Tarek, really like your videos on Math! Very well structured and with important references in Time. That is how Math should be taught at schools and commeges\unis!
Thank you so much for your kind words! 😊 I’m glad to hear that you enjoy my videos and appreciate the to way they’re structured. The plan with the channel is to explain many concepts through a historical lens
Thank you so much for your kind words and support! 😊 It truly means a lot to me that you’re enjoying the content. Sharing the vlog is one of the best ways to help, and I deeply appreciate it 🙌
Haha, I know!! 😅 When I first started the series, I thought it would be completed within 3 months!! Thank you for sticking around...it means so much! 🙌📚
Thank you, my friend! Your support and encouragement mean so much to me. I’ll definitely keep sharing more videos. Knowing they’re appreciated makes the effort all the more worthwhile!
Thank you so much, Ben! 😊 It really means a lot coming from you. I’ve been meaning to get more active in the Discord group. Hopefully now that this is out, I can catch up. I am looking forward to your video
Thank you so much for your continued support and encouragement! 😊 You’ve been there since the beginning, and it truly means the world to me. Happy New Year to you as well!
By the way, at 12:43 min. isn't the Areas of the rectangles actually overlapping and the actual rectangles are rotated 90°? A₁ = a/5 × x² = a/5 × a²/5² = a³/5³ - this one is the actual smallest rectangle but then… A₂ = (a/5 + a/5) × x² = will include A₁ and the whole area above and below the curve?! Or am I seeing it wrong as calculated?
No, the width is a/5 for all rectangles, so in your formula for A_2 the first factor should just be a/5. It is the expression for x² that changes: for A_2 this is (a/5 + a/5)². Thus, A_2 = a/5*(2a/5)² = 2²a³/5³
Haha, I know!! 😅 When I first started the series, I thought it would be completed within 3 months…Thank you for sticking around and for your support-it means so much! 🙌📚
Thank you for letting me know! I believe the issue has been resolved now, but please don’t hesitate to reach out if you encounter any other problems. I really appreciate your support and feedback!
من اروع السلاسل في موضوع التفاضل و التكامل !!😍😍 تحياتي لك استاذ طارق انا قد فكرت بموضوع تكامل x^n قبل فترة و طلعت بتفسير عنها وهو S{0,a)(x^n)dx= a (base x axis) * a^n (y axis) / some number و بذلك نلاحظ ان a^n > ( S{0,a}(x^n)dx ) > a^(n+1) بسبب وجود فراغ بالمستطيل و كون x^n
شكرًا جزيلًا على كلماتك الطيبة، وأقدّر مشاركتك لأفكارك حول موضوع التكامل. لدي استفسار بسيط حول النقطة التي ذكرتها: “و من خلال حساب المساحة يلاحظ أنها تأخذ حيزًا قدره 1/(1+n) من مساحة المستطيل”. هل يمكنك توضيح كيف توصلت إلى هذه النتيجة؟ ذكرت أن الفكرة ستتضح أكثر عند a= 1 من خلال مقارنة المربع المحيط بالمساحة تحت المنحنى بمربع مجاور. هل يمكنك شرح هذا الجزء بشكل أعمق، خاصة فيما يتعلق بكيفية استنتاج العلاقة بشكل هندسي؟” أتطلع لتوضيحك، وشكرًا مرة أخرى على مساهمتك!
@@tareksaid81 calculator/fpc7ksntjm ( go to desmos and paste this on the end of it to find the diagram i made ) اما عن كيف توصلت لهذه النتيجة هي عندما حاولت ان اجد تكامل x^1 اولا اضرب الطول بالعرض و لكن هناك فراغ و من خلال الملاحظة او بعض التحليل الهندسي تجد انه نصف مساحة المربع اذن S(x^1)=(x^2)/2 فكرت كيف ممكن ان اعمم هذا على باقي الاسس الممكنة فانتهجت نفس طريقة الحل تقريبا في حالة x^2 , S{0,a}(x^2)dx the point (a,a^2) makes a rectangle with base (a) and height (a^2) resulting to an area of (a^3) but there is an empty space inside the shape so the area of the integral is a^2
@@tareksaid81 i made this in desmos , just pste this in the end of the lnk fpc7ksntjm
اما عن كيف توصلت لهذه النتيجة هي عندما حاولت ان اجد تكامل x^1 اولا اضرب الطول بالعرض و لكن هناك فراغ و من خلال الملاحظة او بعض التحليل الهندسي تجد انه نصف مساحة المربع اذن S(x^1)=(x^2)/2 فكرت كيف ممكن ان اعمم هذا على باقي الاسس الممكنة فانتهجت نفس طريقة الحل تقريبا في حالة x^2 , S{0,a}(x^2)dx the point (a,a^2) makes a rectangle with base (a) and height (a^2) resulting to an area of (a^3) but there is an empty space inside the shape so the area of the integral is a^2
@@tareksaid81Thank you so much for sharing the historical development of the Calculus Tarek, and for sharing the mathematical development also, this makes it easier to grasp how Calculus was conceived and developed, and so easier to learn the skills of Calculus.
I am working through the history of calculus bit by bit. I may cover it in a later video in the series or create a separate series for it. Thanks for suggesting it :)
Yessss!!! The man who knows how to explain math
Thank you so much! I’m glad my explanations resonate with you :)
This upload is so rare, I'm framing my notification.
Jokes apart, finally the wait is over.
Haha..thanks I hope you’d like it :)
Tarek, really like your videos on Math! Very well structured and with important references in Time. That is how Math should be taught at schools and commeges\unis!
Thank you so much for your kind words! 😊 I’m glad to hear that you enjoy my videos and appreciate the to way they’re structured. The plan with the channel is to explain many concepts through a historical lens
Wonderful to see you back!
Thanks 😊
Thank you Tarek. Another excellent exposition. Please keep up, and we'll support you by sharing your vlog as much as possible.
Thank you so much for your kind words and support! 😊 It truly means a lot to me that you’re enjoying the content. Sharing the vlog is one of the best ways to help, and I deeply appreciate it 🙌
Welcome back Tarek 🎉
Much awaited, 😊
Thank you so much for the warm welcome! It has indeed been a while. I hope you liked it :)
@tareksaid81 You have maintained the high quality 👍
It's been a long time! I'll have to go back and revisit pt.1, 2, 3!😂 Thank you for your work!
Haha, I know!! 😅 When I first started the series, I thought it would be completed within 3 months!! Thank you for sticking around...it means so much! 🙌📚
It has been a long time since your last video, but worth the wait.
Thank you so much for your patience and kind words! It truly means a lot to hear that the wait was worth it. I’m glad you enjoyed the video :)
Thank you dear friend for this new amazing video. Please keep on sharing videos which are very informative.
Thank you, my friend! Your support and encouragement mean so much to me. I’ll definitely keep sharing more videos. Knowing they’re appreciated makes the effort all the more worthwhile!
Im such a fan. The gift of clear explaining is so rare. Thanks! can’t wait for next part!
Thank you so much! 😊 Your kind words mean a lot to me. I’m glad you’re enjoying the series, and I am working already on the next part
Thank's Mr. Darek, I Always waiting your content
You’re very welcome! I’m so glad you enjoy the content. Thank you it mean a lot to me :)
Tarek, your video series on calculus is the best! I'm really enjoying it!
Thanks.. I am really glad that you are enjoying the videos. Comments like yours motivate me to keep going
Great video Tarek!
Thank you so much, Ben! 😊 It really means a lot coming from you. I’ve been meaning to get more active in the Discord group. Hopefully now that this is out, I can catch up. I am looking forward to your video
Thank you Tarek. Excellent!
Thanks :)
Another fantastic vid! Glad to see you back!
Thanks for your kind words. I really appreciate it :)
Welcome Professor! Happy New Year!! As always: Your work is IMPRESSIVE! Thank you.
Thank you so much for your continued support and encouragement! 😊 You’ve been there since the beginning, and it truly means the world to me. Happy New Year to you as well!
The subtitles after 7:07 are missing
Thanks for letting me know. I think the problem has been solved now. Please let me know if it hasn't :)
Welcome back sir!
Thanks 🙏
Thank you Tarek. I very much enjoyed watching 😊
You’re most welcome Jeremy! I’m glad you enjoyed it 😊
Thank you Tarek that was beautiful
You’re most welcome Simon! I’m so glad you enjoyed it-thank you for your kind words 😊
thank you.. keep it up
thanks :)
I hope to catch the next one, thanks.
I will try to publish asap :)
15:22 My God … that’s Isaac Barrow’s music!
Interesting... do you mean the fact that Barrow was the one who discovered the inverse relation between areas and tangents?
Thankyou very much sir .. your style and presentation is superb ..
love and best wishes from India
Thank you so much for your kind words and support! Sending love and best wishes to you in India. Your encouragement keeps me motivated :)
Perfect 👍
By the way, at 12:43 min. isn't the Areas of the rectangles actually overlapping and the actual rectangles are rotated 90°?
A₁ = a/5 × x² = a/5 × a²/5² = a³/5³ - this one is the actual smallest rectangle
but then…
A₂ = (a/5 + a/5) × x² = will include A₁ and the whole area above and below the curve?! Or am I seeing it wrong as calculated?
No, the width is a/5 for all rectangles, so in your formula for A_2 the first factor should just be a/5. It is the expression for x² that changes: for A_2 this is (a/5 + a/5)². Thus, A_2 = a/5*(2a/5)² = 2²a³/5³
Haha, I know!! 😅 When I first started the series, I thought it would be completed within 3 months…Thank you for sticking around and for your support-it means so much! 🙌📚
Tarek, the subtitle in Brazilian Portuguese stopped at minute three and four seconds.
Thank you for letting me know! I believe the issue has been resolved now, but please don’t hesitate to reach out if you encounter any other problems. I really appreciate your support and feedback!
@@tareksaid81 Thank you Tarek.
Christmas always comes late. 😊
Ha ha.. thanks 🎄🎅
من اروع السلاسل في موضوع التفاضل و التكامل !!😍😍 تحياتي لك استاذ طارق
انا قد فكرت بموضوع تكامل x^n قبل فترة و طلعت بتفسير عنها وهو
S{0,a)(x^n)dx=
a (base x axis) * a^n (y axis) / some number
و بذلك نلاحظ ان
a^n > ( S{0,a}(x^n)dx ) > a^(n+1)
بسبب وجود فراغ بالمستطيل و كون x^n
شكرًا جزيلًا على كلماتك الطيبة، وأقدّر مشاركتك لأفكارك حول موضوع التكامل.
لدي استفسار بسيط حول النقطة التي ذكرتها:
“و من خلال حساب المساحة يلاحظ أنها تأخذ حيزًا قدره 1/(1+n) من مساحة المستطيل”.
هل يمكنك توضيح كيف توصلت إلى هذه النتيجة؟
ذكرت أن الفكرة ستتضح أكثر عند a= 1 من خلال مقارنة المربع المحيط بالمساحة تحت المنحنى بمربع مجاور. هل يمكنك شرح هذا الجزء بشكل أعمق، خاصة فيما يتعلق بكيفية استنتاج العلاقة بشكل هندسي؟”
أتطلع لتوضيحك، وشكرًا مرة أخرى على مساهمتك!
@@tareksaid81
calculator/fpc7ksntjm
( go to desmos and paste this on the end of it to find the diagram i made )
اما عن كيف توصلت لهذه النتيجة هي عندما حاولت ان اجد تكامل x^1
اولا اضرب الطول بالعرض و لكن هناك فراغ و من خلال الملاحظة او بعض التحليل الهندسي تجد انه نصف مساحة المربع
اذن S(x^1)=(x^2)/2
فكرت كيف ممكن ان اعمم هذا على باقي الاسس الممكنة فانتهجت نفس طريقة الحل تقريبا
في حالة x^2 , S{0,a}(x^2)dx
the point (a,a^2) makes a rectangle with base (a) and height (a^2) resulting to an area of (a^3)
but there is an empty space inside the shape so the area of the integral is a^2
@@tareksaid81 i replied but youtube deleted my comment 😐
@@tareksaid81
i made this in desmos , just pste this in the end of the lnk
fpc7ksntjm
اما عن كيف توصلت لهذه النتيجة هي عندما حاولت ان اجد تكامل x^1
اولا اضرب الطول بالعرض و لكن هناك فراغ و من خلال الملاحظة او بعض التحليل الهندسي تجد انه نصف مساحة المربع
اذن S(x^1)=(x^2)/2
فكرت كيف ممكن ان اعمم هذا على باقي الاسس الممكنة فانتهجت نفس طريقة الحل تقريبا
في حالة x^2 , S{0,a}(x^2)dx
the point (a,a^2) makes a rectangle with base (a) and height (a^2) resulting to an area of (a^3)
but there is an empty space inside the shape so the area of the integral is a^2
@@tareksaid81 on the case of a=1 it was made in my project made in desmos , hope you know how to access it
Finally
🙈
Where can we get part 5?
It hasn't been posted yet. I am still working on it. Will do so as soon as I can
Thank you Tarek.@@tareksaid81
@@tareksaid81Thank you so much for sharing the historical development of the Calculus Tarek, and for sharing the mathematical development also, this makes it easier to grasp how Calculus was conceived and developed, and so easier to learn the skills of Calculus.
Can you cover variational calculus 😢😢😢😢😢😢
I am working through the history of calculus bit by bit. I may cover it in a later video in the series or create a separate series for it. Thanks for suggesting it :)
From Pakistan really appreciates your effort in history of math.
Thank you so much! Sending my warmest greetings to Pakistan! 🇵🇰😊
Brilliant ! Your lecture should be compulsory
Thanks ☺️