for bookmark 1:05:21 check for intersection 1:10:14 break 1:34:38 plane 1:48:30 plane example 2:06:37 plane example given a line and point 2:29:31 "two planes are || if normals are ||"
To the best professor (truly), Thank you so much professor! By the end of this semester, i feel like i will have been apart of your class from Calc 2 through Calc 3 yet from miles away! My grades and attitude have changed, my knowledge and love for math can't stop multiplying! just know that you are changing the world by sharing your brilliance and inspiring the next generations to be the best today & tomorrow! God bless you a tone
19:15 Parametric equation for a line in 3D Definition of normal vector 1:33:25 1:43:38 standard form equation of a plane -1:49:12 example of finding equation of plane If a plane 1 is parallel to plane 2, then the normal vector of plane 1= normal vector of plane 2 2:30:40 How to find angle between line and plane 2:35:20 Finding Intersection between line and plane
I was at the verge of tears in class not understanding one thing. This lecture just saved my life, thank you! I really appreciate the work you do Professor Leonard!! 🤩🤩
After 3 weeks of having no idea what is going on in my Calculus 3 class I found these lectures and couldn't be happier that I did. God bless this man for his immaculate teaching style and ability to continuously connect and review previously covered concepts. This is how math should be taught.
Can i just say I love how he takes his time explaining things and repeating important concepts, for those of us who might have missed a small detail somewhere. And just a question, how does he have so much time for each lecture? In my class we get maybe an hour per section, but this video is over 3 hours. I love his videos but they sure are time consuming. which is actually good for me since i need all this extra time and explaining to understand haha
This is a community college class, which the students would take as a preparation for future studies, so he might have extra time reserved for this specific course. He also arranges these videos by chapter sections, and the longer sections will end up as longer videos.
Yeah his lectures are absurdly long. That's why I don't get people complaining that their prof only spends a short time covering these topics. Like.... the guy has twice the lecture time most people get. My ass only gets 30 hours of lectures for this class. Of course these profs are speed running through these topics. Obviously some profs are objectively terrible. But the universities themselves aren't geared for teaching like this and does not incentivize teaching like this. Like one chapter is almost 1/2 of my total lecture time this semester. It's ridiculous.
The vast majority of teachers just give you the formula and they keep going and I really hate this particular way of teaching so I just wanna say thank you your videos are very helpful 🙏
Leonard, thank you for making these videos. Since youve left merced college, the only way students will be able to succeed is by watching your lectures!!! Thanks for such a great tool, wish you the best.
Hi professor lenonard, at 2:19:39 for the problem finding the perpendicular plane shouldn't the cross product be ? or is there some reason it changed to positive?
To be honest, I don’t care what school I go to as long as they teach me what I need to do, ya know train you. the school I’m going to now does not do that. Professor Leonard on the other hand, Break things down so nicely and explains where things come from instead of just throwing stuff on the board and saying just memorize it or that your an engineer just figure it out. First of all we’re not, we’re engineers in training who have no idea what we are doing; because if we did there would be no reason to pay or go to the class. Secondly education is the duty of the individual and should have the greatest hand in the learning process, but if the attitude towards the class or material is nonchalant students generally are t inspired enough to keep pursuing their education. Please for the love of humanity be more like professor Leonard.
Dear Professor Leonard, You're the best teacher I've ever had, you changed my views and approach to mathematics, and never fail to make it fun and interesting. Thank you!
16:58 The fact that we're already doing (or, trying to do) calculus with parametric equations, stuff with quadric surfaces, etc. in my class and I hadn't even learned or realized this yet is painful to think about. I really don't know what I'd do without these wonderful resources that actually keep me excited about what I'm learning by moving at a reasonable pace and explaining everything clearly. Going to calc lectures when you're not ahead can feel like a choking sensation mixed with tension in the chest, wondering whether you should keep doing what you're doing or just give up and get a dead end job so you can march to the end of your life diligently without having to worry about this anymore. Watching Professor Leonard is like getting a big hug while you feel the love for math and enjoy doing it. Some of the best things in life are free, after all.
i know this doesn't help your present situation, but some really solid advice given to me was to check a resource like ratemyprofessor.com to see if you can get a better teacher. Math is a subject that definitely requires a good teacher for most people to truly grasp the material. I always compare the sections of math classes at my school to see which has the teacher I would prefer.
@@jakemiller8981 Yeah the thing about that is it's only reliable to the extent that you trust the reviews as a reflection of what you're looking for. For one thing, when it comes to difficult subjects, a lot of negative reviews will just come from students who struggled for various reasons and won't always be reliable as a means of judging the professor. The subjectivity depending on the student and my lack of trust of the opinions of the majority of people I don't know made me take those a lot less seriously. A few of my favorite professors of all time- people who I absolutely loved the way they taught and with whom I shared similar ways of thinking about and explaining things- had loads of negative reviews and I've had many people disagree with me on their effectiveness as an instructor. My Physics professor has a 3.5 and the reviews led me to think I should avoid him if possible- but I got "stuck" with him for Physics 1 and he turned out to be the best professor I've had to this day, for Physics 2 as well.
This lecture has SO MUCH KNOWLEDGE... learn so much within this 3 hours and have never felt so confident and understand so much along the way. Just proves a good teacher makes Math less scary
I finally understand because of this lecture. You teach like a combination of the best professors I've had in the past. I wish we had you here. The way you organize problems is beautiful.
I have never taken a class from you, but I have been watching these lectures since I started Calc 1. They're the only reason I've made it to calc 3, and I'm so grateful for these videos.
10:25 Punchline 1. 15:10 Formula 1) 1:24:00 Angle 1:35:00 Normal, Plane 2:55:00 Distance Point Plane 2:45:00 Plane plane intersection I went through the whole thing twice. Thank you for your genuinely interesting explanation.
I’m going back to school after 10 years and Calculus 3 is my first class. Thank you so much for being so thorough with your explanation. Makes so much sense and I’m so grateful. Thank you!
this video may be four years old but you had no idea how much this series would help me and others with spring/summer classes that are now online due to covid, thank you so much for making me feel like i am in a classroom
Prof Leonard, you the real MVP. I've learned more about Calc 3 in just a few youtube videos than I have in my first three weeks of Calc 3 at my University. Thank you. Unlike a lot of crappy college professors, you don't try to flaunt your mastery of the subject in an attempt to inflate your ego. Please don't ever change.
Discovered your channel when I was struggling with Vectors and Vectors Calculus. Have always hated Vectors but thanks to you, you made it a whole lot interesting and I am finally understanding it better. Thank you and looking forward to other videos.
you are truly the greatest math professor I have ever watched . Without you I would not know what to do. I wish I could personally come and thank you for your hardwork. May God bless you Prof Leonard
Literally about to cry because I'm so stressed with my calc 3 class. But you saved me once again, I can't thank you enough! I hope you win teacher of the year.
Sometimes I just wish my professor could watch this video so that he feels shame about himself of teaching Cal 3 in my class. We spend over 2 hours in class for writing tons of paragraph from him. I hate going to the lecture. Thank you so much Professor Leonard, I cannot survive in Cal 3 without you.
I had to watch this one 3 times , first time i thought i got it ; then tried doing my homework and became confused ...so i watched it again , figured out how to do the homework . Went to bed woke up and watched it again . 3rd time i was able to follow along with out getting lost & work ahead a bit as-well . i actually learned more the 3rd time around than the other 2 times combined . Thank you for being my professor. I would love to make you a 3d drawing stick for white boards . ( the ones at my school are magnetic , and i have access a 3rd printer ) so i print a plastic pieces and mount magnets to them so they stick on the board . they slide on the axis and scale up & down .If you ever want to try one out let me know.
Thank you so much Professor, you have made this topic so much simpler compared to my own lectures, may you be you blessed and I hope you continue using your brilliant gifts and talents and to influence the lives of students. Shout out all the way from South Africa...
Holy shit, I have an exam in Linear algebra tomorrow and the main thing I struggled hard with to understand is Lines and planes, you made it SO easy to understand. Thank you so much! You have an incredible talent for teaching
wow, I never comment on youtube videos, but this guy literally saved my life. I honestly thought this stuff was all abstract until I saw this video. Great job making tough sound easy and for the little tricks and connections between points. THANK YOU
Awesome, awesome, awesome. Thanks a million for the videos Professor Leonard. I'm taking Calculus III at the moment along with a tough schedule of classes and your videos have definitely given me a chance to really analyze and understand what my professor seems to speed through during our lectures. I cannot appreciate what you're doing enough, not even because it's helped me but the hundreds, if not thousands (I'm probably not being very generous here but regardless) of people that you've helped. You're the greatest!
I go to a supposedly top school and you are a hundred times better at explaining these concepts than my professor. I wish you the best of luck in your career, thank you so much!
(1:19:00) This seems misleading. Yes, the lines intersect. But if you model the airplanes as points, then they cross they same point but at different 𝘵𝘪𝘮𝘦𝘴, one at t= -1/2, the other at t = 1/2. So in that sense they do not crash.
I'm reading Gilbert Strang's book on linear algebra while watching Prof Leonard's calc 3 videos, the vector stuff is mostly the same so it's a good idea to do lin alg while studying calc 3
Lemme tell you how good prof. Leonard is In our class no one understands the teacher, so we only learn our materials through Prof. L, everyone in my class loves Prof. Leonard so much that we made a discord server called SIMPS FOR LEONARD, ALL HAIL THE ALMIGHTY CHAD! ALL HAIL THE MESSIAH OF MATH! HE'LL SHOW YOU THE PATH TO GRADUATION!
Professor Leonard, thank you for another lengthy and powerful video/lectures on Lines and Planes in 3-D in Calculus Three. This is a tremendous amount of information for all students to absorb in one full college semester. I will continue to review this material for a full understanding of this monster topic.
With your airplane example (around 50:00). you showed the lines don't intersect, since there isn't a t1 and t2 that satisfy all three equations simultaneously. However, even if there was a t1 and t2 that satisfy all three equations, that would show the two lines intersect, but that wouldn't be enough to show the airplanes collide unless you knew the relationship between t1 and t2. You said it yourself at the start of the problem "they have to be at the same place at the same time", but later on you seemed to forget about the "same time" part.
The fact that my school has us in an hour long class and we go through one unit a day is the exact reason I have to come home and spend five more hours learning exactly what I was supposed to learn at school.
Greetings Sir, Just So You Know, I Still Do U-Subs The Way You Taught Us (UA-cam) In Calc 1...Followed You In Calc 2, I Can Personally Vow For Your Legendary Teaching. Thank You! I am Now In Calc 3 Getting Ready to Dive Into Partial Derivatives This Week Here In NC. Please and Thank You Hit Us With Some Knowledge on This Multiple Integration and Vector Calculus material. I'm Willing To Pay For These Videos To Show My Appreciation. I Would've Came To Merced, CA and Payed For Your Seated Class To Help Lay A Good Foundation In This 3-Dimensional Land. Our Brains Are Sponges Right Now.
quote: "In order to determine a line in space, you need a point and you need a vector in the same direction of that line ... So, you need to know where it's headed ... between any two points you can find a vector" source: above Excellent!
Awesome lecture, so far, one hour in!! This is the fortieth anniversary of my Mechanical Eng degree, but this is gonna be so helpful in reviewing and prepping for non-parallel planes computations I'm trying to set up in Excel for a work assignment.
I am so glad to have found this video. See, we study this in high school but without really addressing the concept. It's all just formulas and methods but no ability to visualize or have any sort of conceptual understanding. I struggled with this chapter, but you make this so much easier, so thank you.
I have been watching you since I started taking calc 2 and i just want you to know your teaching method is awesome and it helped me get an 99 in that class. Now im taking calc 3 and i go to your videos for complete understanding. Thank you!!!
Sir I am from Bangladesh. My name is Pranto Mollah. I am greatful to you because I have learnt more from your class than my university class. Thanks a lot.
Thank you so much for sharing your classes with the world professor. Really, you are helping so many people by sharing your knowledge. I'm taking calculus III and it's amazing to find resources like yours.
One thing I don't understand at 2:19:00--- We find a plane with points P and Q, so a plane with vector PQ. But with only that information, there are an infinite amount of planes that rotate around that vector. So is the question just asking to find one of them? I don't understand. That also means there's an infinite amount of perpendicular planes to that plane which means there's an infinite amount of normal vectors.
Love the way he teaches, i would start with planes (the main object) then i would go backwards to a line but i know that everybody follows the same path as he does...and he really conveys the meaning. Chapeau
Started watching your lessons today and I gotta say you are the best!!! My professor rushes through the topics and doesn't take the time to make sure we understand. Also, your students need to realize how lucky they got it. I mean there is no enthusiasm. If I were one of your students I would be shouting out the damn answer.
I'm not sure how I got here. your students are lucky bc it seems like you genuinely care about their understanding not necessarily their success. Theres definitely a difference between and its a good one.
stop apologizing about overtalking or rumbling or thinking that you are boring your students. When you overtalk that is when i actually get deeper and understand the concept, even more, You are an amazing professor, during my whole scholar experience i have 2 top favorites teaches in north Africa you are part of those top three now. you are just a fantastic Math_superman
You are the best teacher ever!! I studied for the finals of Calc 1 here and in a week I was able to understand the INTEGRALS/ SERIES that I suffered with for a month, and I was really afraid of starting it. I'm so thankful to have found you, I'm no longer confused by ur very clear explanation. Plus your classes are never boring and I did recommend you for everyone suffering. I'm here again as I started my Cal 2 course, just don't want to miss any of your notes. thank uuuuuu🤍🤍
at 1:19 Does Dr. Leonard really demo that the planes intersect (CRASH) at point (1/2, 2,1/2) AT THE SAME TIME?? Their paths obviously cross at this point, but plane #1 arrives at this point at T=1/2 and plane #2 arrives at T=minus 1/2. What am I missing? If they arrive at different times, there is no crash.
The example problem at 2:39:00 can be solved very easily by row-reducing a 2x4 matrix. Simply row-reduce the matrix [2, -3, 4, 3; 1, 4, -2, 7] and then write the components as functions of some arbitrary z-parameter, such as "t" - this will give you the parametric equation for the line.
1:56:46 If you remember from geometry, “For ANY 3 non-collinear points, there is exactly 1 plane that contains those points.” That’s exactly what we’re proving here. Awesome right?!
this man doesnt single out kids in class he forms them as a group left siders and right siders. This would make me feel so much more confortable in class if my teacher wouldnt just blankly stare at the class and look for the person who isnt doing anything. What a master class teacher!
Around 1:40 he says that the vector P-P0 (assuming that both P and P0 are in the plane) is also in the plane. I don't agree! If we assume that P and P0 are both position vectors (indicate two points in the plane), then their difference yields a vector that is parallel to the plane; but unless the plane goes through the origin, P-P0 will not define a position vector! This vector will still be orthogonal to n, so in the end the whole point is valid. Thoughts?
for bookmark
1:05:21 check for intersection
1:10:14 break
1:34:38 plane
1:48:30 plane example
2:06:37 plane example given a line and point
2:29:31 "two planes are || if normals are ||"
Bless you
* 1:44:25 epic dad joke
To the best professor (truly), Thank you so much professor! By the end of this semester, i feel like i will have been apart of your class from Calc 2 through Calc 3 yet from miles away! My grades and attitude have changed, my knowledge and love for math can't stop multiplying! just know that you are changing the world by sharing your brilliance and inspiring the next generations to be the best today & tomorrow! God bless you a tone
you aint never lie
That was hell of a lecture Prof. Can't believe such high quality material is available for free. Thanks a lot sir.
I am paying 20k a year to my college and I still have to watch this video in order to learn.
lol
I'm paying $28K/yr 😂
75k ......
80k man
10k
19:15 Parametric equation for a line in 3D
Definition of normal vector 1:33:25
1:43:38 standard form equation of a plane
-1:49:12 example of finding equation of plane
If a plane 1 is parallel to plane 2, then the normal vector of plane 1= normal vector of plane 2
2:30:40 How to find angle between line and plane
2:35:20 Finding Intersection between line and plane
I was at the verge of tears in class not understanding one thing. This lecture just saved my life, thank you! I really appreciate the work you do Professor Leonard!! 🤩🤩
I wish I had you as my professor when I was in college. You actually care.
After 3 weeks of having no idea what is going on in my Calculus 3 class I found these lectures and couldn't be happier that I did. God bless this man for his immaculate teaching style and ability to continuously connect and review previously covered concepts. This is how math should be taught.
Can i just say I love how he takes his time explaining things and repeating important concepts, for those of us who might have missed a small detail somewhere. And just a question, how does he have so much time for each lecture? In my class we get maybe an hour per section, but this video is over 3 hours. I love his videos but they sure are time consuming. which is actually good for me since i need all this extra time and explaining to understand haha
I started watching them at 1.5 times so I could get done sooner.
block period classes
This is a community college class, which the students would take as a preparation for future studies, so he might have extra time reserved for this specific course. He also arranges these videos by chapter sections, and the longer sections will end up as longer videos.
Yeah his lectures are absurdly long. That's why I don't get people complaining that their prof only spends a short time covering these topics. Like.... the guy has twice the lecture time most people get. My ass only gets 30 hours of lectures for this class. Of course these profs are speed running through these topics. Obviously some profs are objectively terrible. But the universities themselves aren't geared for teaching like this and does not incentivize teaching like this. Like one chapter is almost 1/2 of my total lecture time this semester. It's ridiculous.
Watch how he magically changes his clothes in between lectures sometimes.
The vast majority of teachers just give you the formula and they keep going and I really hate this particular way of teaching so I just wanna say thank you your videos are very helpful 🙏
I watched this 3 hour vid in one sitting and I can barely keep my concentration in a 45min lecture. Thank you so much.
1:52:20 best part, your welcome.
Leonard, thank you for making these videos. Since youve left merced college, the only way students will be able to succeed is by watching your lectures!!! Thanks for such a great tool, wish you the best.
Hey! Thanks for posting on here! I know it was abrupt, but it was time. You're a smart guy Parminder and you'll do great! Keep up your hard work.
You left the college? Did you win the lottery? Are you going to be doing calculus 4 and or linear algebra?
Hi professor lenonard, at 2:19:39 for the problem finding the perpendicular plane shouldn't the cross product be ? or is there some reason it changed to positive?
Professor Leonard , Are you ever going to start making videos again?
Parminder Singh he was at merced college? tf i live in merced lmao
To be honest, I don’t care what school I go to as long as they teach me what I need to do, ya know train you. the school I’m going to now does not do that. Professor Leonard on the other hand, Break things down so nicely and explains where things come from instead of just throwing stuff on the board and saying just memorize it or that your an engineer just figure it out. First of all we’re not, we’re engineers in training who have no idea what we are doing; because if we did there would be no reason to pay or go to the class. Secondly education is the duty of the individual and should have the greatest hand in the learning process, but if the attitude towards the class or material is nonchalant students generally are t inspired enough to keep pursuing their education. Please for the love of humanity be more like professor Leonard.
I hope you cover Differential Equations and Linear Algebra in the future. Your videos are always useful.
I hope this as well D:
YES PLEASE
I think he already had video on differential equations. Actually they were differential equations of the first order. It was in Calc 2, section 8.1.
that's an intro. she meant the actual course
Another vote for Differential Equations
Dear Professor Leonard,
You're the best teacher I've ever had, you changed my views and approach to mathematics, and never fail to make it fun and interesting. Thank you!
16:58 The fact that we're already doing (or, trying to do) calculus with parametric equations, stuff with quadric surfaces, etc. in my class and I hadn't even learned or realized this yet is painful to think about. I really don't know what I'd do without these wonderful resources that actually keep me excited about what I'm learning by moving at a reasonable pace and explaining everything clearly. Going to calc lectures when you're not ahead can feel like a choking sensation mixed with tension in the chest, wondering whether you should keep doing what you're doing or just give up and get a dead end job so you can march to the end of your life diligently without having to worry about this anymore. Watching Professor Leonard is like getting a big hug while you feel the love for math and enjoy doing it. Some of the best things in life are free, after all.
i know this doesn't help your present situation, but some really solid advice given to me was to check a resource like ratemyprofessor.com to see if you can get a better teacher. Math is a subject that definitely requires a good teacher for most people to truly grasp the material. I always compare the sections of math classes at my school to see which has the teacher I would prefer.
@@jakemiller8981 Yeah the thing about that is it's only reliable to the extent that you trust the reviews as a reflection of what you're looking for. For one thing, when it comes to difficult subjects, a lot of negative reviews will just come from students who struggled for various reasons and won't always be reliable as a means of judging the professor. The subjectivity depending on the student and my lack of trust of the opinions of the majority of people I don't know made me take those a lot less seriously.
A few of my favorite professors of all time- people who I absolutely loved the way they taught and with whom I shared similar ways of thinking about and explaining things- had loads of negative reviews and I've had many people disagree with me on their effectiveness as an instructor. My Physics professor has a 3.5 and the reviews led me to think I should avoid him if possible- but I got "stuck" with him for Physics 1 and he turned out to be the best professor I've had to this day, for Physics 2 as well.
Thank you Prof. Leonard! You always come to the rescue with your phenomenal free content! Thanks again!
Now I am ahead of my class. Thank you!
+Julio C. S mention not
+Maaz Ahmed ?
This lecture has SO MUCH KNOWLEDGE... learn so much within this 3 hours and have never felt so confident and understand so much along the way. Just proves a good teacher makes Math less scary
I finally understand because of this lecture. You teach like a combination of the best professors I've had in the past. I wish we had you here. The way you organize problems is beautiful.
I have never taken a class from you, but I have been watching these lectures since I started Calc 1. They're the only reason I've made it to calc 3, and I'm so grateful for these videos.
I'm in the same boat! I love Professor Leonard's videos!
I have a calculus exam 3 days from now. I'm watching every video in 1.5 speed. You know what? I like when Professor Leonard talks in fast motion
10:25 Punchline 1. 15:10 Formula 1)
1:24:00 Angle 1:35:00 Normal, Plane
2:55:00 Distance Point Plane
2:45:00 Plane plane intersection
I went through the whole thing twice. Thank you for your genuinely interesting explanation.
I’m going back to school after 10 years and Calculus 3 is my first class. Thank you so much for being so thorough with your explanation. Makes so much sense and I’m so grateful. Thank you!
Almost started dancing on my desk when I noticed you're posting new videos!!!! Soooo happy!
this video may be four years old but you had no idea how much this series would help me and others with spring/summer classes that are now online due to covid, thank you so much for making me feel like i am in a classroom
Prof Leonard, you the real MVP. I've learned more about Calc 3 in just a few youtube videos than I have in my first three weeks of Calc 3 at my University. Thank you. Unlike a lot of crappy college professors, you don't try to flaunt your mastery of the subject in an attempt to inflate your ego. Please don't ever change.
I hope if I change, it's only for the better.
Yes, you helped me with my 10th grade calc 3 class.
Prof Leonard’ lecture is clear and informative, and well organized. He made math fun.
Discovered your channel when I was struggling with Vectors and Vectors Calculus. Have always hated Vectors but thanks to you, you made it a whole lot interesting and I am finally understanding it better. Thank you and looking forward to other videos.
you are truly the greatest math professor I have ever watched . Without you I would not know what to do. I wish I could personally come and thank you for your hardwork. May God bless you Prof Leonard
Literally about to cry because I'm so stressed with my calc 3 class. But you saved me once again, I can't thank you enough! I hope you win teacher of the year.
professor Arnold is my immortal Hero
You are a true blessing from God. Thank you, Prof. Leonard. May God bless you.
That STD joke flew right over their heads.. that was a good joke
Sometimes I just wish my professor could watch this video so that he feels shame about himself of teaching Cal 3 in my class. We spend over 2 hours in class for writing tons of paragraph from him. I hate going to the lecture. Thank you so much Professor Leonard, I cannot survive in Cal 3 without you.
I had to watch this one 3 times , first time i thought i got it ; then tried doing my homework and became confused ...so i watched it again , figured out how to do the homework . Went to bed woke up and watched it again . 3rd time i was able to follow along with out getting lost & work ahead a bit as-well . i actually learned more the 3rd time around than the other 2 times combined . Thank you for being my professor. I would love to make you a 3d drawing stick for white boards . ( the ones at my school are magnetic , and i have access a 3rd printer ) so i print a plastic pieces and mount magnets to them so they stick on the board . they slide on the axis and scale up & down .If you ever want to try one out let me know.
Thank you so much Professor, you have made this topic so much simpler compared to my own lectures, may you be you blessed and I hope you continue using your brilliant gifts and talents and to influence the lives of students. Shout out all the way from South Africa...
Professor Leonard... Saving more lives than a doctor
If it wasn't for you I would have never passed calc 2. Thank you so much your work is much appreciated!
Holy shit, I have an exam in Linear algebra tomorrow and the main thing I struggled hard with to understand is Lines and planes, you made it SO easy to understand. Thank you so much! You have an incredible talent for teaching
You are the best professor I've ever had online. Thank you so much.
Prof Leonard posting Calc 3?!?! Yes!!!
+Deasert Fox obvio
wow, I never comment on youtube videos, but this guy literally saved my life. I honestly thought this stuff was all abstract until I saw this video. Great job making tough sound easy and for the little tricks and connections between points. THANK YOU
Awesome, awesome, awesome. Thanks a million for the videos Professor Leonard. I'm taking Calculus III at the moment along with a tough schedule of classes and your videos have definitely given me a chance to really analyze and understand what my professor seems to speed through during our lectures. I cannot appreciate what you're doing enough, not even because it's helped me but the hundreds, if not thousands (I'm probably not being very generous here but regardless) of people that you've helped. You're the greatest!
This is what real professors do ! I easily understand everything from your lectures YOU ARE THE BEST
You are a God sent. I love the way you teach. Thank you so much for sharing your talent witih the world and with me.
I go to a supposedly top school and you are a hundred times better at explaining these concepts than my professor. I wish you the best of luck in your career, thank you so much!
(1:19:00) This seems misleading. Yes, the lines intersect. But if you model the airplanes as points, then they cross they same point but at different 𝘵𝘪𝘮𝘦𝘴, one at t= -1/2, the other at t = 1/2. So in that sense they do not crash.
we need linear algebra man. please come back !
I'm reading Gilbert Strang's book on linear algebra while watching Prof Leonard's calc 3 videos, the vector stuff is mostly the same so it's a good idea to do lin alg while studying calc 3
@@none_of_your_business
At my university we have two courses that delve into Linear Algebra before we start Calculus 3.
@@Peter_1986 what's your major?
Lemme tell you how good prof. Leonard is
In our class no one understands the teacher, so we only learn our materials through Prof. L, everyone in my class loves Prof. Leonard so much that we made a discord server called SIMPS FOR LEONARD,
ALL HAIL THE ALMIGHTY CHAD!
ALL HAIL THE MESSIAH OF MATH!
HE'LL SHOW YOU THE PATH TO GRADUATION!
uhhhh... link to discord plz?
@@TheSebastian9000 It changed to LSSS (Leonard Secret Simping Society) sorry m8 u need a referral
@@Amir-kt2lk am cri
@@Amir-kt2lk no need your sucked up link,
Professor Leonard, thank you for another lengthy and powerful video/lectures on Lines and Planes in 3-D in Calculus Three. This is a tremendous amount of information for all students to absorb in one full college semester. I will continue to review this material for a full understanding of this monster topic.
With your airplane example (around 50:00). you showed the lines don't intersect, since there isn't a t1 and t2 that satisfy all three equations simultaneously. However, even if there was a t1 and t2 that satisfy all three equations, that would show the two lines intersect, but that wouldn't be enough to show the airplanes collide unless you knew the relationship between t1 and t2. You said it yourself at the start of the problem "they have to be at the same place at the same time", but later on you seemed to forget about the "same time" part.
This video is literally amazing. Professor Leonard is the best!
What a g of a professor. Learned more in thirty minutes than I did in 4, 1 hour lectures.
The fact that my school has us in an hour long class and we go through one unit a day is the exact reason I have to come home and spend five more hours learning exactly what I was supposed to learn at school.
Greetings Sir,
Just So You Know, I Still Do U-Subs The Way You Taught Us (UA-cam) In Calc 1...Followed You In Calc 2, I Can Personally Vow For Your Legendary Teaching. Thank You! I am Now In Calc 3 Getting Ready to Dive Into Partial Derivatives This Week Here In NC. Please and Thank You Hit Us With Some Knowledge on This Multiple Integration and Vector Calculus material. I'm Willing To Pay For These Videos To Show My Appreciation. I Would've Came To Merced, CA and Payed For Your Seated Class To Help Lay A Good Foundation In This 3-Dimensional Land. Our Brains Are Sponges Right Now.
Focus in a little more on that English class though... this was a tough read, buddy.
@@vetacoth it was not difficult. maybe you should learn English
quote: "In order to determine a line in space, you need a point and you need a vector in the same direction of that line ... So, you need to know where it's headed ... between any two points you can find a vector"
source: above
Excellent!
Awesome lecture, so far, one hour in!! This is the fortieth anniversary of my Mechanical Eng degree, but this is gonna be so helpful in reviewing and prepping for non-parallel planes computations I'm trying to set up in Excel for a work assignment.
Im literally learning everything from you. I even stopped going to my calculus lessons. Love ya ❤❤
1:18:40 The planes do not necessarily crash. They are at the same points, but at different times. Their flight paths simply intersect.
Hey bro is this a part of cal3 or whole Cal 3
I am so glad to have found this video. See, we study this in high school but without really addressing the concept. It's all just formulas and methods but no ability to visualize or have any sort of conceptual understanding. I struggled with this chapter, but you make this so much easier, so thank you.
taking calc 3 over the summer for a 6 week course this has been the most helpful session for an exam review
God bless this professor, a huge help for all of my calculus classes
I have been watching you since I started taking calc 2 and i just want you to know your teaching method is awesome and it helped me get an 99 in that class. Now im taking calc 3 and i go to your videos for complete understanding. Thank you!!!
Sir I am from Bangladesh. My name is Pranto Mollah. I am greatful to you because I have learnt more from your class than my university class. Thanks a lot.
HE LIVES!!!!!!!!!!!!!!!!!!!!!! HE LIVES!!!!
Thank you so much for sharing your classes with the world professor. Really, you are helping so many people by sharing your knowledge. I'm taking calculus III and it's amazing to find resources like yours.
One thing I don't understand at 2:19:00--- We find a plane with points P and Q, so a plane with vector PQ. But with only that information, there are an infinite amount of planes that rotate around that vector. So is the question just asking to find one of them? I don't understand. That also means there's an infinite amount of perpendicular planes to that plane which means there's an infinite amount of normal vectors.
I cant thank you enough. You make calc 3 easy its unbelievable.
16:30
19:12 - 2 equations for a line, parametric
23:25
2:53:12 for distance between 3-D objects
Love the way he teaches, i would start with planes (the main object) then i would go backwards to a line but i know that everybody follows the same path as he does...and he really conveys the meaning. Chapeau
Started watching your lessons today and I gotta say you are the best!!! My professor rushes through the topics and doesn't take the time to make sure we understand. Also, your students need to realize how lucky they got it. I mean there is no enthusiasm. If I were one of your students I would be shouting out the damn answer.
thank you my professor , i have no word about you , really you are gentle
🇪🇹🇪🇹🇪🇹🇪🇹🇪🇹❤❤❤
I'm not sure how I got here. your students are lucky bc it seems like you genuinely care about their understanding not necessarily their success. Theres definitely a difference between and its a good one.
Prof Leonard is the name I trust for math...... :) THANK U PROF, YOUR VIDEOS ARE SO HELPFUL
I was thrilled to find out you teach Calc 3 as well. I have no idea how I would get though my courses without you! Just wanted to say thanks!
I love your dedication, knowledge and Skill of tutoring. It is a great work.
2:53:46 dist b/w point and a plane ; 3:10:05 dist b/w skew lines; 3:14:30 line and a point
stop apologizing about overtalking or rumbling or thinking that you are boring your students. When you overtalk that is when i actually get deeper and understand the concept, even more, You are an amazing professor, during my whole scholar experience i have 2 top favorites teaches in north Africa you are part of those top three now. you are just a fantastic Math_superman
Your explanations are far more detailed than those of my own professor
Thanks for this video
(This is just a bookmark just in case I come back so feel free to ignore this)
38:20
1:19:00
You are the best teacher ever!! I studied for the finals of Calc 1 here and in a week I was able to understand the INTEGRALS/ SERIES that I suffered with for a month, and I was really afraid of starting it. I'm so thankful to have found you, I'm no longer confused by ur very clear explanation. Plus your classes are never boring and I did recommend you for everyone suffering. I'm here again as I started my Cal 2 course, just don't want to miss any of your notes. thank uuuuuu🤍🤍
Sir, drop the physics and linear algebra videos. Like a mixtape
ilectureonline is very good at teaching physics
Wow!!!!! These videos are simply magnificent.
Professor Leonard, thank the freakin lord for you buddy. The savior and peace bringer to my math world.
Thank you Professor Leonard, Glad you're back.
Holy shit thank you. My exam is on Tuesday, I needed this.
at 1:19 Does Dr. Leonard really demo that the planes intersect (CRASH) at point (1/2, 2,1/2) AT THE SAME TIME??
Their paths obviously cross at this point, but plane #1 arrives at this point at T=1/2 and plane #2 arrives at T=minus 1/2. What am I missing? If they arrive at different times, there is no crash.
The example problem at 2:39:00 can be solved very easily by row-reducing a 2x4 matrix.
Simply row-reduce the matrix [2, -3, 4, 3; 1, 4, -2, 7] and then write the components as functions of some arbitrary z-parameter, such as "t" - this will give you the parametric equation for the line.
Wow - you a tremendous and caring educator. These videos are a life saver. Thank you!
1:56:46
If you remember from geometry, “For ANY 3 non-collinear points, there is exactly 1 plane that contains those points.”
That’s exactly what we’re proving here. Awesome right?!
thank you for this prof leonard. you saved me !!!
this man doesnt single out kids in class he forms them as a group left siders and right siders. This would make me feel so much more confortable in class if my teacher wouldnt just blankly stare at the class and look for the person who isnt doing anything. What a master class teacher!
One of the most informative lectures I've ever seen on UA-cam! It has very helpful :)
Notes:
---- Line ----
0:00 - 25:09 - Definiton of a line in 3-D
25:09 - Note
29:44 - Ex. 1
49:30 - Ex. 2
1:10:15 - Ex. 3
1:19:40 - Angle between two lines
1:28:00 - Lines crossing the coo
---- Plane ----
I might be wrong but I believe at 2:21:07 the z coordinate in the vector should be -13 not positive.
Around 1:40 he says that the vector P-P0 (assuming that both P and P0 are in the plane) is also in the plane. I don't agree! If we assume that P and P0 are both position vectors (indicate two points in the plane), then their difference yields a vector that is parallel to the plane; but unless the plane goes through the origin, P-P0 will not define a position vector!
This vector will still be orthogonal to n, so in the end the whole point is valid.
Thoughts?
Yayyy exam on friday, Professor Leonard to the rescue!!