I’m de-mystified!!! Understood completely both the concept & mechanics about the problem! More intriguing is that I have only UP TO college level algebra (first 3weeks)!!!
These videos are refreshers for me. I had 16 hours of calculus and differential equations 50 years ago. We were taught the mechanics of calculus until differential equations and I saw the power of the subject. I went into highway and traffic engineering and never used it. We had formulas to use for everything. You are teaching a use instead of the mechanics and I understand it better now than I did then.
I really enjoyed this Video for beginning Calc. Later on, a more difficult problem will be that in reality when you are using a simple drain the flow rate is not a constant. The flow rate is dependant on the water pressure at the bottom of the tank, so as the water height drops the flow rate will also drop. And assuming the same starting water volume in both tanks, the pressure will be greater at the bottom of the tall, skinny tank. This will cause an even bigger difference in dh/dt between the two tanks.
You need to account for the conversion factor, so 3 years for 40 minutes of video, each titled as "10 minutes), you need this differentiated by time. So dy over dt, using the first derivative should give you f prime (x) = 3y/dt, where dt = 40 min/2(10 min lies), which can be solved as a big variable, so just X.
Well, since you asked. I'm old, 58, and a few years back I jumped in a physics rabbit hole (history, concepts etc. and a lot of popular/communicator books) and I'm at a point that a need the math to really get some of the higher concepts. Along the way I learned a bit about the rivalries and collaborations between Mathematicians and Physicists, and I just got caught up now in a math fascination. This is all for fun, I'm too old to contribute anything- I just want to know, the best I can, about how things work. My brothers are teachers. You're doing this video for free. Folks like you, my brothers and anyone who teaches- you are the best and I thank you. Really great easy style you have. Thanx again!
I'm a sophomore in high-school and thought it would be fun to learn some calculus as I want to be in aerospace engineering. Your videos are very comprehensive and I enjoy learning.
Just watched part 1. You’re at like 6-7 million lol Definitely helped break it down. I’m in my early 30s, decided it’s time for a career change. Gonna need to learn this so here I am.
Sweet. From what to what, do you think? I like construction, but it's too easy on the neurons, and too hard on the joints. I can't be stuck in an office, all day, though, so I've gotta make a way.
You make it easy. In high school, too many distractions. Accents, no chance to hear the distorted message but once. Your message is without the distractions. Thank you.
I took calc 1 twice. I bombed on teh related rates test and ruined my grade each time. never got past it. I did learn more about integrals, I was totally not getting them but your video #1 helped me undertand them a little more. This is the hardest part of calc 1., related rates. I"m 53, wish I would of stuck with it. I got drawn out of school years ago with a good tech job offer. I hate computer work now, ie repairing networks servers, dektops, and wish I would have stck with it. My son is good at math and his brother is in columbia now taking calc 3 this semester. I would love to finish my degree in engineering. I works on pool cues now doing machine work, cnc.
Hi Teacher, You taught me calculus in two videos. Thank you so much. All the fear of calculus are gone. Thank you very much. I’m going to continue watching your videos and following your advices ❤
I'm just interested in it, I used to barley understand basic geometry and never heard of algebra, now I think that this calculus stuff ins't that difficult and I have learned about algebra.
Thank you John. I missed such clarity in teaching when I was young kid. Now going through these concepts one more time through your vdeos which i think are an excellent resource for math students
John you're the best teacher, I never know about calculus but those video a very clear to me, so I recommend that you're the best teacher very talented. Thank you John!
You are one fantastic teacher. How I wish I was taught this in middle school or high school. I have to get that book! Some years ago I read that during World War II, they wanted to reduce the amount of metal that that was used for cans in canned food. And they used calculus to do it. That would be a good problem to demonstrate.
Hi John, This is really explaining what calculus can be about. You take enough time to do it in some parts of the video, and not in other parts, assuming the viewers understand or already know. To give an example would be when you gave the formula for calculating Volume. Luckily I understood. As a mathteacher on the other hand you are supposed to know how to change meters in centimeters. So when you write 0.095m this is equal to 9,5cm and not 0.9cm. In this case the correct answer was indeed 0.95cm
Your calculus videos are terrrific. I watched a few today. I'm 77 years young, took calculus in college and did not grasp it to be able to use it. Math and science have always been my 2 favorite subjects. I understand what calculus does but the mechanics have always escaped me. Your explanations and solutions are clear and logical. Thank you for your You Tubes. I'll look for more to watch.
Stimulating video and is a great refresher for me. The simplified concept makes the math so much more concrete. The mechanics of algebra have always been fun for me, but until I took physics in HS and College did the functionality smack me in the forehead. Now lets complicate the problem of fluid height, and lay your cylinder on the side. We still need to know the volume at different fluid level heights and time to empty the tank. Then thinking about one of your previous videos I see the surface area of the liquid in the tank change as height changes. I thought about the integrals and using rectangles to follow the curve. I see it tying the two concepts together. I also had fun thinking about different methods to approximate the measurement and physically measure the system. No cheating looking at the tank charts. Thank you for suppling me several hours of entertainment and thought experiments to flex a few mental muscles.
How do you figure out the change of rate if the flow is by gravity rather than by a pump? I have tried to brute force an acceleration problem of a theoretical spaceship leaving earth at a constant thrust. The acceleration changes as the square of the distance to the center of the earth and the distance changes as the square of the time AND the acceleration. Distance = .5 acceleration * time squared. At 1.5 g for 30 minutes at which point thrust is reduced to 1 g. How far will you have traveled after 4 hours from takeoff. At 1.5 g initial acceleration is ~ 16.1 ft/sec/sec. At 1000 miles acceleration =~28 ft/sec/sec. At what point does acceleration stabilize at ~48.3 ft/sec/sec?
Hmm... so, shouldn't the negative symbol be removed from the answer? I think the premise of the original question is very important: "How fast does the fluid level drop". Specifically, we are NOT asking "What is the fluid level with respect to volume of flow?" In other words, because the original question specifically uses the word "Drop", it already implies a negative. For example, if I say... A ball is dropped from 100' high, how fast does it drop after 1 second... the answer is NOT a negative number. So, shouldn't the negative sign be removed from the answer?
Ah, the gentle art of autodidacticism. Didn't like my middle school maths teacher. He was a psychotic freemason who couldn't teach. Ended up leaving his wife for a much younger woman. Didn't like my my high school math teacher either. She engaged in an adulterous relationship with a male student. He wasn't very good at math, but won a prize that she marked. You however are an excellent teacher. I finally got it. Thanks!
It is confusing a bit because your name is John Zimmerman but the link to your recommended the book is authored by W. Michael Kelley. Could you please provide a clarity.
Isn’t this just a d=rt problem? Distance is the volume. Rate is the surface area of the out tube. Kinda assumes viscosity and flow rate is a certain amount. And assumes height has no bearing on pressure though. I guess the liter conversion is needed if the flow rate is given in liters. Would love to set up actual experiment with water and oil and get a 5gal buck or a tall 4” pvc pipe.
Not sure, but if you already know the radius of the cylinder, I don't think it's necessary to use calculus. Basic geometry and arithmetic should give you the answer.
Thank you Professor, I agree Calculus is amazing, and the thigs it can accomplish, I'm just starting out with it, but like it, altugh I'm not very good at it, yet?
instead of calculating in litres as volume you could have turned it round and converted volume into Xm3....instead of converting by 1000 instead converting on the other side by 3 (m3)....the whole thing should now be expanded upon where its not a cylinder but a , say, cone shape.....
It is wrong, if pr^2r litter means radius can be to be in meter or 1 litter can be in sm^3 which is 1000 times. secondly dh/dt is contant., permanent and not negative. it looks like velocity (speed) s/t. h/t not acceleration which can be positive or negative.
even 1 m radius tank release more faster than 10m r tank ,,, both get emptied on the same time ,,, since amount of water in both are same...... thanks alot for more brain cells ,,,,
OK... now, what if the rate of change *changes* over time? Like, what if the hole gets clogged at a constant rate? Heck, what if it clogs at an accelerating rate? What if we have a crazy cylinder that changes radius over time... at an accelerating rate?
It’s called a second derivative where you just take the derivative of the derivative for example the second derivative of x^2 is 2x and the derivative of 2x is 2 also the notation is (d^2)y/dx^2 there’s also third derivatives and so on
Literally just bought your recommended book and returned it within 10 minutes because problem numero uno goes against what the book says it will do and literally just doesn’t explain the process of what they’re doing. What a joke
Even though I never took Calculus, I find this video to be very clear and understandable. That says a lot about this teacher!
I’m de-mystified!!! Understood completely both the concept & mechanics about the problem! More intriguing is that I have only UP TO college level algebra (first 3weeks)!!!
These videos are refreshers for me. I had 16 hours of calculus and differential equations 50 years ago. We were taught the mechanics of calculus until differential equations and I saw the power of the subject. I went into highway and traffic engineering and never used it. We had formulas to use for everything. You are teaching a use instead of the mechanics and I understand it better now than I did then.
I'm with you Harold. Wish I'd had these videos when I was in class.
Me too!
I really enjoyed this Video for beginning Calc. Later on, a more difficult problem will be that in reality when you are using a simple drain the flow rate is not a constant. The flow rate is dependant on the water pressure at the bottom of the tank, so as the water height drops the flow rate will also drop. And assuming the same starting water volume in both tanks, the pressure will be greater at the bottom of the tall, skinny tank. This will cause an even bigger difference in dh/dt between the two tanks.
3 years for a part two
😂😂😂😂
Math keeps getting better and better
Haha
You need to account for the conversion factor, so 3 years for 40 minutes of video, each titled as "10 minutes), you need this differentiated by time. So dy over dt, using the first derivative should give you f prime (x) = 3y/dt, where dt = 40 min/2(10 min lies), which can be solved as a big variable, so just X.
@@EmpyreanLightASMR To simplify, the answer is 42. -- Hitchhikers Guide to the Galaxy.
Well, since you asked. I'm old, 58, and a few years back I jumped in a physics rabbit hole (history, concepts etc. and a lot of popular/communicator books) and I'm at a point that a need the math to really get some of the higher concepts. Along the way I learned a bit about the rivalries and collaborations between Mathematicians and Physicists, and I just got caught up now in a math fascination. This is all for fun, I'm too old to contribute anything- I just want to know, the best I can, about how things work. My brothers are teachers. You're doing this video for free. Folks like you, my brothers and anyone who teaches- you are the best and I thank you. Really great easy style you have. Thanx again!
I'm a sophomore in high-school and thought it would be fun to learn some calculus as I want to be in aerospace engineering. Your videos are very comprehensive and I enjoy learning.
Same
Loved the video. Really like real world problems. Learning calculus on my own. Thanks!
Thanks very much for this. I just watch your videos because I enjoy mathematics and they refresh my knowledge gained from my long distant school days
Just watched part 1. You’re at like 6-7 million lol
Definitely helped break it down. I’m in my early 30s, decided it’s time for a career change. Gonna need to learn this so here I am.
Sweet.
From what to what, do you think?
I like construction, but it's too easy on the neurons, and too hard on the joints.
I can't be stuck in an office, all day, though, so I've gotta make a way.
I do automotive Currently. Aftermarket Suv and Truck suspension to be specific. Thinking of going to engineering of some sort. Likely mechanical.
Thanks for what you're doing. I'm a retired Nuclear Med Tech and have been out of the Math arena for awhile. You make it easy. Thanks again. John Cox
You make it easy. In high school, too many distractions. Accents, no chance to hear the distorted message but once. Your message is without the distractions. Thank you.
I am a 56 year old women returning to college this sept. My first class being calculus! Thanks for the easy to understand video
I took calc 1 twice. I bombed on teh related rates test and ruined my grade each time. never got past it. I did learn more about integrals, I was totally not getting them but your video #1 helped me undertand them a little more. This is the hardest part of calc 1., related rates. I"m 53, wish I would of stuck with it. I got drawn out of school years ago with a good tech job offer. I hate computer work now, ie repairing networks servers, dektops, and wish I would have stck with it. My son is good at math and his brother is in columbia now taking calc 3 this semester. I would love to finish my degree in engineering. I works on pool cues now doing machine work, cnc.
Great video! Good for gueezers too who are trying to stay young in mindd. Thanks much.
Thanks for posting these videos. I’m using them to prep for a coding boot camp. I appreciate the help.
How was it
Incredible and relatable example of real world. Watching from Pakistan.
One of the best videos that I have seen on the use of differentials. Thanks for posting.
Hi Teacher,
You taught me calculus in two videos. Thank you so much. All the fear of calculus are gone. Thank you very much. I’m going to continue watching your videos and following your advices ❤
Instructions unclear, my floor is flooded now. On a real note though, thanks for these videos! Very informative yet digestible.
Same
I'm just interested in it, I used to barley understand basic geometry and never heard of algebra, now I think that this calculus stuff ins't that difficult and I have learned about algebra.
I took calculus in 1977. I always wished to go back and do it again. This video series is AWESOME!¡!!¡!¡!¡! i!¡!¡!¡!¡!¡!¡¡!¡!¡!
Thank you John. I missed such clarity in teaching when I was young kid. Now going through these concepts one more time through your vdeos which i think are an excellent resource for math students
John you're the best teacher, I never know about calculus but those video a very clear to me, so I recommend that you're the best teacher very talented. Thank you John!
Because of you sir, I finally understood this topic. I haven't understood it in my calculus 1 course and got low grades. Thank you so much.
Thanks for your time to teach us so easy to understand, I learnt basic calculus 50 years ago but you explained very nice way.
You are one fantastic teacher. How I wish I was taught this in middle school or high school. I have to get that book! Some years ago I read that during World War II, they wanted to reduce the amount of metal that that was used for cans in canned food. And they used calculus to do it. That would be a good problem to demonstrate.
Hi John,
This is really explaining what calculus can be about. You take enough time to do it in some parts of the video, and not in other parts, assuming the viewers understand or already know. To give an example would be when you gave the formula for calculating Volume. Luckily I understood. As a mathteacher on the other hand you are supposed to know how to change meters in centimeters. So when you write 0.095m this is equal to 9,5cm and not 0.9cm. In this case the correct answer was indeed 0.95cm
Thankful for what you’re doing 🙏🏾🙏🏾
Your calculus videos are terrrific. I watched a few today. I'm 77 years young, took calculus in college and did not grasp it to be able to use it. Math and science have always been my 2 favorite subjects. I understand what calculus does but the mechanics have always escaped me. Your explanations and solutions are clear and logical. Thank you for your You Tubes. I'll look for more to watch.
Stimulating video and is a great refresher for me. The simplified concept makes the math so much more concrete. The mechanics of algebra have always been fun for me, but until I took physics in HS and College did the functionality smack me in the forehead.
Now lets complicate the problem of fluid height, and lay your cylinder on the side. We still need to know the volume at different fluid level heights and time to empty the tank.
Then thinking about one of your previous videos I see the surface area of the liquid in the tank change as height changes. I thought about the integrals and using rectangles to follow the curve. I see it tying the two concepts together. I also had fun thinking about different methods to approximate the measurement and physically measure the system. No cheating looking at the tank charts.
Thank you for suppling me several hours of entertainment and thought experiments to flex a few mental muscles.
How do you figure out the change of rate if the flow is by gravity rather than by a pump?
I have tried to brute force an acceleration problem of a theoretical spaceship leaving earth at a constant thrust. The acceleration changes as the square of the distance to the center of the earth and the distance changes as the square of the time AND the acceleration.
Distance = .5 acceleration * time squared. At 1.5 g for 30 minutes at which point thrust is reduced to 1 g. How far will you have traveled after 4 hours from takeoff.
At 1.5 g initial acceleration is ~ 16.1 ft/sec/sec. At 1000 miles acceleration =~28 ft/sec/sec. At what point does acceleration stabilize at ~48.3 ft/sec/sec?
Wonderful video. Well put together!!! The name of the mentioned was not displayed…
carlitos
I love it.sir.how could I get my maximum practice,I want to use these in daily life.
Cant wait for part three next year!
What a beautifull explanation ❤❤❤.
Sir, please make more and more Calculus videos. Your method is super awesome. And please make a brief video on the Differential Equations.
So fun learning !!!
This helped me so much thanks!
Thanks for making the video,
40 years old, and finally curious about calculus.
Hmm... so, shouldn't the negative symbol be removed from the answer? I think the premise of the original question is very important: "How fast does the fluid level drop".
Specifically, we are NOT asking "What is the fluid level with respect to volume of flow?"
In other words, because the original question specifically uses the word "Drop", it already implies a negative.
For example, if I say... A ball is dropped from 100' high, how fast does it drop after 1 second... the answer is NOT a negative number.
So, shouldn't the negative sign be removed from the answer?
Ah, the gentle art of autodidacticism. Didn't like my middle school maths teacher. He was a psychotic freemason who couldn't teach. Ended up leaving his wife for a much younger woman. Didn't like my my high school math teacher either. She engaged in an adulterous relationship with a male student. He wasn't very good at math, but won a prize that she marked. You however are an excellent teacher. I finally got it. Thanks!
Very clear and helpful, thank you for this
That's the kind of teaching I want
Is the book you recommended includes Electric engineering calculus ?
It is confusing a bit because your name is John Zimmerman but the link to your recommended the book is authored by W. Michael Kelley. Could you please provide a clarity.
Sir is that book really useful?
Please reply. I am preparing for IIT so, please recommend books of good level of difficulty
Isn’t this just a d=rt problem?
Distance is the volume. Rate is the surface area of the out tube.
Kinda assumes viscosity and flow rate is a certain amount. And assumes height has no bearing on pressure though.
I guess the liter conversion is needed if the flow rate is given in liters.
Would love to set up actual experiment with water and oil and get a 5gal buck or a tall 4” pvc pipe.
Thanks
Just looking to learn a bit more as a hobby.
Not sure, but if you already know the radius of the cylinder, I don't think it's necessary to use calculus. Basic geometry and arithmetic should give you the answer.
what about pressure that will decay while volume decreases.
I’m 9 and I’m learning calculus
Can I please ask the name of the software program you are using? Thanks.
Thanks... It has been an amazing Aha moment!
Thank you Professor, I agree Calculus is amazing, and the thigs it can accomplish, I'm just starting out with it, but like it, altugh I'm not very good at it, yet?
Is it possible that you might train yourself to stop saying _"mmm, OK?"_ Or _"OK?"_ or even _"K?"_
Probably a stupid question but where did the 1 cubic meter bit come from?
Thank you.
tysm for this!
instead of calculating in litres as volume you could have turned it round and converted volume into Xm3....instead of converting by 1000 instead converting on the other side by 3 (m3)....the whole thing should now be expanded upon where its not a cylinder but a , say, cone shape.....
It is wrong, if pr^2r litter means radius can be to be in meter or 1 litter can be in sm^3 which is 1000 times. secondly dh/dt is contant., permanent and not negative. it looks like velocity (speed) s/t. h/t not acceleration which can be positive or negative.
I just wish there was an E-book of that
liked the pith ))
even 1 m radius tank release more faster than 10m r tank ,,, both get emptied on the same time ,,, since amount of water in both are same...... thanks alot for more brain cells ,,,,
I love the video. you inspired me to make my own RUclips channel . I would love some support
It would help if you stop over explaining.
Is it possible to score a 75 on math placement after scoring a 30?
youll have to calculate the derivative of change in order to find out....LOL
What if you were draining a cone?
@patchesdf
…then you’d use the formula for the volume of a cone, instead, V = 1/3•pi•r^2•h, then proceed as done here.
Add a link to part one here son!
I wanted to go into high school knowing a bit of calculus lol
Hello John
'a whole nother' - ouch!
OK... now, what if the rate of change *changes* over time? Like, what if the hole gets clogged at a constant rate? Heck, what if it clogs at an accelerating rate? What if we have a crazy cylinder that changes radius over time... at an accelerating rate?
It’s called a second derivative where you just take the derivative of the derivative for example the second derivative of x^2 is 2x and the derivative of 2x is 2 also the notation is (d^2)y/dx^2 there’s also third derivatives and so on
I'm the only 7th grader in my school who knows this stuff lol... other kids treat me like a god.
Literally just bought your recommended book and returned it within 10 minutes because problem numero uno goes against what the book says it will do and literally just doesn’t explain the process of what they’re doing. What a joke
alternate title: how long til my pool drains?
I’m a college dropout cause calculus was too hard for me 😭
hi
why would i take calculus as a junior in highschool just why
Hi can you reply to me
I'm doomed
Thumbnail says "derivitivities" lol
Ha! "You're probably a calculus student" , No I am not.
Repetitious. Needs an editor
Yes
Do u know u look like the rock
I cant type worth a darn . I do really. Know how to spell lol
More than 10 minutes. :/ Like please just be honest in your titles.
bro calm down lmao it's not that deep.