I’m 76 years old and I always wondered what calculus was. This is the closest I’ve gotten. I am going to keep trying until I completely understand. Please publish more o these examples. You are a good teacher.
This is hands down the best explanation of The Fundamental Theorem of Calculus that I've seen. The reason is because you explain the WHY behind it all and give a real world example of how it is applicable and WHY its needed. Thank you for the video!
Of all the Calculus videos I've seen on UA-cam, yours are definitely my favorite. Concise, clear, conceptual - they're really good for understanding the concepts. I'm going to school for engineering and plan on viewing your Physics videos soon! Right now, I'm hoping to survive Calc. 2 online over the summer... Thanks!
awesome...the most lucid, direct, clear explanation EVER !!...SO many thanks for this excellent demonstration of what was once a mind boggling concept... !! very much appreciated !!
I am 60yrs old. As a kid, I was a maths wizz and spent my working life as a betting shop manager. I have always been comfortable with probability theory; but calculus always bemused me. This is excellent!
I've been teaching for 25 years, and the past 12 years have been Introductory Calculus and APCalculusAB, and I want to tell you that this is an outstanding video of FTC Pt.1. Fantastic job! Looking forward to checking out your others, which is why I subscribed. :-)
very good explanation . now i have got the sense of using calculus. though i was able to solve problems in my schooldays i was not able to understand it in reality . we blindly used formulas, and how to solve typical problems just to score for exams not enough time to think over it ,due to law imagination power , and due to pressure of completing the courses . basically the purpose of calculus were not taught . and this still may be a problems for some students.. THANK YOU SIR.
J K J yes thats a problem with math in general. Some people are able to instantly click with the concept but some like me spend countless hours to understand but end up memorizing how to do it instead of understanding it. Videos like these help alot.
Veey true and this is one of the reason why students hate science classes.. the application part of it is missing (so that makes science classes look solid and horrible)
Loving these videos. I had to leave school at 14 - 15 and have been using these as prep for the Uni entrance exam next year for a Bachelor of Engineering , keep up the great work.
I just bumped into your video by accident. I must say it was excellent. I have been studying calculas on-line and I think your video is the best I have seen. I have subscribed to your site. Thank you.
@Kaiyazu Yes, the capital F notation is fairly common, and I see that used some on AP exams also. The concept, though, is what is critical, and the goal is for it to make sense, in either notation. Glad you liked the video! DO
Well explained. I have never learnt calculus but I was able to after watching your video. One thing I did not understand is how to get the anti derivative of a function
The explanation excellent for those that already have enrolled or take a course on Integral Calculus, not for those who doesn't. JUst a comment: Constant aceleration doesn't mean that the veocity doesn't change, it will change since there is acceleraion. Thanks for this excellent video.
@derekowens, surely you are the bestest tutor that I have seen so far. The way you explain makes maths soo easy. If you were my primary school teacher and taught me this at the age of 7, I am sure I would of passed Calculus course even then, But I have to say I owe you for your time and doing this for students. Thanks a lot, ur truely a LIFESAVER!
Only If I had a physics mentor like you I would have been doing a course to be a physicist instead of engineering but I am happy that I found someone who can even teach physics to toddlers
I always thought Khanacademy was good while although slow, but this is so much better, more professional, and both neat and concise. I know I'm subscribing.
Dude that lecture blew my mind I haven't taken calc 1 yet but I've looked up diif quotient and out of curiosity anti derivitves. I wasn't sure how you got the anti derivitives to plug into the equation but I knew you did and everything else was easy to follow.
Nice explanation - linking why calculus is needed when acceleration is changing. Found it very useful. Wish I had seen this in 1983 when I learnt calculus for the first time 😀
Thanks very much, and if I remember, I do address the Constant of Integration in a later video in this series. And yes, it's an important for beginners, and an easy item to miss.
Excellent. He has a good voice and is very concise. Took me a while to get that dx means derivative of x. I didn't notice what dx is, only saw what its anti-derivqtive g is.
Weight is typically defined as the force of gravity on an object, and the calculation is W = mg, in which m is the mass, and g is the acceleration due to gravity. In the metric system, that's kg times m/s^2, which works out to force in Newtons. In the English system the units can be a little confusing.
You are my favorite teacher. Nameste Sir, I am from India. Please make some more videos. The world needs teachers like you. I am waiting for my son to start learning by watching your video lectures. My son is only 5 years old.
Can you tell me which software you used to write and draw the stuff? seemed pretty interesting that the colours were changing pretty fast and they were disappearing too.
Hi Derek, What program or software did you use to create this video? The colors on the black make the work easy to see and the logic easy to follow. Thanks in advance for your reply!
Could you please tell me what program did you use for this video? It's really helpful to understand. I like the function of changing colors and instant redo functions.
It often helps to think of it from top-down instead of bottom-up. Let's say you have a function that gives the area under a graph up to any point on the x axis. Take for example the area (A) of a triangle formed under the line y = x. Its area will be 1/2bh, i.e. 1/2 x^2. Now consider how A changes with regard to x, i.e. dA/dx. It's x, the same equation (y = x) as the upper boundary line. If you don't know the original area function, you get back to it by integrating this line equation.
You are correct. That is the KEY issue, and in fact the physics of motion was one of the key motivators for the development of calculus. That is essentially one of the problems that Newton himself was thinking of when he produced this. I do cover the physics of motion in more detail in other parts of the course, though, just not all in this video.
You are correct, there certainly should be a constant! However, when we are calculating a _definite_ integral, the constant disappears. It disappears because it would show up once in g(b) and again in g(a), and we subtract. I'm going to redo these videos soon, and I'll address the constant of integration when I do.
@MsBabyBlue0 The area under the acceleration curve is what gives us the change in velocity, and we find this area by finding the antiderivative and evaluating, which is what I think you mean by finding g(7). If it starts with a velocity of 0, then the change in velocity from t=0 to t=7 will be the velocity at t=7. Hope that helps, DO.
honestly I know this is just pure calculus 2 but now I see how calculus based physics makes more sense than just using algebra formulas and plugging in numbers, calculus rules. I need calculus for my major computer engineering tech and this is a good course for that major
Im very new to learning calculus, took me a while to understand why the speed is measured by the area. Paused the video and studied the graph and equation and i understood that the speed equals to the sum(integral) accelaration throughout all the 7 seconds. It confused me cause im used to highschool math with y being speed and x being time but in this case y is acceleration so speed is the product of y and x... the area under the acceleration curve for 7 seconds. Very helpful videos, thanks
I’m 76 years old and I always wondered what calculus was. This is the closest I’ve gotten. I am going to keep trying until I completely understand. Please publish more o these examples. You are a good teacher.
Thanks for such a thoughtful and encouraging comment!
This is hands down the best explanation of The Fundamental Theorem of Calculus that I've seen. The reason is because you explain the WHY behind it all and give a real world example of how it is applicable and WHY its needed. Thank you for the video!
Thanks for the Great job with the video, Derek. After years of working up to Calc III, this is the first time the fundamental theorem made any sense.
I FINALLY get this, I wish online classes were just watching your videos, because it's SO much more helpful than just a wall of text. THANK YOU!
reviewing this after 35 years for my son - wish I had a teacher like this
and explanations like this
Most of our teachers memorised the formulas
I wish college professors would take the time to teach like you do.
Of all the Calculus videos I've seen on UA-cam, yours are definitely my favorite. Concise, clear, conceptual - they're really good for understanding the concepts. I'm going to school for engineering and plan on viewing your Physics videos soon! Right now, I'm hoping to survive Calc. 2 online over the summer... Thanks!
Very good. Thank you.
What a champ you are professor!! Explicit and clear explanation without any confusion.
These are the best videos on this subject in UA-cam. By a country mile!
awesome...the most lucid, direct, clear explanation EVER !!...SO many thanks for this excellent demonstration of what was once a mind boggling concept... !! very much appreciated !!
Thanks for the excellent video. Very concise and to the point with a good example!!
I love you! Everyone made this so complex but you kept it really simple!! Thank you!!
I am 60yrs old. As a kid, I was a maths wizz and spent my working life as a betting shop manager. I have always been comfortable with probability theory; but calculus always bemused me. This is excellent!
I've been teaching for 25 years, and the past 12 years have been Introductory Calculus and APCalculusAB, and I want to tell you that this is an outstanding video of FTC Pt.1. Fantastic job! Looking forward to checking out your others, which is why I subscribed. :-)
OMG- now it all makes sense.
thanks very much for keeping it simple.
very good explanation . now i have got the sense of using calculus. though i was able to solve problems in my schooldays i was not able to understand it in reality . we blindly used formulas, and how to solve typical problems just to score for exams not enough time to think over it ,due to law imagination power , and due to pressure of completing the courses . basically the purpose of calculus were not taught . and this still may be a problems for some students.. THANK YOU SIR.
J K J yes thats a problem with math in general. Some people are able to instantly click with the concept but some like me spend countless hours to understand but end up memorizing how to do it instead of understanding it. Videos like these help alot.
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Veey true and this is one of the reason why students hate science classes.. the application part of it is missing (so that makes science classes look solid and horrible)
Ok I know this comment is 6 years old, but what are those spaces between the words?
Excellent presentation. I feel I understand the Fundamental Theorem in a much deeper sense. Thank you.
are u so stupid
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Loving these videos.
I had to leave school at 14 - 15 and have been using these as prep for the Uni entrance exam next year for a Bachelor of Engineering , keep up the great work.
Beautifully clear and concise. Bravo 👏 and thanks 🙏
I just bumped into your video by accident. I must say it was excellent. I have been studying calculas on-line and I think your video is the best I have seen. I have subscribed to your site. Thank you.
I'm an English teacher who avoided higher level math, but In 5 Minutes of your video I was hooked.
Brilliant explanation, this put so much of Calculus 1 and Physics in perspective for me... awesome work!!!!!
Such a clear video, even clearer than the Kahn Academy video, and that's quite a statement, because Kahn academy videos are usually outstanding.
@Kaiyazu Yes, the capital F notation is fairly common, and I see that used some on AP exams also. The concept, though, is what is critical, and the goal is for it to make sense, in either notation. Glad you liked the video!
DO
Great video. I understand this concept much better now, thank you.
Thanks very much for the encouraging comment! I'm very glad you enjoyed the video!
Thank you so much , you are my calculus teacher ^^
Well explained. I have never learnt calculus but I was able to after watching your video.
One thing I did not understand is how to get the anti derivative of a function
Extremely clear, thanks a lot! Great refresher.
The explanation excellent for those that already have enrolled or take a course on Integral Calculus, not for those who doesn't. JUst a comment: Constant aceleration doesn't mean that the veocity doesn't change, it will change since there is acceleraion. Thanks for this excellent video.
🙏👌 clearly & very good to declare the topics ❤️
Yes, that is a very good suggestion! Thanks, and thanks.
Thank you soooo much!!! It's a amazing thing you're doing making all these videos for everyone!!:D You're great at explaining!!
Yes.. indeed.
@derekowens, surely you are the bestest tutor that I have seen so far. The way you explain makes maths soo easy. If you were my primary school teacher and taught me this at the age of 7, I am sure I would of passed Calculus course even then, But I have to say I owe you for your time and doing this for students. Thanks a lot, ur truely a LIFESAVER!
I actually searched for your channel
I read physics from your channel some 8 years ago
Still the best channel
Yes, you nailed it. That's a more difficult problem, but it could be solved later in the course.
Thank you, thank you! I'm very glad you liked it.
tnk u so much . i didn't understand till now after watching this video i understood perfectly.
Thank you so much Mr. O! I miss your class SO MUCH.
Only If I had a physics mentor like you I would have been doing a course to be a physicist instead of engineering but I am happy that I found someone who can even teach physics to toddlers
Excellent videos - thanks so much.
A very perfect video. It explains in a very simple way
Thank you u are a really good teacher :D
can we take a moment to appreciate that perfect ellipse at 1:14
Watched the series and it is very good ! Thank you !
OMG, I haven't even taken Calculus, yet I understand it clearly. Well done sir
I always thought Khanacademy was good while although slow, but this is so much better, more professional, and both neat and concise. I know I'm subscribing.
Really brilliant love it more more ..please.👍
Perfect stuff, I liked it
You are a legend!
thank you very much, with the detailed examples to clear my fundamental...
Dude that lecture blew my mind I haven't taken calc 1 yet but I've looked up diif quotient and out of curiosity anti derivitves. I wasn't sure how you got the anti derivitives to plug into the equation but I knew you did and everything else was easy to follow.
I found this video very helpful and clear. Thank you very much!!
Simply Superb explanation Sir.....👍
I love this video...I learned a lot from this...
Big thanks from Ireland, the fundamental principle was well outlined with nice examples
Regards Tom
I cant wait and subcribed..
One of the best teacher I have seen. Mind blowing. Better than Khan academy. I would like to touch his feet in reverence. Nameste Sir.
Really enjoying maths videos...m loving maths lately..
Nice explanation - linking why calculus is needed when acceleration is changing. Found it very useful. Wish I had seen this in 1983 when I learnt calculus for the first time 😀
1983 happens to be when I also first learned calculus. Shout out to Mr. Wayne Murrah for being a great teacher!
Thanks very much, and if I remember, I do address the Constant of Integration in a later video in this series. And yes, it's an important for beginners, and an easy item to miss.
Great video and explanation. A+
Excellent. He has a good voice and is very concise. Took me a while to get that dx means derivative of x. I didn't notice what dx is, only saw what its anti-derivqtive g is.
Weight is typically defined as the force of gravity on an object, and the calculation is W = mg, in which m is the mass, and g is the acceleration due to gravity. In the metric system, that's kg times m/s^2, which works out to force in Newtons. In the English system the units can be a little confusing.
These "Fundamental Theorem" videos are about to get redone. I think I can improve the explanation.
Derek Owens no need
You are my favorite teacher. Nameste Sir, I am from India. Please make some more videos. The world needs teachers like you. I am waiting for my son to start learning by watching your video lectures. My son is only 5 years old.
Waooooo good aid
Very nice and clear presentation. Thank you.
Thanks for refressing my memory
Awesome! Thank you very much, I have to say, you're on par with KhanAcademy when it comes to clarity and organization with your problems.
nice review and style. Thanks Derek
Wooow thank you so much I told everyone in my maths class to watch this keep posting vids lyk this, integration is a piece of piss now!:)
You make Calculus sound great. Thanks.
Can you tell me which software you used to write and draw the stuff? seemed pretty interesting that the colours were changing pretty fast and they were disappearing too.
Wow, these are amazing. I love your quick, clear, and clean drawings. what do you use? Very easy to understand.
You made it. Good job.
Hi Derek,
What program or software did you use to create this video? The colors on the black make the work easy to see and the logic easy to follow. Thanks in advance for your reply!
you're awesome, thanks so much
Derek, these videos are GREAT. Very clear and articulate. Nice work!!
Thanks
Shailee! Good to hear from you, and we miss seeing you around LAC! I hope all your studies, and everything else, are all going very well.
Could you please tell me what program did you use for this video?
It's really helpful to understand. I like the function of changing colors and instant redo functions.
Thanks SIR you did your best l like your way of teaching thanks
Took this in college and I got a "mercy " pass. Whew!
It often helps to think of it from top-down instead of bottom-up.
Let's say you have a function that gives the area under a graph up to any point on the x axis. Take for example the area (A) of a triangle formed under the line y = x. Its area will be 1/2bh, i.e. 1/2 x^2.
Now consider how A changes with regard to x, i.e. dA/dx. It's x, the same equation (y = x) as the upper boundary line.
If you don't know the original area function, you get back to it by integrating this line equation.
Thanks man,, Great Teaching
You are correct. That is the KEY issue, and in fact the physics of motion was one of the key motivators for the development of calculus. That is essentially one of the problems that Newton himself was thinking of when he produced this. I do cover the physics of motion in more detail in other parts of the course, though, just not all in this video.
Very cool, love the graphics and modern version of chalkboard. What software are you using?
You are correct, there certainly should be a constant! However, when we are calculating a _definite_ integral, the constant disappears. It disappears because it would show up once in g(b) and again in g(a), and we subtract.
I'm going to redo these videos soon, and I'll address the constant of integration when I do.
The constant c you are talking about? 🤔
thanks man easy and simple explained!!
These so good teachings even monkey could understand. 1000 thanks for this guy
Thank you very much for your explications.
@MsBabyBlue0 The area under the acceleration curve is what gives us the change in velocity, and we find this area by finding the antiderivative and evaluating, which is what I think you mean by finding g(7). If it starts with a velocity of 0, then the change in velocity from t=0 to t=7 will be the velocity at t=7. Hope that helps, DO.
mr.Derek thanks for this work. please could you tell me the name of the software you used to as the board and screen recorder. thanks
great video!
Excellent Vid - thank you!!!!!!
honestly I know this is just pure calculus 2 but now I see how calculus based physics makes more sense than just using algebra formulas and plugging in numbers, calculus rules. I need calculus for my major computer engineering tech and this is a good course for that major
Well explain very clear to understand
Im very new to learning calculus, took me a while to understand why the speed is measured by the area. Paused the video and studied the graph and equation and i understood that the speed equals to the sum(integral) accelaration throughout all the 7 seconds.
It confused me cause im used to highschool math with y being speed and x being time but in this case y is acceleration so speed is the product of y and x... the area under the acceleration curve for 7 seconds.
Very helpful videos, thanks
Hi Derek
very good explanation. Would you please inform me which program are you using to make this video.
Very helpful video !
Great! Thanks very much!
You rock!