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.
Of all the Calculus videos I've seen on RUclips, 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!
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!
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 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.
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.
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.
@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!
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.
@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
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 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.
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.
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
@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.
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!
@@nahrafe Yessir I am! Though I definitely did not take the math route, hahaha. I am going to Rhema Bible College. And 6 years ago lol, it's been a little while
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.
Nice Videos , but you missed a small thing which is , when you calculated the anti-derivative of x^2 , you have forgotten to add the constant of the integration C . of course this constant would be neglected when we take the definite integral as C-C=0 , but it may be important point to be mentioned for the beginners who face fundamental theorem of calculus for the first time . This is of course Great Video so keep up the good work! Regards.
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 😀
0:58 I see, because even if you trying to find the area of figures without curves say a rectangle, this do work as well. Say the area of rectangle with length 3 and width 4 which =12 Here f(x)= 3 a=0 b=4 and the integral (or anti derivative )of 3 = 3 x 3 x 4 - 3 x 0 = 4 here we finding the area under f(x) or y=3 (a vertical line) from x=0 to x=4 so yes it works. And if we are doing a triangle (area of triangle base x height all divided by 2) with base 3 and height 3 where f(x)= x and a =0 and b= 3 then the integral of x = x^2/2 3^2/2 - 0^2/2 = 9/2-0 = 4.5. here it work not triangle as well as rectangle.
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.
Your method is great but I think you should share the workbooks for free. You would do a big favor to people and specially to those with limited resources. Take care.
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!
Of all the Calculus videos I've seen on RUclips, 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.
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!
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.
These are the best videos on this subject in RUclips. By a country mile!
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!
What a champ you are professor!! Explicit and clear explanation without any confusion.
Thanks very much for the encouraging comment! I'm very glad you enjoyed the video!
Nice explanation 🙏🙏🙏🙏🙏🙏 sir...
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!
Excellent presentation. I feel I understand the Fundamental Theorem in a much deeper sense. Thank you.
are u so stupid
DIFFERENTIABILITY , SHORTCUT , WBJEE , JEE MAINS , ADVANCE , Any other competitive Exams.: ruclips.net/p/PL0o1IL6EH-hmuCDFxxLBk1Jxmm3hsn6qv
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.
YOU CAN FOLLOW MAXIMUM SHARE ------------ ruclips.net/p/PL0o1IL6EH-hmAI6PppvpjasHyy-zhRWOR
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?
can we take a moment to appreciate that perfect ellipse at 1:14
Beautifully clear and concise. Bravo 👏 and thanks 🙏
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'm an English teacher who avoided higher level math, but In 5 Minutes of your video I was hooked.
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.
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.
Good Job preofessor
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.
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
@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!
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
Simply Superb explanation Sir.....👍
I actually searched for your channel
I read physics from your channel some 8 years ago
Still the best channel
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.
@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
Good math lesson.thanks for vdo
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 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.
Well explain very clear to understand
OMG, I haven't even taken Calculus, yet I understand it clearly. Well done sir
Very nice and clear presentation. Thank you.
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.
Thank you, thank you! I'm very glad you liked it.
I love you! Everyone made this so complex but you kept it really simple!! Thank you!!
A very perfect video. It explains in a very simple way
I cant wait and subcribed..
Really brilliant love it more more ..please.👍
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.
Yes, you nailed it. That's a more difficult problem, but it could be solved later in the course.
I teach classes to homeschool students. I have live classes in the Atlanta area during the school year, and online courses available year round.
Hello Mr. Owens, I understand everything except how did you get x^3 or x3. Did you add x2 dx together to get x3 or did you multiply?
@@megatton7207 there is a general way for getting there that's simple
∫ x^n dx= x^(n+1)/(n+1) (when n≠1)
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.
Superb
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
Big thanks from Ireland, the fundamental principle was well outlined with nice examples
Regards Tom
Extremely clear, thanks a lot! Great refresher.
Such a clear video, even clearer than the Kahn Academy video, and that's quite a statement, because Kahn academy videos are usually outstanding.
Great video and explanation. A+
"Calculus is special." It stands out from all the other branches in math. Calculus is king."Very fascinating."
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.
@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.
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!
Brilliant explanation, this put so much of Calculus 1 and Physics in perspective for me... awesome work!!!!!
Really enjoying maths videos...m loving maths lately..
Thanks for the excellent video. Very concise and to the point with a good example!!
You make Calculus sound great. Thanks.
Thanks man,, Great Teaching
wow, you did a better job than kahn academy. very clear and quick
Im in 8th grade taking geometry right now and this just blew my mind how many variables to the whatever
hi
Lel I am in 7th grade and I am learning Calculus
Saaaaame but I’m in 7th taking geometry
Hi, now you must be on college.
@@nahrafe Yessir I am! Though I definitely did not take the math route, hahaha. I am going to Rhema Bible College. And 6 years ago lol, it's been a little while
Very helpful video !
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.
🙏👌 clearly & very good to declare the topics ❤️
Gee, you make it so easy to understand.
I love this video...I learned a lot from this...
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.
Thank you Father.
you are a life saver
Nice Videos , but you missed a small thing which is , when you calculated the anti-derivative of x^2 , you have forgotten to add the constant of the integration C . of course this constant would be neglected when we take the definite integral as C-C=0 , but it may be important point to be mentioned for the beginners who face fundamental theorem of calculus for the first time . This is of course Great Video so keep up the good work! Regards.
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.
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.
You are a legend!
Great video. I understand this concept much better now, thank you.
You made it. Good job.
Awesome video. What is the software used by the way or is it any software??
sir you are so amazing teacher
Perfect sir
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!
Excellent videos - thanks so much.
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
good job
Hi Derek
very good explanation. Would you please inform me which program are you using to make this video.
MUST SEE VIDEO !!!
Watched the series and it is very good ! Thank you !
0:58 I see, because even if you trying to find the area of figures without curves say a rectangle,
this do work as well. Say the area of rectangle with length 3 and width 4 which =12
Here f(x)= 3 a=0 b=4 and the integral (or anti derivative )of 3 = 3 x
3 x 4 - 3 x 0 = 4 here we finding the area under f(x) or y=3 (a vertical line) from x=0 to x=4
so yes it works.
And if we are doing a triangle (area of triangle base x height all divided by 2) with base 3 and height 3
where f(x)= x and a =0 and b= 3 then the integral of x = x^2/2 3^2/2 - 0^2/2 = 9/2-0 = 4.5. here it work not triangle as well as rectangle.
Excellent Vid - thank you!!!!!!
Thanks SIR you did your best l like your way of teaching thanks
Very clear.
nice review and style. Thanks Derek
Wow, these are amazing. I love your quick, clear, and clean drawings. what do you use? Very easy to understand.
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.
Because when you integrate variables to a power you add one and divide by the
new variable.So x^2 becomes x^3/3.
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!:)
Your method is great but I think you should share the workbooks for free. You would do a big favor to people and specially to those with limited resources. Take care.
greenyblu he is all ready contributing to our education
thank you very much, with the detailed examples to clear my fundamental...
Me too! As a science major I have to take all of the Calculus classes. Are you a Professor somewhere and teach online classes?
Thank you so much , you are my calculus teacher ^^