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 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!
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!
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)
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.
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
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. :-)
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.
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 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.
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.
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 !!
@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!
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.
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 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.
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
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 😀
I don’t know if it’s because I live in Europe, but here we put a « +c » by every primitive function we calculate. Just because the derivatives of x^3/3 and x^3/3 + (a constant number like 1,2,3,4,...) are the same: x^2. To me this seems quite important. Great video still
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.
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 agree with some comments below which state in school the mechanics of operations are taught. But where and how is the actual equation generated? Where did a=1.2t squared come from as an example? How is the original curve found? Without figuring out how to generate the function the mechanics could just as easily be done by a computer and plugging in values. It seems to me the development of the actual function is the first step to solving the problem: Which I will add totally illudes me.
I'll try to weigh in on this. In a given situation, the actual function comes from an analysis of the particular situation. In this example we simply started with a given function. Regarding where the function actually comes from in the real world: In some simpler situations, the function is easily intuited from certain known facts. In simple cases involving a constant rate of change, for example, it may be easily seen that the function is clearly linear with respect to time. in more complicated situations, we have multiple variables and varying rates of change. In these cases an analysis of the situation leads us to a differential equation which then needs to be solved. Finding and solving the DE is a more advanced topic, which is typically introduced a couple of chapters after the Fundamental Theorem, and covered in more detail in later courses. After third semester calculus, students often take a full course in differential equations. Personally, that was the hardest math course I took. One fact not often emphasized is that many situations are actually extremely complicated, with too many variables or too many unknowns, and we simply can't model it effectively without certain simplifying assumptions. In some other cases we can produce a DE describing the situation, but can't easily solve the DE to find the function.
for a case, A rocket is lift off. The location of rocket from the starting point is measured using distance meter at every micro seconds. Now, the data gives rocket distance verses time. Using arithmetic operators, the velocity of rocket may calculated. however, it may not be accurate. somewhat, a function is created. then, think on how to develop acceleration vs time curve? Curves, can be developed using athematic operators. It depends on how much accuracy the market need. In a shop, seller can measure ideal 1kg mass with error of 20%. The population in the area is okey with that. market balance occurred. However, In some field, more accuracy is required to achieve or demonstrate some products or services. In this need, human explore any ideas that fulfills his satisfaction at his understanding about nature.
@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.
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.
Acceleration = change in velocity / time. Therefore, change in velocity = acceleration * time. As the area under the graph also equals acceleration * time, it represents the change in velocity.
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
@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
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!
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
Excellent video ! Question. in the first example you obtain the area between the curve and the coordinate system as g(2)-g(1) = 7/3, would that be named a suffix of square lenght units as of 7/3 = 2.3 square units = 2.3 meter^2, if in meters . If so, in example 2 with the rocket, you obtain a value of 1.2t * 7^3 / 3 = 137.2 meter per second ( if meter is chosen). but that would not be an area (?) , even thou the method is the same in both examples. The value of the rocket 137.2m/s would be a value on the Y axis at t = 7 seconds. How can you tell if you have an area or a point on the coordinate system ? Is it because g(1) = 0 ? and having just 1 dimension left ?
@@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
Mr. Derek Owensthank you for this detailed explanationhowever, I think, when there is a function given as a derivative, the area under the curve of that function is the distance
+Hassan Alanazi You're welcome! If the function is a graph of velocity vs. time, then the area under the curve would be the distance or the displacement. That would be one specific application of the concept.
Last video I watched last night before I went to bed. Enjoyed it immensely. Going to watch the others now. Would say something about the word 'anti-derivative' but that is more like that old 'tomay-toe'/'tomaa-toe' arseholery that leads to folks calling 'the whole thing' off. We used the word 'primitive' where I read maths, but the definition of that is what you say. Excellent.
I should have pronounced antiderivative differently. Thought about re-recording it for that reason but I never had time. Glad you liked the video, though!
In the rocket example, why does the area under the curve represents the speed of the rocket at the end of the 7th second? Wouldn't the value of the y axis be the speed?
Wolfgang, In this example we have a graph of acceleration vs. time, so in this case the value on the vertical axis is the value of the acceleration at any moment. The area under the graph is the change in velocity. If we have a graph of velocity, then the slope of the velocity graph would be the acceleration. Hope that helps. D.O.
(I hope the following questions won't offend your minds) While I do understand the idea of calculus in general, at some point I start to be baffled. That point is when I try to apply units. The solution for the first example is 7/3 - but of what? I assume the answer: of any unit that the axis x and y have, but squared. But it doesn't click with me really. The rocket example is difficult for me in a different way: why is the answer to "how fast" buried in the area of this 1.2t^2 fragment? Why does area depict velocity here?
pls see what are in x and y axis. In simple, Area means, multiplication of Length and width . X axis shows time, and y axis shows acceleration. Now, time X acceleration is velocity ?
What a great set of videos. I teach at a community college, and your videos will help me explain the FTC more clearly. One other thing. Your videos have inspired me to perhaps make some of my own for my students. Would you mind sharing with me what software you used when writing with your pen on your tablet? Thank you.
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.
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.
In my problem I am asked to find the lower limit of the area that the integral has. I have a graph but It's not constant , it's a simple with straight lines but the lines don't touch each other. F(x) = integral of 0 to x f(t) dt. But I don't have f(x).
Newton's attempt at quantifying energy/force fluxions......or energy as the sum of the forces exerted......integral=sum total of forces exerted from time a to time b.
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.
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.
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!
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.
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 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!
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?
I wish college professors would take the time to teach like you do.
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.
Excellent presentation. I feel I understand the Fundamental Theorem in a much deeper sense. Thank you.
are u so stupid
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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.
I'm an English teacher who avoided higher level math, but In 5 Minutes of your video I was hooked.
These are the best videos on this subject in RUclips. By a country mile!
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
Beautifully clear and concise. Bravo 👏 and thanks 🙏
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. :-)
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.
Nice explanation 🙏🙏🙏🙏🙏🙏 sir...
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 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.
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 actually searched for your channel
I read physics from your channel some 8 years ago
Still the best channel
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 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.
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.
@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!
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.
Good Job preofessor
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.
Brilliant explanation, this put so much of Calculus 1 and Physics in perspective for me... awesome work!!!!!
Thank you, thank you! I'm very glad you liked it.
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 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.
can we take a moment to appreciate that perfect ellipse at 1:14
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
Because when you integrate variables to a power you add one and divide by the
new variable.So x^2 becomes x^3/3.
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)
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!
Such a clear video, even clearer than the Kahn Academy video, and that's quite a statement, because Kahn academy videos are usually outstanding.
I don’t know if it’s because I live in Europe, but here we put a « +c » by every primitive function we calculate. Just because the derivatives of x^3/3 and x^3/3 + (a constant number like 1,2,3,4,...) are the same: x^2. To me this seems quite important.
Great video still
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.
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 agree with some comments below which state in school the mechanics of operations are taught. But where and how is the actual equation generated? Where did a=1.2t squared come from as an example? How is the original curve found? Without figuring out how to generate the function the mechanics could just as easily be done by a computer and plugging in values. It seems to me the development of the actual function is the first step to solving the problem: Which I will add totally illudes me.
I'll try to weigh in on this. In a given situation, the actual function comes from an analysis of the particular situation. In this example we simply started with a given function.
Regarding where the function actually comes from in the real world: In some simpler situations, the function is easily intuited from certain known facts. In simple cases involving a constant rate of change, for example, it may be easily seen that the function is clearly linear with respect to time.
in more complicated situations, we have multiple variables and varying rates of change. In these cases an analysis of the situation leads us to a differential equation which then needs to be solved. Finding and solving the DE is a more advanced topic, which is typically introduced a couple of chapters after the Fundamental Theorem, and covered in more detail in later courses. After third semester calculus, students often take a full course in differential equations. Personally, that was the hardest math course I took.
One fact not often emphasized is that many situations are actually extremely complicated, with too many variables or too many unknowns, and we simply can't model it effectively without certain simplifying assumptions. In some other cases we can produce a DE describing the situation, but can't easily solve the DE to find the function.
for a case, A rocket is lift off. The location of rocket from the starting point is measured using distance meter at every micro seconds. Now, the data gives rocket distance verses time. Using arithmetic operators, the velocity of rocket may calculated. however, it may not be accurate. somewhat, a function is created.
then, think on how to develop acceleration vs time curve?
Curves, can be developed using athematic operators.
It depends on how much accuracy the market need.
In a shop, seller can measure ideal 1kg mass with error of 20%. The population in the area is okey with that. market balance occurred.
However, In some field, more accuracy is required to achieve or demonstrate some products or services. In this need, human explore any ideas that fulfills his satisfaction at his understanding about nature.
@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.
A very perfect video. It explains in a very simple way
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.
Acceleration = change in velocity / time. Therefore, change in velocity = acceleration * time. As the area under the graph also equals acceleration * time, it represents the change in velocity.
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
@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
Thanks very much for the encouraging comment! I'm very glad you enjoyed the video!
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!
Derek Owens is a top-notch instructor
Thanks SIR you did your best l like your way of teaching thanks
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
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
Excellent video ! Question. in the first example you obtain the area between the curve and the coordinate system as g(2)-g(1) = 7/3, would that be named a suffix of square lenght units as of 7/3 = 2.3 square units = 2.3 meter^2, if in meters . If so, in example 2 with the rocket, you obtain a value of 1.2t * 7^3 / 3 = 137.2 meter per second ( if meter is chosen). but that would not be an area (?) , even thou the method is the same in both examples. The value of the rocket 137.2m/s would be a value on the Y axis at t = 7 seconds. How can you tell if you have an area or a point on the coordinate system ? Is it because g(1) = 0 ? and having just 1 dimension left ?
Simply Superb explanation Sir.....👍
Thanks for the excellent video. Very concise and to the point with a good example!!
"Calculus is special." It stands out from all the other branches in math. Calculus is king."Very fascinating."
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
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.
Mr. Derek Owensthank you for this detailed explanationhowever, I think, when there is a function given as a derivative, the area under the curve of that function is the distance
+Hassan Alanazi You're welcome! If the function is a graph of velocity vs. time, then the area under the curve would be the distance or the displacement. That would be one specific application of the concept.
OMG, I haven't even taken Calculus, yet I understand it clearly. Well done sir
Last video I watched last night before I went to bed.
Enjoyed it immensely. Going to watch the others now.
Would say something about the word 'anti-derivative' but that is more like that old 'tomay-toe'/'tomaa-toe' arseholery that leads to folks calling 'the whole thing' off. We used the word 'primitive' where I read maths, but the definition of that is what you say.
Excellent.
I should have pronounced antiderivative differently. Thought about re-recording it for that reason but I never had time. Glad you liked the video, though!
Derek Owens
Nah - sounds fine to me. And yes - they _are_ really awesome videos.
In the rocket example, why does the area under the curve represents the speed of the rocket at the end of the 7th second? Wouldn't the value of the y axis be the speed?
Wolfgang, In this example we have a graph of acceleration vs. time, so in this case the value on the vertical axis is the value of the acceleration at any moment. The area under the graph is the change in velocity. If we have a graph of velocity, then the slope of the velocity graph would be the acceleration. Hope that helps. D.O.
But then you used the word, maths and I had to call the whole thing off. :-P
Really enjoying maths videos...m loving maths lately..
wow, you did a better job than kahn academy. very clear and quick
I love you! Everyone made this so complex but you kept it really simple!! Thank you!!
(I hope the following questions won't offend your minds)
While I do understand the idea of calculus in general, at some point I start to be baffled. That point is when I try to apply units. The solution for the first example is 7/3 - but of what? I assume the answer: of any unit that the axis x and y have, but squared. But it doesn't click with me really.
The rocket example is difficult for me in a different way: why is the answer to "how fast" buried in the area of this 1.2t^2 fragment? Why does area depict velocity here?
pls see what are in x and y axis. In simple, Area means, multiplication of Length and width .
X axis shows time, and y axis shows acceleration. Now, time X acceleration is velocity ?
Very nice and clear presentation. Thank you.
Yes, you nailed it. That's a more difficult problem, but it could be solved later in the course.
Superb
Awesome video. What is the software used by the way or is it any software??
What a great set of videos. I teach at a community college, and your videos will help me explain the FTC more clearly.
One other thing. Your videos have inspired me to perhaps make some of my own for my students. Would you mind sharing with me what software you used when writing with your pen on your tablet? Thank you.
KCC Math
Well explain very clear to understand
What software are you usig or it's a tablet with electronic pen?
Great video. I understand this concept much better now, thank you.
hi,
Thank you it is very helpful. I like the colors and the program. It is very clear. Which program/application did you use for this video?
I am going to eight grade and I was always wondering what this was and how you do it.
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.
Good math lesson.thanks for vdo
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.
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
Can you use this video to calculate the work done with force changing?
Very cool, love the graphics and modern version of chalkboard. What software are you using?
Tahnks for your break down! but I gotta ask... if this is so much more effecient than the Reimann Sums, then what's the point of learning that method?
No point lol they just wanna make us suffer
Great video and explanation. A+
I cant wait and subcribed..
In my problem I am asked to find the lower limit of the area that the integral has. I have a graph but It's not constant , it's a simple with straight lines but the lines don't touch each other. F(x) = integral of 0 to x f(t) dt. But I don't have f(x).
I found this video very helpful and clear. Thank you very much!!
Big thanks from Ireland, the fundamental principle was well outlined with nice examples
Regards Tom
Newton's attempt at quantifying energy/force fluxions......or energy as the sum of the forces exerted......integral=sum total of forces exerted from time a to time b.
Really brilliant love it more more ..please.👍
thank you very much ...im 60 and heard first time abaut non constant acceleration..
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.
These so good teachings even monkey could understand. 1000 thanks for this guy
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.
Watched the series and it is very good ! Thank you !
Extremely clear, thanks a lot! Great refresher.