Calculus - The Fundamental Theorem, Part 1

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  • Опубликовано: 18 янв 2025

Комментарии • 420

  • @herbertduncan5838
    @herbertduncan5838 2 года назад +21

    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.

    • @derekowens
      @derekowens  2 года назад +6

      Thanks for such a thoughtful and encouraging comment!

  • @jamescboyd
    @jamescboyd 15 лет назад +16

    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!

  • @tomt.9211
    @tomt.9211 Год назад +2

    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!

  • @miketooth8119
    @miketooth8119 11 лет назад +14

    reviewing this after 35 years for my son - wish I had a teacher like this
    and explanations like this

  • @bilu2458
    @bilu2458 6 лет назад +14

    I wish college professors would take the time to teach like you do.

  • @jamesrobertson9149
    @jamesrobertson9149 7 лет назад +1

    These are the best videos on this subject in RUclips. By a country mile!

  • @altoclef4989
    @altoclef4989 4 года назад +2

    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!

  • @kingmanyeung8834
    @kingmanyeung8834 4 года назад +1

    What a champ you are professor!! Explicit and clear explanation without any confusion.

  • @derekowens
    @derekowens  11 лет назад +2

    Thanks very much for the encouraging comment! I'm very glad you enjoyed the video!

  • @pawanyadav3399
    @pawanyadav3399 6 месяцев назад

    Nice explanation 🙏🙏🙏🙏🙏🙏 sir...

  • @iancoult7875
    @iancoult7875 Год назад

    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!

  • @WilliamSoto
    @WilliamSoto 5 лет назад +7

    Excellent presentation. I feel I understand the Fundamental Theorem in a much deeper sense. Thank you.

    • @zkzk5334
      @zkzk5334 5 лет назад

      are u so stupid

    • @Inspiredmathematicsclasses
      @Inspiredmathematicsclasses 5 лет назад

      DIFFERENTIABILITY , SHORTCUT , WBJEE , JEE MAINS , ADVANCE , Any other competitive Exams.: ruclips.net/p/PL0o1IL6EH-hmuCDFxxLBk1Jxmm3hsn6qv

  • @thedrumman64
    @thedrumman64 11 лет назад +1

    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. :-)

  • @jkj1459
    @jkj1459 10 лет назад +78

    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.

    • @Bentami
      @Bentami 5 лет назад +4

      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.

    • @Inspiredmathematicsclasses
      @Inspiredmathematicsclasses 5 лет назад +1

      YOU CAN FOLLOW MAXIMUM SHARE ------------ ruclips.net/p/PL0o1IL6EH-hmAI6PppvpjasHyy-zhRWOR

    • @Pattrices1
      @Pattrices1 4 года назад +1

      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)

    • @luiswittrock223
      @luiswittrock223 3 года назад +1

      Ok I know this comment is 6 years old, but what are those spaces between the words?

  • @cameronnekerekian1712
    @cameronnekerekian1712 5 лет назад +10

    can we take a moment to appreciate that perfect ellipse at 1:14

  • @peterhunt1968
    @peterhunt1968 4 года назад +2

    Beautifully clear and concise. Bravo 👏 and thanks 🙏

  • @GTiR94
    @GTiR94 12 лет назад +1

    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.

  • @alaricblair3264
    @alaricblair3264 4 года назад +1

    I'm an English teacher who avoided higher level math, but In 5 Minutes of your video I was hooked.

  • @mariomaruf
    @mariomaruf 14 лет назад +1

    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.

  • @derekowens
    @derekowens  16 лет назад +1

    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.

  • @carlosalbertocuadros5469
    @carlosalbertocuadros5469 2 года назад +1

    Good Job preofessor

  • @shep7484
    @shep7484 8 лет назад +2

    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.

  • @derekowens
    @derekowens  12 лет назад +1

    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.

  • @derekowens
    @derekowens  16 лет назад +8

    These "Fundamental Theorem" videos are about to get redone. I think I can improve the explanation.

    • @peterhunt1968
      @peterhunt1968 4 года назад

      Derek Owens no need

    • @ALWAYSGOODENGLISH
      @ALWAYSGOODENGLISH 4 года назад +1

      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.

    • @jacksonnyanokwi7766
      @jacksonnyanokwi7766 3 года назад

      Waooooo good aid

  • @balochan1
    @balochan1 13 лет назад +1

    @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!

  • @sk4434
    @sk4434 5 лет назад +4

    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

  • @rahulv9946
    @rahulv9946 Год назад

    Simply Superb explanation Sir.....👍

  • @nikhilpant6428
    @nikhilpant6428 2 года назад

    I actually searched for your channel
    I read physics from your channel some 8 years ago
    Still the best channel

  • @MrFernandoBedoya
    @MrFernandoBedoya 5 лет назад +1

    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
    @derekowens  13 лет назад +1

    @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

  • @sisounthonethongthep5445
    @sisounthonethongthep5445 3 года назад

    Good math lesson.thanks for vdo

  • @dijonstreak
    @dijonstreak 5 лет назад

    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 !!

  • @denconstutube
    @denconstutube 11 лет назад

    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.

  • @studio2038
    @studio2038 3 года назад

    Well explain very clear to understand

  • @iiEdgR
    @iiEdgR 11 лет назад

    OMG, I haven't even taken Calculus, yet I understand it clearly. Well done sir

  • @fahmylina123
    @fahmylina123 12 лет назад

    Very nice and clear presentation. Thank you.

  • @ALWAYSGOODENGLISH
    @ALWAYSGOODENGLISH 4 года назад

    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
    @derekowens  11 лет назад +4

    Thank you, thank you! I'm very glad you liked it.

  • @queenodein
    @queenodein 12 лет назад

    I love you! Everyone made this so complex but you kept it really simple!! Thank you!!

  • @majdyayoub2879
    @majdyayoub2879 4 года назад

    A very perfect video. It explains in a very simple way

  • @bujanginin9971
    @bujanginin9971 3 года назад

    I cant wait and subcribed..

  • @markrunnalls7215
    @markrunnalls7215 5 лет назад

    Really brilliant love it more more ..please.👍

  • @timotheospetros
    @timotheospetros 12 лет назад +1

    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.

  • @derekowens
    @derekowens  11 лет назад +1

    Yes, you nailed it. That's a more difficult problem, but it could be solved later in the course.

  • @derekowens
    @derekowens  11 лет назад +16

    I teach classes to homeschool students. I have live classes in the Atlanta area during the school year, and online courses available year round.

    • @megatton7207
      @megatton7207 3 года назад

      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?

    • @harshallkohli8458
      @harshallkohli8458 3 года назад

      @@megatton7207 there is a general way for getting there that's simple
      ∫ x^n dx= x^(n+1)/(n+1) (when n≠1)

  • @derekowens
    @derekowens  12 лет назад

    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.

  • @RajeshKumar-ch4rv
    @RajeshKumar-ch4rv 6 лет назад

    Superb

  • @osamamalik3290
    @osamamalik3290 5 лет назад +1

    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

  • @Tom.Connolly
    @Tom.Connolly 12 лет назад

    Big thanks from Ireland, the fundamental principle was well outlined with nice examples
    Regards Tom

  • @DTM636
    @DTM636 12 лет назад +1

    Extremely clear, thanks a lot! Great refresher.

  • @skeltor575
    @skeltor575 8 лет назад

    Such a clear video, even clearer than the Kahn Academy video, and that's quite a statement, because Kahn academy videos are usually outstanding.

  • @Adrian_Gutier
    @Adrian_Gutier 5 лет назад

    Great video and explanation. A+

  • @jayti1827
    @jayti1827 6 лет назад +1

    "Calculus is special." It stands out from all the other branches in math. Calculus is king."Very fascinating."

  • @Fenyx46
    @Fenyx46 12 лет назад

    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.

  • @derekowens
    @derekowens  14 лет назад

    @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.

  • @llasnier
    @llasnier 12 лет назад +1

    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!

  • @antonbashkin6706
    @antonbashkin6706 2 года назад

    Brilliant explanation, this put so much of Calculus 1 and Physics in perspective for me... awesome work!!!!!

  • @mlotshwa100
    @mlotshwa100 8 лет назад

    Really enjoying maths videos...m loving maths lately..

  • @lleaves
    @lleaves 11 лет назад +1

    Thanks for the excellent video. Very concise and to the point with a good example!!

  • @cheersfornads
    @cheersfornads 14 лет назад

    You make Calculus sound great. Thanks.

  • @bebancos
    @bebancos 16 лет назад +1

    Thanks man,, Great Teaching

  • @BYMYSYD
    @BYMYSYD 14 лет назад

    wow, you did a better job than kahn academy. very clear and quick

  • @ethanpierce324
    @ethanpierce324 10 лет назад +18

    Im in 8th grade taking geometry right now and this just blew my mind how many variables to the whatever

    • @carloscerritoslira328
      @carloscerritoslira328 7 лет назад +2

      hi

    • @juujzilla2103
      @juujzilla2103 7 лет назад

      Lel I am in 7th grade and I am learning Calculus

    • @dayzonmurray8880
      @dayzonmurray8880 5 лет назад

      Saaaaame but I’m in 7th taking geometry

    • @nahrafe
      @nahrafe 4 года назад

      Hi, now you must be on college.

    • @ethanpierce324
      @ethanpierce324 4 года назад

      @@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

  • @vincentperrier2122
    @vincentperrier2122 7 лет назад

    Very helpful video !

  • @theknacke
    @theknacke 11 лет назад +1

    Thank you soooo much!!! It's a amazing thing you're doing making all these videos for everyone!!:D You're great at explaining!!

  • @nhanguyen-gu8tn
    @nhanguyen-gu8tn 6 лет назад

    🙏👌 clearly & very good to declare the topics ❤️

  • @drurenia
    @drurenia 11 лет назад +1

    Gee, you make it so easy to understand.

  • @leormhan
    @leormhan 12 лет назад

    I love this video...I learned a lot from this...

  • @derekowens
    @derekowens  11 лет назад +1

    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.

  • @ian.ambrose
    @ian.ambrose 3 года назад

    Thank you Father.

  • @vaishnavchandra5220
    @vaishnavchandra5220 3 года назад

    you are a life saver

  • @fawzyhegab
    @fawzyhegab 11 лет назад +1

    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.

  • @derekowens
    @derekowens  12 лет назад +3

    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.

  • @ashton982
    @ashton982 5 лет назад +1

    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.

  • @danielbarnett6009
    @danielbarnett6009 11 лет назад +2

    You are a legend!

  • @jorgegonzalez-ec5fl
    @jorgegonzalez-ec5fl 6 лет назад

    Great video. I understand this concept much better now, thank you.

  • @michaelgebremeskel6622
    @michaelgebremeskel6622 6 лет назад

    You made it. Good job.

  • @rutamvarm
    @rutamvarm 10 лет назад

    Awesome video. What is the software used by the way or is it any software??

  • @knowledgeworld3044
    @knowledgeworld3044 5 лет назад

    sir you are so amazing teacher

  • @mathecian
    @mathecian 4 года назад

    Perfect sir

  • @arj123sub
    @arj123sub 5 лет назад

    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 😀

    • @derekowens
      @derekowens  5 лет назад

      1983 happens to be when I also first learned calculus. Shout out to Mr. Wayne Murrah for being a great teacher!

  • @deanbrown2542
    @deanbrown2542 9 лет назад

    Excellent videos - thanks so much.

  • @monoor5639
    @monoor5639 8 лет назад +1

    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

  • @naifkhan8600
    @naifkhan8600 8 лет назад

    good job

  • @mattam66
    @mattam66 12 лет назад

    Hi Derek
    very good explanation. Would you please inform me which program are you using to make this video.

  • @richardvillier536
    @richardvillier536 2 года назад

    MUST SEE VIDEO !!!

  • @BMGBOX
    @BMGBOX 7 лет назад

    Watched the series and it is very good ! Thank you !

  • @devondevon4366
    @devondevon4366 5 лет назад

    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.

  • @VFizz
    @VFizz 4 года назад

    Excellent Vid - thank you!!!!!!

  • @zuhairalsaffar7001
    @zuhairalsaffar7001 4 года назад

    Thanks SIR you did your best l like your way of teaching thanks

  • @harrymason1053
    @harrymason1053 Год назад

    Very clear.

  • @epijonix
    @epijonix 11 лет назад

    nice review and style. Thanks Derek

  • @xROFLawsonx
    @xROFLawsonx 14 лет назад

    Wow, these are amazing. I love your quick, clear, and clean drawings. what do you use? Very easy to understand.

  • @UserName-sj8fg
    @UserName-sj8fg 8 лет назад

    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.

  • @dsakjet78
    @dsakjet78 11 лет назад

    Because when you integrate variables to a power you add one and divide by the
    new variable.So x^2 becomes x^3/3.

  • @brucelee3711
    @brucelee3711 12 лет назад +1

    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!:)

  • @qwaydonize
    @qwaydonize 11 лет назад +1

    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.

    • @RanBlakePiano
      @RanBlakePiano 4 года назад

      greenyblu he is all ready contributing to our education

  • @mihir2781
    @mihir2781 12 лет назад

    thank you very much, with the detailed examples to clear my fundamental...

  • @tracibullara3934
    @tracibullara3934 11 лет назад +1

    Me too! As a science major I have to take all of the Calculus classes. Are you a Professor somewhere and teach online classes?

  • @tienduong5752
    @tienduong5752 9 лет назад +1

    Thank you so much , you are my calculus teacher ^^