That moment when you get an 'A' in calculus and your university takes all the credit of being a great institution but all you did was skip class and watch Professor Leonard all day. Lol
I completed a BS in mechanical engineering from the University of Arizona in 1995. Otherwise my life has been such that I have never been able to do any engineering work or scientific work. It puts me in constant misery.
Thank you! I had MIT professors in my mind. If you skip steps, you turn it to black magic. The worst part is that they publish the videos, making you waste SO MUCH TIME.
I have never seen your approach of teaching before. You spend twice as much time on explaining things compared to my own lecturers. Your examples are good! I usually find it a hard time to understand things, but once I understand, I learn. You have facilitated that process for me. Many thanks Prof. Leonard Superman. Regards from Sweden.
Wow I'm almost through his entire Calc III playlist. Its amazing looking back at all the notes I've taken during his lectures, the time that has passed, and the material that I have learned. I'm surprised organizations haven't reached out and donated to Leonard the way they did with Salmon Khan. He really explains the material in a concise way that has educated so many students.
I dont even attend my Calc 3 class, its pointless. I just study from your vids. So technically I pay my proffesor to just give me the exam, cuz all the knowledge comes from Mighty Leonard
I’ve had two great professors for calculus 1&2, however calculus 3 is a whole different story. I have finals in two weeks, thinking back, I could have saved time and watched prof Leonard vids instead.
I stopped paying attention to anything to do with my class after i found his videos. It was about 1 week into the semester and i haven't viewed course content since.
I watched this playlist instead and skipped all my classes to learn this course. Now, 1 year later im using the same videos to brush up my vector calculus before starting a course in electrodynamics. Real legend!
Watched this guy when I was in calc 3. Watching him again for a upper-division mathematical methods of physics class! Thanks Prof. Leonard! Truly amazing!
This is why I donate to his Patreon. A quality professor needs to be rewarded for the great work they bring into society and helping people understand complex concepts.
0:00 Explanation of line integrals over conservative vector fields 20:58 Example 1 40:24 Example 2 (important shortcut) 59:50 Example 3 1:11:30 Example 4 1:23:55 Example 5 (shortcut in 3-space) 1:34:42 Example 6
This guy is a beast. He has the knowledge of a great math teacher, and the ability to convey his thoughts like a psychologist. What a beast that our world doesn't deserve. I ABSOLUTELY HATE watching long videos but watching yours; every minute of it is worth it. Man, thanks. And for those who struggle with this, try using the IDAHO tactic that I thought of: Integrate the i component, DifferentiAte what you've just integrated, notice HOw your answer has a g'(y) that could be put equals to the j component, set it up together and find what g(y) is by integrating again, and now it's really easy; you just gotta plug in the points the question has given to you and you're done. GG.
One thing that I really like about professor Leonard's lectures is that they always feel like big events. They are almost like parties sometimes, where he fools around with the students and makes jokes and stuff, and this makes everything a lot more interesting.
Your videos should definitely be translated into as many languages as possible. I wish professors at my university had only a fraction of the passion for teaching that you have.
I seen a UA-cam add on this video trying to force me to pay for 3 professors to do what one professor (Professor Leonard) does I'm offended lol. This man has done more for me than all my math teachers ever. He's a super hero
Life Changing experience. I studied Calculus 3 from you Sir. Thanks. Idk for what reason, my school jus let us do up to Calculus 2 with some double integrals. Glad I know this stuff which is very vital in my field of study. God Bleshyaaaaa btw, you are so kind and friendly even on the videos. It's hard to not stay focused. Lucky students you got over there!
Thank you AGAIN, Professor Leonard! ANOTHER "A"!!! This time in Calculus III!!! I appreciate you SO MUCH! Onward to your Differential Equations playlist (on #9 now)!
Professor Leonard ,thank you for another awesome video/lecture on Line Integrals on Conservative Vector Fields in Calculus Three. In this case, the conservative Vector Fields are easy to calculate from start to finish. For f(x,y,z), the calculation is lengthy and problematic. The probability of making an error increases with more calculation.
@@ProfessorLeonard omg i was just watching your last video from calc 3, hopefully you will be back with your new video classes as soon as you can! Thank you, will be waiting for them😊! P.S I understand calculus 3 thanks to you, Professor! Appreciate your work!
You are absolutely amazing. Im studying for my final and at every step of the way I can just go back to your vids and refresh my memory (or entirely learn a whole new thing hours before the finals.. whoops ).. Thank you so much for posting these
I have a non-cumulative final coming up (because of ZoomSchool), and I came across Professor Leonard while being frustrated taking notes from the book. I've watched 3 hours of your lecturing tonight on this material, and I believe I can get that 93 on my final to get by with a B in the class. I will definitely be back here to leave a comment if I end up with a B by the end of the semester. I must transfer so I can have you as a professor!
math2011 has been completed on 4/18/2022 but last day of semester is 5/11/2022! Thanks Prof Leonard for making me finish and understand the syllabus 21 days before the rest of the students! Watch me crush the final on 5/27!
You know Prof.Leonard is good when; my prof sends out an email letting us know the next lecture is up and attaches Prof.Leonards video along in the email lol.
For the last example, you can take the integral of the partial w.r.t. y instead of the partial w.r.t x like how we've always been doing. Then the integral gives you (something) + g(x,z). But if you take the partials of the (something), it gives you back the original function, so, by Prof Leonard's trick, you can thus say that g(x,z)=0. Then you just take the (something), sub in the coords and you get 2pi+1
Professor Leonard you are by far better than any of my calculus professors I have ever taken. Also is there like 4 students in your class? I only ever hear at most 4 of them lol
I am a b.tech student in India from one of the top most prestigious engineering colleges and these calcis 3 Videos have helped me a lot during this 1st sem. as we are taught Engineering Mathematics -1 and Your explanation skills are awesome and divine level which have helped me to score vey good marks in my University exams , Thank You So much Sir, Love from India🤩
6:54 let this be known that at this point, I made the connection between the FTOC and gradients/line integrals for the first time. I feel quite happy right now. It seems so obvious, but aren't the best things in math like that?
@@david-yt4oo The silence from these students amazes me. I always hear that Americans think that we Swedes are much more reserved than they are, and not even my college class (which almost exclusively consists of Swedish students) is this quiet - there will always be at least 2-3 persons who say _something,_ even if there is only like 15-20 of us in some given class.
Just found this with 6 days before the test on chapter 15 and final exam is still left. Seeing people's success stories, I wonder: will Professor Leonard help me pull up my grade to an A (or at least A-)? I will update after I get the grade!
In the first example, the integral was zero in a conservative field , not because the end points at x and y were the same for the two points but because the functio had the same vales at those two points. A simple one dimentional analogy if the function cos theta, the integral is zreo between o and pi because sine pi and sine zero both have the same values; name zero.
You're right in thing that because it's the same technique. The nomenclature is slightly different, but the necessary conditions and the results are the same.
I was a bit confused at 33:00 when Prof Leonard mentions that no work is done even though the particle was supposed to move from (0,0) to (-1,1). This path does not look like a round trip.
i was thinking the same thing. I think he's just trying to say there are times when work done can be 0. and if you move in a complete circle work will ALWAYS be 0. I think he stresses this because its important in greens theorem later in the chapter. But ive also learned from physics that if motion is perpendicular to force no work is done either, this may be an example of that. in other words the force field here would be everywhere perpendicular to the curve/line to produce 0 work.
An example of a situation where no physics work is done is if one were to walk across the top of a hill to a height at the same elevation. As you walk from your starting elevation to the top of the hill, you are doing positive work against the gravitational field. Then, when you walk down the other side of the hill to an elevation that is the same as your starting height, you will experience negative work the same magnitude as the work you did to go to the top of the hill. The sum of the work to the top of the hill plus the work recovered as you walk down the hill will equal zero. Additionally, it won't matter what exact path you take horizontally as long as your starting and ending altitudes are the same.
I had a question, you mentioned that if the mix partials are equal then the vector field is conservative and there exists a potential function. But I'm confused because in DE when mix partials are not equal, we would make them exact and find the potential function. Can't we do the same here ?
That moment when you get an 'A' in calculus and your university takes all the credit of being a great institution but all you did was skip class and watch Professor Leonard all day. Lol
fucking hell this is mega relate
yup
Itachi speaks facts
2 years later and still true. Literally paying my school just for the privilege of being evaluated by an accredited institution.
Iioiiplo
Once I get my Mechanical Engineering degree and start making money, I will donate money to this man. Best teacher I've never had
Same
FR!
Im also pursuing Mechanical Engineering. From which University are you pursuing your degree?
Had the same exact thought lmao
I completed a BS in mechanical engineering from the University of Arizona in 1995. Otherwise my life has been such that I have never been able to do any engineering work or scientific work. It puts me in constant misery.
Professor Leonard is the best online Math instructor I've came across!
This guy tells it like it is. No shortcuts or black magic like the MIT guys. Thank you very much!
the fact that MIT students NEED to watch his videos bc the school can't hire good professors is just downright depressing...
@@charlieherman6711 they hire professors based on their research, not so much their teaching skills.
Thank you! I had MIT professors in my mind. If you skip steps, you turn it to black magic. The worst part is that they publish the videos, making you waste SO MUCH TIME.
He teaches Calc the way you wish it would be taught by your professor.
My professor might very well be teaching it this way. I just don't speak Romanian.
Professor Leonard is my Professor! :)
So true
@@evank7858why is it that universities choose professors with the thickest accents to teach the hardest courses?
I have never seen your approach of teaching before. You spend twice as much time on explaining things compared to my own lecturers. Your examples are good! I usually find it a hard time to understand things, but once I understand, I learn. You have facilitated that process for me.
Many thanks Prof. Leonard Superman.
Regards from Sweden.
Haha coolt, jag är också från Sverige. 8-)
I think he actually understands the work. Our lecturers had the same lecturers (not a Prof Leondard!)
Wow I'm almost through his entire Calc III playlist. Its amazing looking back at all the notes I've taken during his lectures, the time that has passed, and the material that I have learned. I'm surprised organizations haven't reached out and donated to Leonard the way they did with Salmon Khan. He really explains the material in a concise way that has educated so many students.
exactly!!
I dont even attend my Calc 3 class, its pointless. I just study from your vids.
So technically I pay my proffesor to just give me the exam, cuz all the knowledge comes from Mighty Leonard
I’ve had two great professors for calculus 1&2, however calculus 3 is a whole different story. I have finals in two weeks, thinking back, I could have saved time and watched prof Leonard vids instead.
My calc 3 teacher literally spent all of 1 example (sometimes not even that) on an entire section at times. Professor Leonard saved my grade.
Same
I stopped paying attention to anything to do with my class after i found his videos. It was about 1 week into the semester and i haven't viewed course content since.
Professor i would like to say THANK YOU i got An (A) in Cal 3
Regards 💐💐
I watched this playlist instead and skipped all my classes to learn this course. Now, 1 year later im using the same videos to brush up my vector calculus before starting a course in electrodynamics. Real legend!
Watched this guy when I was in calc 3. Watching him again for a upper-division mathematical methods of physics class! Thanks Prof. Leonard! Truly amazing!
thank you ..genuinely I thank u for reaching out to the larger audience. Your efforts are benefiting people thousands of miles away from your homeland
This is why I donate to his Patreon. A quality professor needs to be rewarded for the great work they bring into society and helping people understand complex concepts.
with the pandemic and my university moving online, This man has saved my engineering career. i owe him a beer
How enthusiastic, authentic and talented you are professor! Thank you very much! Much Respect!
Thanks for posting these videos! I love how you put an emphasis on understanding the material, and linking things together, not simply computations.
0:00 Explanation of line integrals over conservative vector fields
20:58 Example 1
40:24 Example 2 (important shortcut)
59:50 Example 3
1:11:30 Example 4
1:23:55 Example 5 (shortcut in 3-space)
1:34:42 Example 6
I just received my final grade on calculus 3 and it's an 'A'.
Thank you Professor Leonard for your amazing explanation.
This guy is a beast. He has the knowledge of a great math teacher, and the ability to convey his thoughts like a psychologist. What a beast that our world doesn't deserve. I ABSOLUTELY HATE watching long videos but watching yours; every minute of it is worth it. Man, thanks.
And for those who struggle with this, try using the IDAHO tactic that I thought of: Integrate the i component, DifferentiAte what you've just integrated, notice HOw your answer has a g'(y) that could be put equals to the j component, set it up together and find what g(y) is by integrating again, and now it's really easy; you just gotta plug in the points the question has given to you and you're done. GG.
One thing that I really like about professor Leonard's lectures is that they always feel like big events.
They are almost like parties sometimes, where he fools around with the students and makes jokes and stuff, and this makes everything a lot more interesting.
i went from a 45 to a 84 in Calc III because of you. I have my final coming up this week, and i really hope i do well!! Thank you Leonard!!
howd it go
@nidhishsharma9471 bro he is noŵ doing his Msc, ✅️
literally been winning all semester with this. thank you, Professor Leonard
Hope I'm not the only one who also raises their hand when he asks if everyone understands
till now I thought , I was the weird one. But Good to know not alone now:)
Your videos should definitely be translated into as many languages as possible. I wish professors at my university had only a fraction of the passion for teaching that you have.
Calculus 3 is super "out there" and you have a great way of describing it! Thank you for these videos
I seen a UA-cam add on this video trying to force me to pay for 3 professors to do what one professor (Professor Leonard) does I'm offended lol. This man has done more for me than all my math teachers ever. He's a super hero
i figure if i just memorize his lessons word for word i could con my way into teaching cal 3 at a univeristy
I really liked your comment. Lol !
I'm studying maths to become a professor myself and I constantly think this, lol. Leonard is GODLIKE though.
Yo that was my idea LMFAO
@@eduardorivera508 you have calculus when you study math ?
What a fabulous lecturer you are, Doctor Lenoard! You might very well have saved my entire Masters degree in technology!
I swear you always makes it easy . which makes u z smartest plus the best Clac teacher i have ever known.
20:59 - Example 1
33:09 - Example 2
I have to say he is best in explaining very complicated stuff in amazingly simple way.....
Life Changing experience. I studied Calculus 3 from you Sir. Thanks. Idk for what reason, my school jus let us do up to Calculus 2 with some double integrals. Glad I know this stuff which is very vital in my field of study.
God Bleshyaaaaa
btw, you are so kind and friendly even on the videos. It's hard to not stay focused. Lucky students you got over there!
These lectures are the only reason I'm not failing calc 3 in zoom academy right now
Thank you AGAIN, Professor Leonard! ANOTHER "A"!!! This time in Calculus III!!! I appreciate you SO MUCH! Onward to your Differential Equations playlist (on #9 now)!
Teachers like this are so valuable
These videos are superbly done! I'm using these to refresh my vector calculus skills prior to taking electrodynamics in the Fall. Thank you!
thank you for all those videos! You literaly are saving me from disaster. I love yours videos. They are so easy to follow. I am big fan of you!
Professor Leonard ,thank you for another awesome video/lecture on Line Integrals on Conservative Vector Fields in Calculus Three. In this case, the conservative Vector Fields are easy to calculate from start to finish. For f(x,y,z), the calculation is lengthy and problematic. The probability of making an error increases with more calculation.
Thank you for taking the time to make these videos. Your videos have helped me tremendously.
He is the best! Hope you make videos for linear algebra🙂
Hi! I am planning on it, but it will take awhile :)
@@ProfessorLeonard omg i was just watching your last video from calc 3, hopefully you will be back with your new video classes as soon as you can! Thank you, will be waiting for them😊!
P.S I understand calculus 3 thanks to you, Professor! Appreciate your work!
you are simply best professor....cleared so many doubts...thank you...
You are absolutely amazing. Im studying for my final and at every step of the way I can just go back to your vids and refresh my memory (or entirely learn a whole new thing hours before the finals.. whoops ).. Thank you so much for posting these
This was great. Finding those partial antiderivatives is so much fun.
I have a non-cumulative final coming up (because of ZoomSchool), and I came across Professor Leonard while being frustrated taking notes from the book. I've watched 3 hours of your lecturing tonight on this material, and I believe I can get that 93 on my final to get by with a B in the class. I will definitely be back here to leave a comment if I end up with a B by the end of the semester. I must transfer so I can have you as a professor!
Well?
My biggest regret, not knowing this legend existed when I started my calc 3 course :((( Saved me for the exams tho
You're saving me from retaking Calculus 3 Professor Leonard. Thank you
Professor Leonard, you make math fun to learn. THANKS !
math2011 has been completed on 4/18/2022 but last day of semester is 5/11/2022!
Thanks Prof Leonard for making me finish and understand the syllabus 21 days before the rest of the students! Watch me crush the final on 5/27!
I've said it a couple times now, and sir you are a god. Thank you so much!
You made my exams a piece of cake Professor .
Thank you very much
Great teaching, I am your regular lesoner.
Sometimes when he says "show hands if you're okay with that one" I raise my hand... it's like I'm there. 😆
fundamental theorem of line integrals was my favorite theorem
Professor Leonard sir,thank you again & again... It's an amazing class..
44:48 "Not the Donald Trump sort of conservative" haha Professor Leonard thanks for the laughs throughout these videos
Saving my butt since calc 1
1:30:32 "This function contains no other y's, otherwise we'd have y's. You know why?" I died
got a 92 on chp 15 test!!! thank you professor leonard
wooww.. my teacher of calculas 3 made me hate math.. now im almost in love with it.. thank you Leonard for this great teaching and explanation
THIS IS THE FIRST EVER UA-cam VIDEO IVE COMMENTED ON BUT I HAD TO BECAUSE OF THE MOMENT THAT IT ALL CLICKED FOR ME IN THIS VIDEO THANK YOU
Pedagogical masterclass from Professor Leonard
Thank you Professor Leonard.
Wish I would have had you teach my class for Calc 3. Understanding everything much better now.
Thank you again Professor Leonard!!
In a split second during 33:08, Professor Leonard went home, slept, and came back.
Thank you for another marvelous lecture!
You know Prof.Leonard is good when; my prof sends out an email letting us know the next lecture is up and attaches Prof.Leonards video along in the email lol.
remember fellas....
C for curl.... and C for cross product
D fro Divergence .... and D for Dot product
Hi professor!!! Will we see any Linear Algebra or DE videos soon?
For the last example, you can take the integral of the partial w.r.t. y instead of the partial w.r.t x like how we've always been doing. Then the integral gives you (something) + g(x,z). But if you take the partials of the (something), it gives you back the original function, so, by Prof Leonard's trick, you can thus say that g(x,z)=0. Then you just take the (something), sub in the coords and you get 2pi+1
Great lecture. Thanks, profe
I liked his method of explaining with many many examples....
your way of teaching is soo good
You are the real life saver. Thank you.
Sir you are the BEST.
Professor Leonard you are by far better than any of my calculus professors I have ever taken. Also is there like 4 students in your class? I only ever hear at most 4 of them lol
The whole earth is full of his students, in virtual class.
I am a b.tech student in India from one of the top most prestigious engineering colleges and these calcis 3 Videos have helped me a lot during this 1st sem. as we are taught Engineering Mathematics -1 and Your explanation skills are awesome and divine level which have helped me to score vey good marks in my University exams , Thank You So much Sir, Love from India🤩
6:54 let this be known that at this point, I made the connection between the FTOC and gradients/line integrals for the first time. I feel quite happy right now. It seems so obvious, but aren't the best things in math like that?
I wish my professor just made us watch your videos in place of his lectures.. (no offense Dr R)
hes the modern day feynman, just as engaging and effective as a teacher
May God bless your heart
36:51 love you man. this whole video on line integrals is amazing
50:14 my god.. thought there were like, 20 people or so
@@david-yt4oo
The silence from these students amazes me.
I always hear that Americans think that we Swedes are much more reserved than they are, and not even my college class (which almost exclusively consists of Swedish students) is this quiet - there will always be at least 2-3 persons who say _something,_ even if there is only like 15-20 of us in some given class.
Just found this with 6 days before the test on chapter 15 and final exam is still left. Seeing people's success stories, I wonder: will Professor Leonard help me pull up my grade to an A (or at least A-)? I will update after I get the grade!
Genuinely curious... Did it work?
@@gmartin.12 Lol, I did get an A- , which, I was relieved to get!
You are better than my math professor at my University
thank you vereeeeeeeeeeeeey much you are the best teatcher in the worid
A great teacher
Professor you are amazing
Part time professor full time Superman 😁
Would be lost without this. I read the Pearson chapters and it isn't enough for the MathLab HW. Then come here and it's easy.
Part time professor
Part time bodybuilder
In the first example, the integral was zero in a conservative field , not because the end points at x and y were the same for the two points but because the functio had the same vales at those two points. A simple one dimentional analogy if the function cos theta, the integral is zreo between o and pi because sine pi and sine zero both have the same values; name zero.
Is it true that you will post D.E in the near future? Man I am so hyped. Also if it is true will you post them before October by any chance?
Yep!! Should START posting before October :)
The Magic Leonard has spoken!!
"Not the donald trump kind of conservative, but one we want to work with" Professor Leonard just gained 50 points for coolest prof
really good lecture. thank you
incredible i wished i found your videos earlier
Mi único héroe en este lío
Saving my butt since cal 1. Thanks a lot
this reminded me of exact differential equations
You're right in thing that because it's the same technique. The nomenclature is slightly different, but the necessary conditions and the results are the same.
"... in thing that..." s/b "in thinking that..."
I was a bit confused at 33:00 when Prof Leonard mentions that no work is done even though the particle was supposed to move from (0,0) to (-1,1). This path does not look like a round trip.
i was thinking the same thing. I think he's just trying to say there are times when work done can be 0. and if you move in a complete circle work will ALWAYS be 0. I think he stresses this because its important in greens theorem later in the chapter. But ive also learned from physics that if motion is perpendicular to force no work is done either, this may be an example of that. in other words the force field here would be everywhere perpendicular to the curve/line to produce 0 work.
An example of a situation where no physics work is done is if one were to walk across the top of a hill to a height at the same elevation. As you walk from your starting elevation to the top of the hill, you are doing positive work against the gravitational field. Then, when you walk down the other side of the hill to an elevation that is the same as your starting height, you will experience negative work the same magnitude as the work you did to go to the top of the hill. The sum of the work to the top of the hill plus the work recovered as you walk down the hill will equal zero. Additionally, it won't matter what exact path you take horizontally as long as your starting and ending altitudes are the same.
32:25 why does he say it was a closed line if the initial point was (0,0) and the last one (-1,1). How can it be closed? PLEASE someone help me
I had a question, you mentioned that if the mix partials are equal then the vector field is conservative and there exists a potential function. But I'm confused because in DE when mix partials are not equal, we would make them exact and find the potential function. Can't we do the same here ?