher the next semester, for Algebra II, who was frankly opposite of him and I ended up dropping out of the class because I didn't understand his way of teaching. Thank God for RUclips for those of us who can't afford college or simply don't have the time for full-fledged college training! In some ways, I'm starting to see how this could be useful in software development. I'm a full-stack web application developer who has learned everything I know from online videos and ebooks. If you got the heart and passion, you can literally accomplish anything! Thanks again for your lectures! I look forward to watching more of them.
Its year 2022 and Im learning way more from you than any of my college professors combined. Teaching is a gift and most people just dont have it anymore. I wish I could have you as my teacher! Thank you so much!
RUclips has changed the game in education. I graduated with a degree in Mechanical Engineering about 25 years ago. I wish this was around. The best thing about YT is that if you miss something you can always rewind and play it over and over again until you understand what he is trying to teach. Also with so many videos on the same subject you can pick and choose what to watch. This has made learning 10 times easier. Great stuff,.
Sorry I do this as a hobby. But this guy is one of the best because he gets into the "How and Whys something is done." Calculus is the so beautiful Its like drinking a nice glass of wine.
I'm a math teacher and a tutor. I watch these, not for the knowledge, but for the style of teaching. The professor knows how to teach in such a way as to keep your interest. I very much want some of this style to rub off on me. My students deserve it. Thanks.
I really benifit from learning calculus in a 1 on 1 intimate setting, possibly over coffee, maybe a stroll in central park in the spring discussing how its so difficult finding someone that really gets us and our natural attraction to math and academics...lol
I'm 13 and excel at school, thus I thought of studying calculus and see how it was as some of my friends claimed it to be really hard despite being really smart but I find It pretty okay due to professor Leonard's methods.
It doesn't matter if it's basic algebra, calculus or geometry, the TEACHER of the subject makes all the diffrence. Great video. Man I wish my professors were as articulate as him in explaining the principles and details of the problems.
Seconds to that; other people talk @ the rate of a speeding train and I get so enraged as I waste so much time with this Many thanks, Gabrielle from Australia.
Your explaination is better than the mit explaination with all respect to both of you . Keep going professor . And always with details please . God bless you man . Mathematician with good body . Good luck
I cannot imagine the number of people including me failed to learn math in their time just because their teacher's were either bad or they couldn't really teach. But Professor Leonard is something else, I might have found you late but you will definetly help me solve my depression. Thank to you for that, I hope one day you will return and continue to teach us with your heart.
I just want to say thank you for teaching mathematics for free this way. In school, I was a slacker. I just did what I had to do to get by. Here I am nearly 20 years after I graduated high school and I regret it deeply. I have always had a deep love of astronomy and science, but I never truly believed that astronomy/science and mathematics REQUIRED each other for one to be good at astronomy. As I have taught myself more and more over the years, I have discovered how wrong I was. So I have slowly been going back to try and relearn the things I barely tried in before. You make this enjoyable and very educational. And on top of that, it's free! I apologize, but I currently cannot provide support through Patreon, but once I am more stable, I promise you will be receiving a lot of support from me! Please continue making education in mathematics easy and understandable!
Thank you professor, I failed my math exam and I have to retake it again, I took the decision to study math during this holiday, having chinese teacher isn’t simple, I didn’t know what all of this was about... but you are helping me so much. Wish me luck for my coming exam 🙏
The day my Business Calculus professor went over limits, one of the students said, "I don't understand any of this. I just wrote 'lim' about 100 times. What does it mean?" The professor said, "don't worry about it, you'll get it." I doubt that kid ever did, I know I didn't. I think 1/4 of the class has already dropped. I've literally learned more about limits in the past hour than in 3 weeks of class.
Just wanted to come pay my respects to the man who is solely responsible for helping me pass Calculus 1-3 in college. You sir are the MAN. Thank you for helping literally millions of students!
+RB Gaming&Others Tbh. me too this teacher his glasses remind me about Clark Ken, and thought about to write a compliment comment that he is my Superman. Until see his profile pic XD
Went through all of his lectures on Calculus (1, 2, and 3)... and his lectures on differential equations. Got 98% on my engineering exam . Only messed up one thing because I didn't sleep the night before the exam (me being nervous) and even then I knew what my mistake was on the drive home. Professor Leonard is the best math teacher on RUclips . If you're here to learn math, you're in the right place. NOTE: It's fun to watch a lecture like this after completing Calc 3.... just to see how far I've come. The world is a very different place with the knowledge I now have. Sort of like Neo in the movie The Matrix when he stops the bullets and can finally see the matrix at the end of the movie and defeat the agents. This is how you feel once you learn Calculus: :) ruclips.net/video/zYwdzYC3uUc/видео.html
Never found someone who can be, while teaching, as interesting as you, Prof. Leonard! I just enjoy the lecture. I feel like I am physically present in your lecture. It is the best calculus I have ever had in my life. Salute!! Thanks for being there! Cheers!
Funny, our Calculus lecturers never mentioned anything about graphs and curves. Next thing I know, they're talking about limits. "Limits of what?" I ask, and they reply "Its just a limit"... "Yes, but limit of what?"... "What do you mean?" I failed Calculus I, not surprising... from now on, I'm watching these videos.
Gregorio Its still very annoying to just try and learn without seeing the bigger picture, it definitely makes it more boring, more robotic and overall way more discouraging to actually engage and enjoy learning.
When there's a random badass professor you found while scouring the interwebs for college lessons (just because, math is fun and why the hell not) and he actually makes it understandable. So you just sit there in shock
I am extremely happy that I have come across your channel. I am almost 60 years old trying to teach my kids math and I want to refresh my calculus and you are gifted to make complex concepts simple, thank you Professor Leonard (Same comment as Emant and thank you too)
watching this during the pandemic gives me some semblance of peace... the quiet noise of the classroom and sounds of other people is actually calming...
Professor, this is one of the most effective tutorials I've ever seen. I appreciate the fact that you made the tutorials public. I'll gladly watch the commercials of youtube's sponsors and even purchase their products in return for making this information free to me as a knowledge seeker. Two thumbs up to a great educator, youtube, and youtube's sponsors. .
This is amazing. I just suffer with basic high-school algebra, but I'm understanding almost everything this man is teaching and I'm grasping the concepts in my head and actually understanding what he is doing.
Professor Leonard, I would like to say you have really hooked me into Calculus. I've spent this entire month going through your videos on Calculus I and trying the exercises you put up on the board. In my opinion, you've done a wonderful job of turning calculus, and math in general, into something enjoyable and exciting. Moreover, you've eased my worries heading into Calculus AB in 11th Grade. Thank you for all your help. I can't simply cannot thank you enough and I can't wait to watch the Calculus 2 playlist next month! Have an awesome summer! :D Joe
Prof.Leonard - Although I took Calculus over 30 years ago, it was never explained the way you are doing. Also, your enthusiasm to teach top notch. I want to thank you for your effort.
went through calculus in high school and taking up calc 1 in college,, couldn't understand calc for the past few weeks cus my prof just be throwing formulas at us. But omg thank God for prof. leonard for letting us understand the reason for calculus & what's behind all those formulas 🫡🫡 big respect for this guy even after 10 yrs he still be saving lives of students
Next year I'm going into college for prerequisites math advanced 4 and 5 and physics and chemistry and then in 2 years , calculus, so I'm just watching this and I love it, you are REALLY passionate and I LOVE learning through these
You are awesome Professor. I studied calculus 25 years back in my engineering. I wanted to get a refresher just for the fun of it. Your course is awesome. You make it so simple. Thanks for these lectures.
Introduction ● [0:00]. Introduction. ● [0:53]. The two objectives of calculus: ○ Objective 1: Find the slope of a curve at a given point. ○ Objective 2: Find the area under a curve between two points. The Problem of the Tangent ● [5:56]. Introduction to the problem of the tangent: how to find the equation of the tangent line to a curve at a given point. ○ [7:24]. The concept of the secant line is introduced as an approximation to the tangent line. ○ [11:28]. It is explained how to move a point on the secant line so that it approaches the tangent line. ○ [16:20]. The concept of a limit is introduced: bringing one point closer to another without them being the same. ● [19:32]. Exercise: Find the equation of the tangent line to the curve y = x² at the point (1,1). ○ [19:52]. A moving point Q is defined with coordinates (x, x²). ○ [21:24]. The equation of the line is recalled. ○ [23:23]. The slope of the secant line passing through points P and Q is calculated. ○ [25:56]. The slope of the secant line is related to the slope of the tangent line using the concept of limit. ○ [27:02]. It is explained why you cannot simply substitute x = 1 in the slope formula. ○ [28:53]. The expression for the slope is simplified by factoring. ○ [31:35]. It is calculated lim_(x→1) (x² - 1)/(x - 1) = 2. ○ [34:04]. It is concluded that the slope of the tangent line at point (1,1) is equal to 2. ○ [35:03]. The equation of the tangent line is written. The Problem of the Area ● [36:20]. Brief introduction to the area problem. ○ [37:19]. The question is posed: how to find the area under a curve. ○ [37:48]. The idea of approximating the area with rectangles is introduced. ○ [38:52]. It is explained that by using an infinite number of rectangles, the area is calculated exactly. Definition of a Limit ● [40:17]. The concept of a limit is defined in general terms: What does the function do as a variable approaches a given value? ● [41:03]. Exercise: Calculate lim_(x→2) x². ○ [41:37]. A table of values is constructed to approximate the limit. ● [44:55]. It is observed that the function approaches 4 from both the right and the left. ● [46:10]. The formal notation of the limit is introduced: lim_(x→a) f(x) = L. ● [47:06]. It is emphasized that the limit does not depend on the value of the function at the point, but on its behavior near the point. ● [48:24]. What are limits? ○ An example is performed with (x² - 1)/(x - 1). ○ Since the function has a hole at x = 1, it is best to create a table again. One-sided Limits ● [57:43]. Introduction to one-sided limits: right-hand limits (lim_(x→a^+) f(x)) and left-hand limits (lim_(x→a^-) f(x)). ○ [58:30]. The notation for one-sided limits is explained. ● [1:00:00]. Exercise: Calculate the one-sided limits of a function represented graphically as x approaches 2. ○ [1:02:33]. It is observed that lim_(x→2^+) f(x) = 1 and lim_(x→2^-) f(x) = -1. ● [1:03:16]. The condition for the existence of a limit is stated: the one-sided limits must be equal. ● [1:04:11]. It is concluded that lim_(x→2) f(x) does not exist in this case. ● [1:05:41]. Exercise: Calculate lim_(x→2) g(x). ○ [1:07:49]. The student is asked to calculate the one-sided limits. ○ [1:08:34]. It is confirmed that lim_(x→2^+) g(x) = 3 and lim_(x→2^-) g(x) = 1. ○ [1:09:32]. It is concluded that lim_(x→2) g(x) does not exist because the one-sided limits are different. ● [1:10:54]. Exercise: Calculate lim_(x→5) h(x). ○ [1:11:31]. The student is asked to calculate the one-sided limits. ○ [1:12:45]. It is confirmed that lim_(x→5^+) h(x) = 3 and lim_(x→5^-) h(x) = 3. ○ [1:13:43]. It is concluded that lim_(x→5) h(x) exists and is equal to 3 because the one-sided limits are equal. Infinite Limits and Asymptotes ● [1:14:12]. The question is posed: What happens to the function 1/x as x approaches 0. ● [1:14:37]. A table of values is constructed to approximate the one-sided limits. ● [1:17:43]. It is observed that lim_(x→0^+) (1/x) is positive infinity and lim_(x→0^-) (1/x) is negative infinity. ● [1:19:18]. The infinite limit is related to the existence of a vertical asymptote. ● [1:20:43]. The four possible cases of vertical asymptotes and their relation to infinite limits are enumerated. ○ [1:23:01]. The behavior of the function in each case is analyzed. ○ [1:25:17]. The question is answered: Does the limit exist when both one-sided limits are positive infinity or both are negative infinity.
I grew up being told I am deficient in math and was placed in the special math room as a teen. I then tried to learn some math on my own with Arthur Benjamin. If it wasn't for my mum I would've never even learned basic multiplication, fractions, decimals. I was then tested in a 7 hour long test on various IQ components where 100 is the average and scored 120 in maths. I am now trying to teach myself calculus and this is my very first video. Not sure if I need to watch precalc first. I learned I'm not deficient, I just learn differently.
+Megan De I can deeply relate with you .It is just very difficult to understand maths for me .I need to know why we are doing the calculations and what is the purpose of the maths we are doing .
This was simplified that I was able to understand with work. I like how you outlined the goals of calculus 1 with you two clear visuals. Outstanding teaching!
I was waiting for Professor Kent to excuse himself for a minute while he ran out of the class, change into his red speedos and save somebody in distress.
Hello I am a 11 year old eager to learn calculus but couldn’t find a reliable source until I came across this.. Thank you sir and I respect you as a teacher
This man still saving lives in 2023. You deserve the world, sir.🖤
2024 still clutching up for me
Getting ready for my calculus midterm and I found this hero of a teacher 🙏😭 I'm blessed
Can someone clarify at 30:28 does it mean by factoring out the x-1 we are not making q=p and not making x=1.What does sir mean when he says "are we letting x=1 and p=q"
@@tyrenluke95 he meant we are getting really really close but not reaching there so we can cancel out the two (x-1)s but if we got to 1 we couldn't do the cancelling out
Kinda gay
new life goals:
-get shredded
-become an amazing calc teacher
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐
@@beoptimistic5853 ?
Hahaha I think I can teach calculus, the shredded part is harder well gonna try it
@@luisitocarrillo then please could you teach me calculus?
Those are exactly my goals this year. I am studying to tutor students calculus😅
Getting jacked would be nice too
I think I was in grade 2 when you uploaded these videos, and now 2022 I am a 1st year engineering student at university who uses these videos to pass my calculus course. You are giving education to generations sir, thank you very much!
Ikr, he's just an amazing teacher
This man still saving lives in 2025. You deserve the world, sir.🖤
so corny
I trust this man's biceps, it helps me focus on the content he is teaching.
Same
Attention Everyone!!! PLEASE Forward quickly to 25:18 and take this ONE very important advise from Professor Leonard - watch it multiple times and embed it in your minds. It is very, very true that you can be successful in Calculus by just memorizing formulas and limits/differentiation/integration rules. For those of you who are serious about studying Math, Science, Physics, Engineering, it is essential that you understand "why you are doing what you're doing," simply memorizing formulas WILL NOT make you successful as it may have had in your lower level maths. I've used the concepts of Calculus in virtually every higher level classes. Since this is the first official lecture in Calculus 1, I thought this would be the best place to post this comment so everyone starting off will have the right mindset. Lastly, I would like to thank Professor Leonard for all his time and effort he put in these excellent videos - I don't know wth I would do without it.
students wont get what u are saying till they are deep in a fluid mechanics book and trying to read it, lost as hell but know how to find sinks and sources. Learn what a derivative is, what it MEANS, same with intergral, surface intergrals, etc. You will have a much richer and deeper understanding everytime you take an advanced course in engineering.
This is VERY true. In my engineering courses we say that we are measuring 'x' with an infinite sum and of course, it implies an integral and everyone is expected to know it. The unit circle is utilized quite often if not in every engineering course that I've taken. I started calc 1 not knowing why I'm using any of this and didn't understand, but just memorized. When I got into calc 3 I had to go back to calc 1 and truly understand what I was doing in order to grasp engineering and physics concepts. THIS IS THE BEST ADVICE. LISTEN TO THIS ADVICE!!
Even when I was in engineering school, students in calculus would still ask "why are we doing this?" Like... you don't get it by now? You've taken years worth of mathematics and witnessed the progression of needing more tools to handle increasingly complex situations? Calculus is all about change. Algebra provides the basis for handling variables and mathematically understanding the 2D and 3D environments. But, how do you mathematically express changes occurring in these environments? Calculus hammers all of it home. Pair it up with its companion physics and, damn, it doesn't get much clearer than that.
@@jasonharris996
noted. bout to go back to Calc 1 and start from first principles.
George Olagov. Precisely. Well said. Anyone can learn the rules...but knowing why and how those rules are derived is difference between true learning and just learning by rote. This man cares that you understand where it all comes from, and this is what makes him a great teacher. There are those who know what they teach and those who can " teach" what they know, and there is a world of difference between the two.
I rarely respond to comments but do appreciate them greatly. You have my thanks for that. However, a comment by Can B. made me feel a response is warranted. A secant is by no means the same as a tangent, nor do I believe that I ever mentioned that was so. If you are under the assumption that a secant IS the same as a tangent, please read about limits, or carefully watch the video again. It should be clear that as the distance between the two points of a secant approaches zero (the idea of a limit), the secant so closely approximates a tangent that there is no difference and we can treat the slope of the secant to be the SAME as the tangent. Hopefully this clears up any confusion. God bless you all.
Thanks for the video Professor.
Can you tell me which textbook has been used in this video?
here's a question, though an answer isn't exactly required. can you use two secants to get the exact slope of a tangent? if the two secants are of equal distance from p, wouldn't you be able to predict the slope of the tangent of P by using the curve? on a perfect curve (such as the edge of a circle) i imagine the tangent would be in the middle but if the curve curves more unpredictably i imagine you could still get it if you know by how much the curve is curving.
If you didn't get the distinction between the use of secant and tangent listen to this bit here 33:45
Adel Suliman Book is written By Soo tan and is named Caclulus: Early Transcendentals
Manhattan Project that big red book? i think i saw that on a bookstore here in the philippines.
I am extremely happy that I have come across your channel. I am 70 years old and I want to refresh my calculus and you are gifted to make complex concepts simple, thank you Professor Leonard
Are you trying to figure out how much longer you have to live?
Sorry couldn't help my self.... Have a nice day....
+Paul Garcia duude... ROFLMAO THAT WAS RUDE
sry couldnt stop myself from laughing xd
you made my day guys now i have to clean my display from coffee:DDDDD
I'm all for non-political correctness, but I didn't even chuckle.
Paul Garcia what do you think? will u live forever...
This man still saving lives in 2021. You deserve the world, sir.🖤
still in 2022
@@bahadrpolat5984 This dude allowing me to enjoy math for the first time in my life
@@bahadrpolat5984 maybe up to 2023 and 24
i am from 3069 and this fella is a frickin' legend over there
@@bahadrpolat5984 💯💯💯💯
Best Calculus professor ever. This man helped me get an A in my calc class. I was sending out emails of all his videos to students to help them as well and they love him. You made me fall in LOVE with calculus. Thank you so much.
That's a great picture
And that's a great profile name
God bless you, brother.
I wish I had him during my college days. He is extremely good in teaching this course and explains things very easily. We need more people like Prof. Leonard in colleges!
We sure do!
Hello my dear friend how are you interacting with the lectures hope to hear from you
1968-9 I failed calc 131 then failed calc 121 then got a D in calc 121. This video helped understand more than the three quarters combined.
ruclips.net/video/S8-97elM3ho/видео.html
You are older than him, so forget about having him teach you at your days🤪😜
Once somebody said: "A good teacher/professor is somebody that can explain very complex things in an easy understandable way"
You're the best!!!!
To anyone wondering if the time commitment to these videos is worth it, *I promise they are.* I go to UT Austin and my professor was atrocious at teaching calculus. I skipped virtually every lecture he gave after the first exam (when I confirmed they were genuinely unhelpful) and, before the curves were applied, averaged a 93.25 between our 3 midterms and final. For reference, the class average on the midterms and final ended up being a 61. Prior to Leonard's lectures, I was subpar at best at math. At this point, I'm very confident in my abilities and Leonard's lectures are why I'm able to say that. Sincerely, Leonard, your lessons are a gift and I'm SO thankful to have watched your videos.
I'm almost in the exact same boat as you, though it took me a bit longer to realize that my professor was not great (3 failed exams). Hopefully, I can turn things around. I'll use his videos to review during this spring break and maybe get ahead :3
@ Ah man I'm sorry your professor isn't helpful, but I hope you can turn it around with Leonard! Best of luck!
DEAR PROFESSOR LEONARD, IM IN CALC RN. HOMEWORK DUE TODAY. MY PROFESSOR IS AN OLD RUSSIAN GUY AND NO ONE CAN HEAR HIM AND NO ONE UNDERSTANDS ANYTHING. BUT IM DOING THE HOMEWORK NOW !!! AT 8 PM. WHY? BECAUSE OF YOUUU. I LOVE YOUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU SOOOOOOO MUCH PROFESSOR LEONARD WISH I COULD GIVE U A BOX OF CHOCOLATES OR SOMETHING AMAZING UR SO BLESSED BY PEOPLE EVERYWHERE FOR THIS GIFT TO THE WORLD I LOVE YOU !!!! AND I WISH FOR NOTHING BUT THE BEST FOR U AND UR FAMILY
Certainly wish we had the internet and videos like this in the 80's. This professor seriously makes calculus as simple as possible. He knows the pitfalls where people get lost and bridges that gap. Great work Professor, you'll succeed as a teacher with just your approach.
learn square numbers from my videos.
Came here to learn about Calc, and noticed the following:
A) He is very good looking.
B) Has a friendly demeanor.
C) Is obviously very intelligent and talented at teaching.
D) He is not wearing a wedding ring.
E) He calls himself a professor, indicating he teaches at the college level. Therefore, practically all students are 18+.
Conclusion: This dude might be the first man in the history of man to successfully use Calculus as a means of getting showered in fresh, young ladies just dying to find a good looking *and* intelligent guy.
Thug level: Off the charts.
thug level: indifferentiable
Thug level: limit x->∞
You are fucking criticized.
Carmen Wong I am criticized? Ahhuh?
LOL this is not college level math, its junior high school. So most "fresh, young ladies" would be 14-16.
Finishes his lifts. Puts on his glasses and teaches us calculus.
The Clark Kent of mathematics. At night, the glasses are off and he fights crime.
connect2reality 😂
LMAOOOOOOOOOOO
He is the alpha mega Virgin, even the chad will stay out of his way.
Kinda hot lol
16:40 was THE MOMENT I learned something. THE MOMENT something went click in my head, took a bunch of new information, and suddenly SNAPPED it into correlation. Sir you are a FANTASTIC teacher, your excitement for the subject is palpable, and you gave m something I can really latch onto... I always had a vague idea of what limit is - but now I KNOW. And that knowing happend RIGHT HERE, RIGHT NOW, thanks to you.
Chillax bruh
....and knowing is half the battle, sir.
it's such a great feeling man
@@Aidssssssssss LMAOASDJ
5
you're the first professor who didn't make me feel stupid, it means a lot to me, I really appreciate that.
To any of you guys who are just starting your journey into calculus and have come across this video. DO NOT STOP. I am a senior in college and just finished differential equations recently. I struggled when this all started until I came across professor Leonard. This legend is everything anyone could ever ask for in a math professor and deserves everything and more. I know the videos may seem long, but you can always speed them up a little. It got to the point where I didn't even attend my lectures for calc classes except on exam days because I wasn't learning anything and quite frankly it was a waste of time when I was learning everything so much better through these videos. I'm not saying skip like I did. But Professor Leonard will get you to the places you wanna be. I owe my degree to this guy.
Thank you for your voice, SJW. How true you have spoken.
high school sophomore here (currently in precalc and taking calc 1 and 2 next year), i've heard that a lot of professers also grade based on attendance. if i get a professor like that who's also bad at teaching calc, should i just watch these videos while at the lectures? i'm asking because both of my older siblings have had some very bad professors in college. thanks!
Professor Leonard, I hope you understand and never forget that you have a great gift. I have come upon your videos looking for review as a 35 year old returning to school for an engineering degree in a couple weeks. Through your videos I actually understand these concepts better now than I ever did before. You will surely receive recognition for your approach if you haven't already. You are thorough, positive, and enthusiastic, without being condescending to the students in the classroom. Superb job professor.
I am here for the same! Almost 30 and getting ready to start a Civil Engineering degree. Need some refreshers and I'm understanding it better now than I did in high school.
Do you get to study at such an old age in your country!...... What are the job prospects?. Will a company be willing to recruit you after you earn your degree? Or are you just doing it for knowledge enhancement?.....I have passed my graduation and have renewed interest in physics and mathematics. But this wont be of much use in my country India, apart from teaching kids and helping them with their study
Greg Mitchell I agree ☝️
@@anwesaroy6998 it doesnt matter in fact it's not uncommon for alot of older people to be in college I'm 26 and currently going towards my engineering degree and so are alot of people I'm rarely in class with anyone below the age of 21
I'm 34 and returning to school too! Knowledge has no age limits it's a basic human rights
If my teacher was this good at explaining things, I would not have dropped out of calculus 30 years ago. Learning it again at age 52 and having a much more enjoyable experience. Thank goodness for teachers like this.
I'm preparing to go back to grad school at 56... i have five months to ramp up to linear algebra.... i think this prof is going to be a great asset. Thanku prof if you happen to read this. you're an amazing teacher!
@@luisavelar9883 Gonna assume you're a kid/teenager. I'm just about to hit 25 and I already can tell you that the years go by faster as you age and before you know it, kids are gonna be calling you old.
Even so, I personally consider up to 13 a kid, 13-19 a teenager, 20-29 a young adult, 30-64 an adult and then 65+ is finally what I would consider "old".
at 51 im finding the exact same thing! :) well said mate
@@luisavelar9883 So I was correct.
@@raymondwilson293 that's awesome, good luck!! :)
Your students are so fortunate to have you as their Calc professor. Colleges should hire you to teach their teachers how to teach. You're a legend dog!
Agreed! Aziz
He is the only teacher that I've seen that has actually thoroughly explained what limits are and why they are used! My professor just sort of brushed through the conceptual part of this lesson and just told us the rules on limits. Thank you, sir!
I got so high that I clicked on a Calculus lecture and watched the whole thing
bruh i had to stop at min 40 and found this comment calculus is lit
same lol but i was drunk
I got it recommended for some reason and then watched it at 2 am
I just had some edibles. Diving in!
Literally smoking and got this recommendation
You are really really really really good Teacher !!
I have never seen a person that explain this concept so clear and easy to digested .
Congrats !!
I know this video was made long ago, but I must say, you are THE BEST teacher I have ever had the pleasure to learn from. If even half of my teachers had the passion for what they do, the teaching style, and the reinforcement of taught concepts that you do, I would have graduated college with a Masters at 18. I'm currently Majoring in Computer Science and Minoring in Mathematics at Texas Tech University, and you alone have taught me more than any math professor I've had.
A very sincere thank you, Professor Leonard
Having taken calculus 15 years, I found these videos to be a great refresher in prep for grad school - thanks!
Hash Tag. Professor Leonard was there for me when no one else was. Much love to you always. So amazing to see your videos has hit millions. Teaching Calculus around the world. I hope your house in Costa Rica is all done and built.
Hi! So glad that you found the videos helpful :)
And yes, the house is done! It took 4 days with a group of us working nonstop. It was for a local Costa Rican family near San Jose.
you’re teaching me more than my college calc teacher is. Couldn’t do my homework without you
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐
Seriously, you are the best Math professor I had so far. You exactly know what questions students has in their minds while understanding the different concepts of math. That's is a talent in itself. Proud of you. Keep up the good work for all of us.
I needed this guy as my Math teacher in High School where I failed miserably in 1985...You are truly a fantastic teacher, I understood a part of Calculus for the first time......:)
i really hope you're right because at this point, i'm going to be in the same situation that you were in during 1985....;-;
+teto Lol, think positive.
Mako 44 i'll try my best lol. it's hard when the teacher has a suuuper strong accent
teto
I hear you man, the teacher I had was a woman, she was mean, would get irritated easily, was short, stocky and manly. lol
Mako 44 yikes, what a handful LOL. yo i have my first test tomorrow, wish me luckkkkkk
he just cured my phobia on calculus which i had for the past 7 years.. thank you professor..
Mohammed Harris Ashraff 7 years? have you failed calculus for seven years or have you been fearing it lol
ZeroSevenTen a year old lol, but maybe his teacher wasnt good and resulting his performance being so bad that he had this fear since 7 years
I am a teacher in Thailand university, I always watch this video to adapt with my class. I like how you teach fundamental or the concept idea. And it make me to improve my work
So I go to school , learn , take my notes , get back home and keep them then log onto RUclips to learn from Prof Leonard. Better explained than the classes I pay for. smh.
I honestly stopped going to lecture for Calc 1 and instead used that time to watch these videos. I'm just here for some limit review for Calc 2.
this guy is a funny professor that makes everything seem so simple. I like how he doesn't really use big words.
Well, he is the quintessence of a certain pedagogical persuasion...no big words used.
lol
Yes..he...does know the subject matter clearly.....that's why he doesn't need big words..just plain and simple....
Like what Einstien said: If you can't explain something to a child....you really don't know the subject matter.....
You're a better teacher than my college calculus professor. I always watch you vids after a lecture to understand a subject better. Thank you so much for your work!
Same!
Same (we are going at a gap of 2 years)
Haha wow, I haven’t seen one of these lectures in years.. i dropped out of my sophomore year of college and worked odd jobs for nearly a decade. However, i was offered the chance to enroll into my university with the condition that i pass calculus 2. At this point i had forgotten even the basics of algebra and was terrified of the prospect of relearning all of math just to pass a calc 2 class to reenroll into my university. Thanks to these lectures and these lectures alone, now i am a first year medical student. Your lectures were the best resource i found online so sincerely thank you!
On a side note, it really is nice when math teachers have good penmanship. I had a professor who drew the most beautiful integral symbols you've ever seen.
Imagine a very complicated crime which has hunted many people over many years. But suddenly an investigator solves that crime by putting together all the pieces of information he has collected. By making logical connections between those pieces of information he will explain it to the public in a way that no doubt remains about the case. The same is true for math. Professor Leonard is a great Mathematics detective.
Next year I start calculus at San Antonio College. I'm a bit nervous about this, but will give it my best shot. Just like I do all my classes.
Oh BTW, I'm 63-years-old and a disabled veteran.
+jvolstad God bless you and your efforts in bettering yourself.
+jvolstad this is fantastic! i'm extremely happy for you, keep the great work up! :)
wow....I didn't know you learn calculus in college in America....here in greece we learn it in the last two grades of high school
+The Pinnacle here in the states, precalculus and calculus are taught in the last two years of High School. However, initial calculus classes are usually only single-var calc. College classes cover far more in depth subjects and topics in calculus, they're usually more oriented to study fields. For example, a calc class for engineering is VASTLY different from a calc class for theoretical physics.
+Bronson I'm not what?
Thanks so much for you lecture(s)! I'm a 38yr old guy who graduated high-school a pretty long time ago but never took Calculus courses. Never understood what it was until I watched your videos. In some ways, you remind me of my high-school Algebra teacher who was very good at explaining the whys and hows of the math and where and how it could be used. Because of that, I got an A+ but then was assigned another teacher the next semester, for Algebra II, who was frankly opposite of him and I ended up dropping out of the class because I didn't understand his way of teaching.
Thank God for RUclips for those of us who can't afford college or simply don't have the time for full-fledged college training! In some ways, I'm starting to see how this could be useful in software development. I'm a full-stack web application developer who has learned everything I know from online videos and ebooks. If you got the heart and passion, you can literally accomplish anything!
Thanks again for your lectures! I look forward to watching more of them.
GeniusSteven you just inspired me a lot. Well said. God bless you x
Its year 2022 and Im learning way more from you than any of my college professors combined. Teaching is a gift and most people just dont have it anymore. I wish I could have you as my teacher! Thank you so much!
Me too
RUclips has changed the game in education. I graduated with a degree in Mechanical Engineering about 25 years ago. I wish this was around. The best thing about YT is that if you miss something you can always rewind and play it over and over again until you understand what he is trying to teach. Also with so many videos on the same subject you can pick and choose what to watch. This has made learning 10 times easier. Great stuff,.
I never thought I'd be binge-watching calculus videos in a million years, but here I am. I actually like math when I understand it.
Me too it’s really fun to raise your hand in excitement to yell your answer.
The best explanation of limits that I have ever heard.This is teaching because the Pro explains the"WHYS and HOWS" and that so good.
kenny kepra
Did anyone take notes from this series if you did i would appreciate it if you could share thanks.
Sorry I do this as a hobby. But this guy is one of the best because he gets into the "How and Whys something is done." Calculus is the so beautiful Its like drinking a nice glass of wine.
kenny kepra I'm going to take notes throughout this video. I'll watch it soon & can share them to you if you like (:
kenny kepra js
I am doing B.E civil Engineering and this man helped me alot
Lots of Love from Pakistan
Pangali
I'm a math teacher and a tutor. I watch these, not for the knowledge, but for the style of teaching. The professor knows how to teach in such a way as to keep your interest. I very much want some of this style to rub off on me. My students deserve it. Thanks.
I really benifit from learning calculus in a 1 on 1 intimate setting, possibly over coffee, maybe a stroll in central park in the spring discussing how its so difficult finding someone that really gets us and our natural attraction to math and academics...lol
This dude is really, really, really awesome.
Wit does that mean?
I'm 13 and excel at school, thus I thought of studying calculus and see how it was as some of my friends claimed it to be really hard despite being really smart but I find It pretty okay due to professor Leonard's methods.
He's kind of cute for a math teacher
I do not focus on the appearance of the teacher I focus on the teaching itself
He is Clark Kent
My lecturer made me hate math
Thanks to Prof. Leonard I can finally pass my exams and understand calculus.
Thanks man
I wish I knew this when I took Calculus. I plan on playing is over and over again. Thank you.
It doesn't matter if it's basic algebra, calculus or geometry, the TEACHER of the subject makes all the diffrence. Great video. Man I wish my professors were as articulate as him in explaining the principles and details of the problems.
Who’s Still Here In This Corona Virus Era? You’re Awesome Prof.✅
me
Sadly
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐
present
Here I am
Dude I wish you taught my class you are great at teaching you go slow and explain everything.
Seconds to that; other people talk @ the rate of a speeding train and I get so enraged as I waste so much time with this Many thanks, Gabrielle from Australia.
Your explaination is better than the mit explaination with all respect to both of you . Keep going professor . And always with details please . God bless you man . Mathematician with good body . Good luck
I appreciate your enthusiasm. You're a good professor.
I cannot imagine the number of people including me failed to learn math in their time just because their teacher's were either bad or they couldn't really teach. But Professor Leonard is something else, I might have found you late but you will definetly help me solve my depression. Thank to you for that, I hope one day you will return and continue to teach us with your heart.
I'd 100% move across the whole globe to attend this mans class. 100%.
I just want to say thank you for teaching mathematics for free this way. In school, I was a slacker. I just did what I had to do to get by. Here I am nearly 20 years after I graduated high school and I regret it deeply. I have always had a deep love of astronomy and science, but I never truly believed that astronomy/science and mathematics REQUIRED each other for one to be good at astronomy. As I have taught myself more and more over the years, I have discovered how wrong I was. So I have slowly been going back to try and relearn the things I barely tried in before. You make this enjoyable and very educational. And on top of that, it's free! I apologize, but I currently cannot provide support through Patreon, but once I am more stable, I promise you will be receiving a lot of support from me! Please continue making education in mathematics easy and understandable!
Thanks for info
I'm interested in astronomy too :)
Gotta focus more on maths and physics now
Thank you professor, I failed my math exam and I have to retake it again, I took the decision to study math during this holiday, having chinese teacher isn’t simple, I didn’t know what all of this was about... but you are helping me so much. Wish me luck for my coming exam 🙏
The day my Business Calculus professor went over limits, one of the students said, "I don't understand any of this. I just wrote 'lim' about 100 times. What does it mean?" The professor said, "don't worry about it, you'll get it." I doubt that kid ever did, I know I didn't. I think 1/4 of the class has already dropped. I've literally learned more about limits in the past hour than in 3 weeks of class.
Just wanted to come pay my respects to the man who is solely responsible for helping me pass Calculus 1-3 in college. You sir are the MAN. Thank you for helping literally millions of students!
I just started calculus and I lowkey want to cry already. This however made it far easier to understand and I feel a lot more prepared for my quiz
Looks like Clark Kent is now teaching calculus.
+RB Gaming&Others Tbh. me too this teacher his glasses remind me about Clark Ken, and thought about to write a compliment comment that he is my Superman. Until see his profile pic XD
i was thinking more ""Matt Damon""
maybe talented Mr. Ripley
yess..!
Lol
Went through all of his lectures on Calculus (1, 2, and 3)... and his lectures on differential equations. Got 98% on my engineering exam . Only messed up one thing because I didn't sleep the night before the exam (me being nervous) and even then I knew what my mistake was on the drive home. Professor Leonard is the best math teacher on RUclips . If you're here to learn math, you're in the right place.
NOTE: It's fun to watch a lecture like this after completing Calc 3.... just to see how far I've come. The world is a very different place with the knowledge I now have. Sort of like Neo in the movie The Matrix when he stops the bullets and can finally see the matrix at the end of the movie and defeat the agents. This is how you feel once you learn Calculus: :)
ruclips.net/video/zYwdzYC3uUc/видео.html
Thank you.Great explanation without skipping any steps as most professors do.
Professor even looks like chad. And helping students with one of the most difficult subjects in Mathematics effortlessly. A chad through and through.
Never found someone who can be, while teaching, as interesting as you, Prof. Leonard! I just enjoy the lecture. I feel like I am physically present in your lecture. It is the best calculus I have ever had in my life. Salute!! Thanks for being there!
Cheers!
I'm crying. You're helping me obtain my chemistry degree. Thank you so much.
As a 1st year engineering student,you're really really really helping me! Thanks
did you complete it?😃
Looks like it with their pfp 😮
@@musicaldoge9412lmfao
Funny, our Calculus lecturers never mentioned anything about graphs and curves. Next thing I know, they're talking about limits. "Limits of what?" I ask, and they reply "Its just a limit"... "Yes, but limit of what?"... "What do you mean?"
I failed Calculus I, not surprising... from now on, I'm watching these videos.
Forde3654Eire is it possible to teach calculus without saying something about slope or graphs? Wtf.
4 years ago... im late
Well TBH limit is just limit by itself, but It's a tool to calculate the tangent and area
How the fuck do....? How the....how the fuck did he teach that without graphs??
Gregorio Its still very annoying to just try and learn without seeing the bigger picture, it definitely makes it more boring, more robotic and overall way more discouraging to actually engage and enjoy learning.
Dude same!! My calc teacher just jumped straight into derivative rules
When there's a random badass professor you found while scouring the interwebs for college lessons (just because, math is fun and why the hell not) and he actually makes it understandable. So you just sit there in shock
You go! Bambi ~
I am extremely happy that I have come across your channel. I am almost 60 years old trying to teach my kids math and I want to refresh my calculus and you are gifted to make complex concepts simple, thank you Professor Leonard (Same comment as Emant and thank you too)
watching this during the pandemic gives me some semblance of peace... the quiet noise of the classroom and sounds of other people is actually calming...
Professor, this is one of the most effective tutorials I've ever seen. I appreciate the fact that you made the tutorials public. I'll gladly watch the commercials of youtube's sponsors and even purchase their products in return for making this information free to me as a knowledge seeker. Two thumbs up to a great educator, youtube, and youtube's sponsors. .
This is amazing. I just suffer with basic high-school algebra, but I'm understanding almost everything this man is teaching and I'm grasping the concepts in my head and actually understanding what he is doing.
ruclips.net/video/XPCgGT9BlrQ/видео.html 💐💐💐💐💐
Professor Leonard,
I would like to say you have really hooked me into Calculus. I've spent this entire month going through your videos on Calculus I and trying the exercises you put up on the board. In my opinion, you've done a wonderful job of turning calculus, and math in general, into something enjoyable and exciting. Moreover, you've eased my worries heading into Calculus AB in 11th Grade. Thank you for all your help. I can't simply cannot thank you enough and I can't wait to watch the Calculus 2 playlist next month!
Have an awesome summer! :D
Joe
Prof.Leonard - Although I took Calculus over 30 years ago, it was never explained the way you are doing. Also, your enthusiasm to teach top notch. I want to thank you for your effort.
went through calculus in high school and taking up calc 1 in college,, couldn't understand calc for the past few weeks cus my prof just be throwing formulas at us. But omg thank God for prof. leonard for letting us understand the reason for calculus & what's behind all those formulas 🫡🫡 big respect for this guy even after 10 yrs he still be saving lives of students
i come here to go to sleep at night. been listening to this for 2 years now. big props to you for getting me to sleep
Do you still come here for sleep?
Next year I'm going into college for prerequisites math advanced 4 and 5 and physics and chemistry and then in 2 years , calculus, so I'm just watching this and I love it, you are REALLY passionate and I LOVE learning through these
Aye, finished math 4 with 96, math 5 so far average is 98, let's see how the final is next week :D
This man still saving lives in 2024. I pooped my pants but that's okay, sir.🖤
You are awesome Professor. I studied calculus 25 years back in my engineering. I wanted to get a refresher just for the fun of it. Your course is awesome. You make it so simple. Thanks for these lectures.
Introduction
● [0:00]. Introduction.
● [0:53]. The two objectives of calculus:
○ Objective 1: Find the slope of a curve at a given point.
○ Objective 2: Find the area under a curve between two points.
The Problem of the Tangent
● [5:56]. Introduction to the problem of the tangent: how to find the equation of the tangent line to a curve at a given point.
○ [7:24]. The concept of the secant line is introduced as an approximation to the tangent line.
○ [11:28]. It is explained how to move a point on the secant line so that it approaches the tangent line.
○ [16:20]. The concept of a limit is introduced: bringing one point closer to another without them being the same.
● [19:32]. Exercise: Find the equation of the tangent line to the curve y = x² at the point (1,1).
○ [19:52]. A moving point Q is defined with coordinates (x, x²).
○ [21:24]. The equation of the line is recalled.
○ [23:23]. The slope of the secant line passing through points P and Q is calculated.
○ [25:56]. The slope of the secant line is related to the slope of the tangent line using the concept of limit.
○ [27:02]. It is explained why you cannot simply substitute x = 1 in the slope formula.
○ [28:53]. The expression for the slope is simplified by factoring.
○ [31:35]. It is calculated lim_(x→1) (x² - 1)/(x - 1) = 2.
○ [34:04]. It is concluded that the slope of the tangent line at point (1,1) is equal to 2.
○ [35:03]. The equation of the tangent line is written.
The Problem of the Area
● [36:20]. Brief introduction to the area problem.
○ [37:19]. The question is posed: how to find the area under a curve.
○ [37:48]. The idea of approximating the area with rectangles is introduced.
○ [38:52]. It is explained that by using an infinite number of rectangles, the area is calculated exactly.
Definition of a Limit
● [40:17]. The concept of a limit is defined in general terms: What does the function do as a variable approaches a given value?
● [41:03]. Exercise: Calculate lim_(x→2) x².
○ [41:37]. A table of values is constructed to approximate the limit.
● [44:55]. It is observed that the function approaches 4 from both the right and the left.
● [46:10]. The formal notation of the limit is introduced: lim_(x→a) f(x) = L.
● [47:06]. It is emphasized that the limit does not depend on the value of the function at the point, but on its behavior near the point.
● [48:24]. What are limits?
○ An example is performed with (x² - 1)/(x - 1).
○ Since the function has a hole at x = 1, it is best to create a table again.
One-sided Limits
● [57:43]. Introduction to one-sided limits: right-hand limits (lim_(x→a^+) f(x)) and left-hand limits (lim_(x→a^-) f(x)).
○ [58:30]. The notation for one-sided limits is explained.
● [1:00:00]. Exercise: Calculate the one-sided limits of a function represented graphically as x approaches 2.
○ [1:02:33]. It is observed that lim_(x→2^+) f(x) = 1 and lim_(x→2^-) f(x) = -1.
● [1:03:16]. The condition for the existence of a limit is stated: the one-sided limits must be equal.
● [1:04:11]. It is concluded that lim_(x→2) f(x) does not exist in this case.
● [1:05:41]. Exercise: Calculate lim_(x→2) g(x).
○ [1:07:49]. The student is asked to calculate the one-sided limits.
○ [1:08:34]. It is confirmed that lim_(x→2^+) g(x) = 3 and lim_(x→2^-) g(x) = 1.
○ [1:09:32]. It is concluded that lim_(x→2) g(x) does not exist because the one-sided limits are different.
● [1:10:54]. Exercise: Calculate lim_(x→5) h(x).
○ [1:11:31]. The student is asked to calculate the one-sided limits.
○ [1:12:45]. It is confirmed that lim_(x→5^+) h(x) = 3 and lim_(x→5^-) h(x) = 3.
○ [1:13:43]. It is concluded that lim_(x→5) h(x) exists and is equal to 3 because the one-sided limits are equal.
Infinite Limits and Asymptotes
● [1:14:12]. The question is posed: What happens to the function 1/x as x approaches 0.
● [1:14:37]. A table of values is constructed to approximate the one-sided limits.
● [1:17:43]. It is observed that lim_(x→0^+) (1/x) is positive infinity and lim_(x→0^-) (1/x) is negative infinity.
● [1:19:18]. The infinite limit is related to the existence of a vertical asymptote.
● [1:20:43]. The four possible cases of vertical asymptotes and their relation to infinite limits are enumerated.
○ [1:23:01]. The behavior of the function in each case is analyzed.
○ [1:25:17]. The question is answered: Does the limit exist when both one-sided limits are positive infinity or both are negative infinity.
I grew up being told I am deficient in math and was placed in the special math room as a teen. I then tried to learn some math on my own with Arthur Benjamin. If it wasn't for my mum I would've never even learned basic multiplication, fractions, decimals. I was then tested in a 7 hour long test on various IQ components where 100 is the average and scored 120 in maths. I am now trying to teach myself calculus and this is my very first video. Not sure if I need to watch precalc first. I learned I'm not deficient, I just learn differently.
+Megan De I can deeply relate with you .It is just very difficult to understand maths for me .I need to know why we are doing the calculations and what is the purpose of the maths we are doing .
God is an atheist ditto
Megan De Very happy to find someone who understands exactly how I feel about my incompetency
God is an atheist fortunately I don't need to take it, I was just looking at it as a self study thing. Good luck to you if this is a required course.
Megan De thanks
This has resurrected me for Calculus, thank you Prof.Leonard.
You're a lifesaver Professor Leonard! You the man! Come to WVU and teach these guys how to teach math!
I have concluded this teacher is the best way to learn calculus. Way better than a textbook!!
dude you are very much underrated,.. it would be Einstein if you were my math's teacher. Never stop updating i'm your student from now on
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hes the kind of teacher I aspire to be. very enthusiastic about his field
"Would you raise your hand if you're okay with what we've talked about so far?"
*Me raising my hand and realizing he doesn't see me* 😂😂
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐
U
and you are raising after almost 8 years lol
This was simplified that I was able to understand with work. I like how you outlined the goals of calculus 1 with you two clear visuals. Outstanding teaching!
Thumbs up for this teacher.
Don't just do it, understand it too.
I love how his sarcasm just goes over their heads.
The best professor I have ever known. Thanks so much. God bless you. Greetings from Africa
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐
I can't believe I'm procrastinating so much on my homework that I'm watching a calculus lecture on youtube.
50+ years - I must be crazy to be here - This guy really knows his shit - Thank you Prof. Leo
I was waiting for Professor Kent to excuse himself for a minute while he ran out of the class, change into his red speedos and save somebody in distress.
trippplefive he’s saving all of us from the distress of bad teachers and finals :D
(Yeah I know I’m 4 years late )
Bob Higgins sad
I'm taking calculus I and online along with physics and this is going to save me!
my school requires me to take calc first before physics
Hello I am a 11 year old eager to learn calculus but couldn’t find a reliable source until I came across this.. Thank you sir and I respect you as a teacher
How're you doing now? I just turned 15 today and I thought THAT was too early to learn calc 1-3..