The Fundamental Theorem of Calculus: Redefining Integration
ฝัง
- เผยแพร่เมื่อ 22 เม.ย. 2018
- So we know a lot about differentiation, and the basics about what integration is, so what do these two operations have to do with one another? Everything! And the discovery of their relationship is what launched modern calculus, back in the time of Newton and pals. Check it out!
Watch the whole Calculus playlist: bit.ly/ProfDaveCalculus
Watch the whole Mathematics playlist: bit.ly/ProfDaveMath
Classical Physics Tutorials: bit.ly/ProfDavePhysics1
Modern Physics Tutorials: bit.ly/ProfDavePhysics2
General Chemistry Tutorials: bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: bit.ly/ProfDaveBiochem
Biology Tutorials: bit.ly/ProfDaveBio
EMAIL► ProfessorDaveExplains@gmail.com
PATREON► / professordaveexplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: amzn.to/2HtNpVH
Bookshop: bit.ly/39cKADM
Barnes and Noble: bit.ly/3pUjmrn
Book Depository: bit.ly/3aOVDlT
I am 72 years old and enjoy substituting in high school science and math classes. I am in the process of teaching myself calculus. I have an appreciation of limits and derivatives but want to understand how and why integration works. Every video I have watched (and I have watched plenty) showed how to perform integration but none in a manner that made me feel that I really understood the concept. This is the best explanation I have seen thus far. Math books labor over formulas and some videos seem to want you to accept the concept because it is so. The implication being, if you do not understand, it is because you are either not trying hard enough or just not bright enough. This video really want us to understand integration. Thank you. For those still struggling with it, relax and do not stress. Watch it again, in a couple of days. Your subconscious mind will work on it, in between views. If a 72 year old can get it, you can too.
Still hate Newton lol
The "dx" actually does have a purpose. It is delta-x from the summation, in the limit as n -> infinity. It is the "width" of a "slice" of the region under the curve, which when multiplied by f(x), the "height", gives us the area of the slice.
Yes but why does the antidervitive gives you the area under the curve
This is one of those videos where it just snaps into place in your brain, "I understand calculus". Officially feel like neo when he said " I know kung-fu".
I can't thank you enough for your colossal contribuation to my understanding of maths and physics. I'm a medicine doctor but I'm fascinated by physics and chemistry. I've read a dozen books about physics but the authors focused on the equations and the formulas rather than the phenomena themselves. Your videos are way better. Thank you again.
So many people told me calculus was hell and hard. But since this is extremly easy for me, it must be the great teacher dave
dx does have a meaning! It means "a little bit of x" as change in x approaches 0. It is the width of the rectangle. Now, dy/dx = f(x), so dy=f(x)dx. The Sum (integral) of dy, then, is the Sum (integral) of f(x)dx, which equals y + C.
I watched it.
Thank you for focusing on the “why” in this video. The formulas are great and all, but if you don’t understand why you are using them, they are practically useless.
Accepting an idea that I don't actually understand is stress.
We are the same age more or less. I studied electronics engineering while hated math all my life. Just decided to binge watch all math from start to finish. With a different viewpoint and mostly with this amazing presentation, calm voice, would love it as should. Thanks for the inspiration.
Watched a 2 hour lecture on this, did not understand a single thing. Watched 9 minutes of this video and it instantly cleared up the doubts I had. Thank you!
I cannot even begin to express how thankful I am to have you as a resource, it feels good to actually understand something. Thanks for doing what you do, Prof Dave!
Can't thank you enough . I've spent entire days trying to self study and search online explanations but you're video explained everything in less than 20mins
If you are a varsity student like me and the textbooks and lectures weren't helping so youtube brought you here, you are safe, just continue watching the series. Thank you Dave.
Will need this for next semester when I take Calc! Good stuff as always
So clear and simple
very clear and straight to the point, thank you !
<3 you're posting these videos just in time for my quizzes and tests thank you so much, I feel like this kind of stuff can be so overwhelming