He teaches all levels of the Calculus in a good geometrical way. His and other videos on economics, physiology, Spanish, Chinese, and electronics are a good escape from isolation and being psychologically destroyed, which what has been happening to me. I have been in Las Vegas, Nevada since 2021. Some of this isolation comes from not being able to talk in detail about these topics in person with other people.
Professor Leonard, today i aced my multivariable calculus course ALL because of you. I wish i could meet you and personally thank you. You don't need to be able to fly or shoot lasers from your eyes to be superman.
I am learning this subject again like I did in the 1990's because I believe it will help me become a better problem solver, and be more creative. I wish I could meet someone in person to discuss this subject in Las Vegas, Nevada. My experience is psychologically destroying me. I do not know why that is happening. Maybe it is a combination of factors. Actually, all levels of Calculus as well as Differential Equations were required courses to get a BS in mechanical engineering from the University of Arizona. I think it is the same way at all colleges. I actually really never got to do engineering and scientific work. That has been part of my psychological destruction. I seem to be alone in failure. The misery is always quite extraordinary. I look back with nostalgia a little bit at being in a library with other students talking about these problems.
14:38 -> changing coordinates to different systems (rect to cyl) 32:11 -> spherical explanation 46:10 -> spherical and rectangular coordinate translation 1:04:00 -> spherical to cylindrical coordinate translation 1:16:40 EQUATIONS in different systems translations
I just started studying electrical engineering and would like to thank you from the bottom of my heart for these videos. You really do make a difference :)
Eloth hello there any advice for your fellow freshman electrical engineering student 🙈 I would really appreciate some tips that would help me for this major
This was absolutely amazing. I came into the video having no clue what this topic was about and left feeling pretty comfortable. You're an amazing lecturer and thank you so much for uploading this.
I'm taking Calculus II right now via mail correspondence at LSU. They cover chapters 11.6 and 11.7 of your book (Larson Calculus vol 6 or 7?) in calc II. I want to thank you for making these Calc III videos, they were right on time and I have learned so much from them. I basically ignore the instruction book they sent me and watch these videos to learn the material. I don't know where I would be without them thanks again!!
I like how Professor Leonard actually erases every single dot when he erases the board. I hate when teachers leave ugly dots and lines all over the place, so it is strangely relieving to see him clear the board the proper way.
I had two calculus 3 teachers just give us the equations and not explain where they came from. Thank you for constructing them so that we really understand them!
One of the most organized, rational, and easy to understand...Thanks from Pakistan... such a nice preparation of lecture to make the stuff easy for his students ...hats off Professor Leonard
Professor Leonard, thank you for another off the charts video/lecture on Using Cylindrical and Spherical Coordinates in Calculus Three. I really enjoy this topic from start to finish. I finally understand the different coordinate systems and how to convert from one system to another.
Thank you so much for making this videos available online. If you could please allow your fans to donate that would make me very happy because honestly i would not have made it through calculus without you. If it is a link please point me to it. At least donating something to you would not make me feel bad. Thanks professor you are the best.
Like the "r is not the distance from the origin to the point... It's to the projection on x-y plane." This makes the whole instruction very clear and intuitive as how polar coordinate is related to the cylindrical coordinate.
A fantastic professor. Good job! Love the videos! I have always been able to execute the operations in Calc 3, but have never been able to visualize the concepts so clearly. I'm using this video course as a review for Engineering school and it is fantastic. Far better than the Calc 3 course I took.
In physics, you will often run into polar coordinates where both the angle and the _radius_ are variables - those equations are pretty interesting, I recommend that you try to derive them by starting with the position vector *r* = r ⋅ *eᵣ.* (or just refer to a Dynamics textbook, those books always derive those equations).
Watching this to prepare for my Advance Calculus repeat module. OMG, WTH my lecturer taught us. I didn't understand a bit in her lecture. But after watch this, things became crystal clear. fog disappearing. thank you so much, sir. best explanation. the way you teach, I can draw it in my mind. Simply WOW...
My teacher skipped this section when I went through calc 3, but now its being heavily used in my gravity and magnetic exploration class. Thanks for the help getting caught up!
This is the third vid I have watched from you. I am taking calc 3 next semester (starts in first week of Feb) but you really helped me prepare for the course! I will revisit you if I have any problems. I am now given odds of -99999 to finish with grade A in calc 3 thanks to you!
How can I perform a transformation where my math teacher is sent to some parallel universe and you become my teacher, so I can finally enjoy calc 3 instead of crying over it?
Im a cnc machinist, i never had a trigonometry lesson in my life. I use polar to Cartesian coordinates all day to calculate positions and tool paths. I don't know anything about solving equations and stuff so every other video was useless to me BUT, this here proofed to me two facts: 1 i figure out my self how to actually calculate coordinates on a sphere with no external aids, just my own exp with basic trigonometry. 2 I should've been studying when it was time! If you create a loop that iterates through 360 degrees by an arbitrary increment and plug the cos and sin functions to the two variables that contains the angles of the spherical system you can draw (or mill in my case) the projection of a circle on a spherical surface 🤯
arctan(-sqrt3) does give-pi/3 which is the same as +5pi/3. arctan on a calculator gives only one answer, but there are two answers, 5 pi/3 - pi is the other. Only one answer is correct for this problem, it has to be in the correct octant, so 2pi/3 is the correct answer
I watch these lectures over and over for several reasons: I am reviewing all of my Calculus to understand what I was so rushed for my degree I did not have time to think about what I was learning and because Professor Leonard is the instructor I wish I'd had. The distance (in spherical) is pronounced, "row," but spelled, "rho."
I have always thought that there is something hugely satisfying about extending graphs from 2D to 3D. Those 3D pictures look great, _especially_ when you graph them in different colours.
Bro, do you even lift? Going to watch your videos to refresh me on calc 3. It took me a long time to find a great Calc teacher at my school, and I found out he transfered to another university. I think it was something he always wanted after getting his PHD in math.
At time 49:53, I don't understand how you got a positive (root 2)/2, I keep getting negative. for Sin (3(pi))/2. There was a question similar where I got a negative answer but got a positive one. I am trying to figure out if my trig was wrong or something. (Edit literally a minute later: Scratch that, just found out I was looking at Cos and not sin. Haha. For those who had a similar question tho.)
best teacher everrrr. Ever since I know you, when I got problem with my Calculus, I've never look for others teacher cause every time I watch your vid, it helps me a lot!
Professor Leonard: Stop writing for a second this is important Me at home: *stops writing and pays attention* I think my next tattoo is going to be a unit circle
@@buddydog1956 yo, if you are on a test and the teacher see it. Are they gonna make you slice it off since it’s technically notes? Just imagine the teacher’s reaction lol.
I suggest that since "r" in cylindrical coords is usually a radius then in sphericals the PROJECTION of rho (radius) on the x-y plane not be called "r" (which term was used for radius) but another term e.g "q" = rho sin phi (where "q" is clearly not confused with radius, as "r" might be). Angle theta stays between X and "q" just like angle theta between X and "r" in cylindricals.
I wish u were my teacher! Thank u so much for your videos if it werent for u I would not havs gotten an A in my calc 2 class! Keep up what ur doing! You are awesome
That will become unnecessarily difficult to do because we have two angles here. We will have more than two ways to write coordinates of one point and it will be hard to manage.
That's odd. I was introduced to spherical coordinates once triple integrals were already established. Feels a little incomplete without the volume element. I'll be ready to watch this once more once I'm out of calc 1. Thanks so much, Leonard.
+Lar M Calculus 4 is commonly considered to be Differential Equations. If you want a good place to study that stuff then I can highly recommend the site "Paul's Online Math Notes".
Oh actually Professor Leonard actually now has a "Differential Equations" playlist available, lol. I think that he is still working on it, but he has uploaded enough material to most likely be finished with it by the time you have watched all those videos.
Professor Leonard. First off thank you, your content is amazing. Trival question but would you not be converting from rectangular to polar and not the opposite? I could be seeing this wrong but I thought you are starting in the Cartesian (retangular plane) and going to polar. If so wouldn't your arrows that imply transformation point in the opposite direction?
In a sphere all radii are equal in length. If r and rho are radii then they should be equal in length. If r is not a radius then it should be called something other than r. However one can allow r to be a radius but then r is NOT rho sin phi. Nevertheless one can still obtain the final equations for X and Y as correctly given.
You have to write bigger on white boards. My laptop is down. I cannot see the math examples ans script that you are doing on my cell phone. I only have a minor in math from VCU; trying to upgrade.
"Raise your hands if you understand"
(°-°)/
Gets me every time. The most common trait of amazing teachers is engagment.
Prof. Leonard gets an A+
He gets O! 💝
O aka outstanding
Beyond A+
So I'm not the only one who nods my head every time he asks if we're good
lol
He teaches all levels of the Calculus in a good geometrical way. His and other videos on economics, physiology, Spanish, Chinese, and electronics are a good escape from isolation and being psychologically destroyed, which what has been happening to me. I have been in Las Vegas, Nevada since 2021. Some of this isolation comes from not being able to talk in detail about these topics in person with other people.
Professor Leonard, today i aced my multivariable calculus course ALL because of you. I wish i could meet you and personally thank you.
You don't need to be able to fly or shoot lasers from your eyes to be superman.
I am learning this subject again like I did in the 1990's because I believe it will help me become a better problem solver, and be more creative. I wish I could meet someone in person to discuss this subject in Las Vegas, Nevada. My experience is psychologically destroying me. I do not know why that is happening. Maybe it is a combination of factors. Actually, all levels of Calculus as well as Differential Equations were required courses to get a BS in mechanical engineering from the University of Arizona. I think it is the same way at all colleges. I actually really never got to do engineering and scientific work. That has been part of my psychological destruction. I seem to be alone in failure. The misery is always quite extraordinary. I look back with nostalgia a little bit at being in a library with other students talking about these problems.
You're the best Calculus teacher I've ever learned from. Clear and thorough explanations. Thank you for these vids.
very nice
calculus knowledge is stored in the arms
Leonard's two extra brains
when he say's "I need YOUR attention up here at the board" he is talking to ME
14:38 -> changing coordinates to different systems (rect to cyl)
32:11 -> spherical explanation
46:10 -> spherical and rectangular coordinate translation
1:04:00 -> spherical to cylindrical coordinate translation
1:16:40 EQUATIONS in different systems translations
I just started studying electrical engineering and would like to thank you from the bottom of my heart for these videos. You really do make a difference :)
Eloth hello there any advice for your fellow freshman electrical engineering student 🙈 I would really appreciate some tips that would help me for this major
yo
I'm studying for my calc midterm in college and I was zoning out exactly when you said listen up this is important. How crazy!
You have inspired me to train calculus and arms
indeed
This was absolutely amazing. I came into the video having no clue what this topic was about and left feeling pretty comfortable.
You're an amazing lecturer and thank you so much for uploading this.
No amount of notes or videos can top what I’ve learned from your video. Thank you for illuminating this topic.
You don't know how much help we are getting from you professor Leonard, god bless you :)
I'm taking Calculus II right now via mail correspondence at LSU. They cover chapters 11.6 and 11.7 of your book (Larson Calculus vol 6 or 7?) in calc II. I want to thank you for making these Calc III videos, they were right on time and I have learned so much from them. I basically ignore the instruction book they sent me and watch these videos to learn the material. I don't know where I would be without them thanks again!!
I go to bed listening to this guy ~ he's incredible !
I like how Professor Leonard actually erases every single dot when he erases the board.
I hate when teachers leave ugly dots and lines all over the place, so it is strangely relieving to see him clear the board the proper way.
I had two calculus 3 teachers just give us the equations and not explain where they came from. Thank you for constructing them so that we really understand them!
One of the most organized, rational, and easy to understand...Thanks from Pakistan... such a nice preparation of lecture to make the stuff easy for his students ...hats off Professor Leonard
Great example of a good teacher. Explains the concepts simply
I'm taking my calc III final exam today. Watching videos to review. So far this video gave me a clearer understanding. Thanks!!!!
How was it? How do you feel now that it's already been 7 years
Professor Leonard, thank you for another off the charts video/lecture on Using Cylindrical and Spherical Coordinates in Calculus Three. I really enjoy this topic from start to finish. I finally understand the different coordinate systems and how to convert from one system to another.
Thank you so much for making this videos available online. If you could please allow your fans to donate that would make me very happy because honestly i would not have made it through calculus without you. If it is a link please point me to it. At least donating something to you would not make me feel bad. Thanks professor you are the best.
I really wish Professor Leonard taught every subject. Great teachers are hard to find.
When I took Calc 3 we never had this lesson. Still aced the class thanks to the Leonard!
Like the "r is not the distance from the origin to the point... It's to the projection on x-y plane." This makes the whole instruction very clear and intuitive as how polar coordinate is related to the cylindrical coordinate.
where were you all my life... thanks lots and lots...I'm gonna do more than I would due to these lessons!!!
A fantastic professor. Good job! Love the videos! I have always been able to execute the operations in Calc 3, but have never been able to visualize the concepts so clearly. I'm using this video course as a review for Engineering school and it is fantastic. Far better than the Calc 3 course I took.
this teacher is great! I haven't learned under a teacher like this ever... these students shouldn't take him for granted
In physics, you will often run into polar coordinates where both the angle and the _radius_ are variables - those equations are pretty interesting, I recommend that you try to derive them by starting with the position vector *r* = r ⋅ *eᵣ.* (or just refer to a Dynamics textbook, those books always derive those equations).
Watching this to prepare for my Advance Calculus repeat module. OMG, WTH my lecturer taught us. I didn't understand a bit in her lecture. But after watch this, things became crystal clear. fog disappearing. thank you so much, sir. best explanation. the way you teach, I can draw it in my mind. Simply WOW...
My teacher skipped this section when I went through calc 3, but now its being heavily used in my gravity and magnetic exploration class. Thanks for the help getting caught up!
@37:07 Spherical Coordinate System Conversion proof. Why we do the x=(rho)sin(phi)cos(theata) and Y respectively. I wont forget this now.
This is the most underrated channel for real.
Professor you've taught me all of calculus until now. Thank you sir. I'm still in grade 12 lol.
You're saving my multivar grade right now.
This is the third vid I have watched from you. I am taking calc 3 next semester (starts in first week of Feb) but you really helped me prepare for the course! I will revisit you if I have any problems.
I am now given odds of -99999 to finish with grade A in calc 3 thanks to you!
Spherical Coordinates start from 31:33
How can I perform a transformation where my math teacher is sent to some parallel universe and you become my teacher, so I can finally enjoy calc 3 instead of crying over it?
There is no teacher without students.
Im a cnc machinist, i never had a trigonometry lesson in my life. I use polar to Cartesian coordinates all day to calculate positions and tool paths. I don't know anything about solving equations and stuff so every other video was useless to me BUT, this here proofed to me two facts: 1 i figure out my self how to actually calculate coordinates on a sphere with no external aids, just my own exp with basic trigonometry. 2 I should've been studying when it was time! If you create a loop that iterates through 360 degrees by an arbitrary increment and plug the cos and sin functions to the two variables that contains the angles of the spherical system you can draw (or mill in my case) the projection of a circle on a spherical surface 🤯
Professor have big muscles 💪
Greetings from Brazil, Prof. Leonard. You are the best!
Thoroughly impressed. Thank you for posting these videos!
At 57:37, I believe the answer the student mentioned is wrong. arctan( -sqrt3) gives -pi/3 and not over 6. So would the final theta be 4/3pi?
arctan(-sqrt3) does give-pi/3 which is the same as +5pi/3. arctan on a calculator gives only one answer, but there are two answers, 5 pi/3 - pi is the other. Only one answer is correct for this problem, it has to be in the correct octant, so 2pi/3 is the correct answer
the best lecture for learning the coordinates
thanks prof. leonard
Hi, Professor. I must tell you, your lectures are outstanding. But, did you cover parametrization of surfaces ?
I watch these lectures over and over for several reasons: I am reviewing all of my Calculus to understand what I was so rushed for my degree I did not have time to think about what I was learning and because Professor Leonard is the instructor I wish I'd had. The distance (in spherical) is pronounced, "row," but spelled, "rho."
I have always thought that there is something hugely satisfying about extending graphs from 2D to 3D.
Those 3D pictures look great, _especially_ when you graph them in different colours.
Ignore:
31:20 start of spherical.
The best reacher of Mathematics on the planet 😍
@@Hasan-wz1nd
What the hell is your problem, dude?
Grow up.
This guy is fantastic! What a great teacher. Thank you Dr. Leonard.
Bro, do you even lift?
Going to watch your videos to refresh me on calc 3. It took me a long time to find a great Calc teacher at my school, and I found out he transfered to another university. I think it was something he always wanted after getting his PHD in math.
At time 49:53, I don't understand how you got a positive (root 2)/2, I keep getting negative. for Sin (3(pi))/2. There was a question similar where I got a negative answer but got a positive one. I am trying to figure out if my trig was wrong or something. (Edit literally a minute later: Scratch that, just found out I was looking at Cos and not sin. Haha. For those who had a similar question tho.)
Unit circle tattoo, haha. I need one of those.
best teacher everrrr. Ever since I know you, when I got problem with my Calculus, I've never look for others teacher cause every time I watch your vid, it helps me a lot!
Thank you Professor!
Professor Leonard: Stop writing for a second this is important
Me at home: *stops writing and pays attention*
I think my next tattoo is going to be a unit circle
LOL! However what would be cooler is a sphere displaying your spherical coordinates, rho, theta and phi and labll which each represent ~
@@buddydog1956 yo, if you are on a test and the teacher see it. Are they gonna make you slice it off since it’s technically notes? Just imagine the teacher’s reaction lol.
Great Video
Spherical starts at 31:20
Learned a lot watching only 5 min of this video :o
Understood this after a long time. Thanks a lottttttt
5 minutes in and this guy is now my math dude! Professor Leonard is ice cold; sub zero.
at 30:00 you show (2,7pi/4,4) but could this be (2,-pi/4,4)?
Theta should be between 0 and 2pi
😂😂I loved the vector because of you
Dhanyavaad gurujii 🌹🌹🌹🌹🌹🌹🙏🙏🙏🙏🙏🙏
I suggest that since "r" in cylindrical coords is usually a radius then in sphericals the PROJECTION of rho (radius) on the x-y plane not be called "r" (which term was used for radius) but another term e.g "q" = rho sin phi (where "q" is clearly not confused with radius, as "r" might be).
Angle theta stays between X and "q" just like angle theta between X and "r" in cylindricals.
What is the name of the textbook that you and your students use for this class?
You are a lifesaver❤
nice work
58:48 We don't have time to F around with this
I wish u were my teacher! Thank u so much for your videos if it werent for u I would not havs gotten an A in my calc 2 class! Keep up what ur doing! You are awesome
52:00 - damn right: much better to understand. Might be a market for a little cardboard/3D printable model that show rho,theta,x,y,z more clearly.
besssssssssssssssssssssssssssssssssssssssssssssssst teacher i have ever seen
extremely useful information.....
37:00 why can't row be negaative and I just flip it like we did for the for the radius?
That will become unnecessarily difficult to do because we have two angles here. We will have more than two ways to write coordinates of one point and it will be hard to manage.
if you want to learn cal3, you should watch professor Leonard's class.
he's very good...
nice deployment of quadrants and octants
That's odd. I was introduced to spherical coordinates once triple integrals were already established. Feels a little incomplete without the volume element.
I'll be ready to watch this once more once I'm out of calc 1. Thanks so much, Leonard.
I am already looking forward to Calculus 4 , 5 and 6 !
+Lar M
Calculus 4 is commonly considered to be Differential Equations.
If you want a good place to study that stuff then I can highly recommend the site "Paul's Online Math Notes".
Oh actually Professor Leonard actually now has a "Differential Equations" playlist available, lol.
I think that he is still working on it, but he has uploaded enough material to most likely be finished with it by the time you have watched all those videos.
Thankkkkks 😊
You are the most awesome mathematics professor! It is very helpful for me! Thanks you so much for your precious help!
Professor Leonard. First off thank you, your content is amazing. Trival question but would you not be converting from rectangular to polar and not the opposite? I could be seeing this wrong but I thought you are starting in the Cartesian (retangular plane) and going to polar. If so wouldn't your arrows that imply transformation point in the opposite direction?
I wish he was my professor..
Good explaination
thankyou and God bless you
In a sphere all radii are equal in length. If r and rho are radii then they should be equal in length. If r is not a radius then it should be called something other than r. However one can allow r to be a radius but then r is NOT rho sin phi. Nevertheless one can still obtain the final equations for X and Y as correctly given.
1:34 how can x = 2 be a plane? I thought a plane had to have extension in two dimensions? Thanks :)
Thank you so much! You are an amazing teacher!!!!
spherical, phi - 34:35
the test is next week ......we'll see
How'd it go
How'd it go
Rho is spelled Rho. Thank you for the free videos!!!
Excellent!
By any chance do you do differential equations videos ?
THANK YOU 👌🏻🙂💙🙂👌🏻
What textbook do you use? Thanks
my text is Engineering Electomagnetics and Waves SECOND EDIION
please just tell me what's your horoscope sign?
Stupid?
Cosine(φ)
Greetings,
on which book your course / tutorial is based ?
i would also like to know
@@AnthonyMoodypretty sure you wouldn’t want to know anymore but its calculus by James Stewart
@@Abdullah-kn5qu hahaha thanks
@@Abdullah-kn5qu yeah i have already graduated by now 😁
typo at 32:37 . it's rho, not row.
you r amazing!! have been struggling with this concept but now I got it :D thank you
You have to write bigger on white boards. My laptop is down. I cannot see the math examples ans script that you are doing on my cell phone. I only have a minor in math from VCU; trying to upgrade.
Not me raising my hand when he says "Does this make sense to you"
thank you very much ! :)
x , y , and z. Now the fourth co-ordinate 't' (time) !