One great thing about Professor Leonard is that he always gives several straightforward example problems fairly early. Most of my math teachers have stood and rambled on forever about proofs and theorems and confusing crap, and then they MIGHT have given one example problem - and it was always a very long, tedious problem, every single goddamn time.
Though I understand your pain, you should also be thanking your teachers. Many students dislike math because they don't know why they're doing it or where it comes from. Many teachers only give several examples and call it a day. When learning math, it's always important to know the derviation of the formulas you learn, and why certain concepts are the way they are. Any college student here would perhaps agree on this.
@@parinpatel5719 That's only useful when we can understand the proofs, and even then they're only really good for math majors. Professor leonard makes it clear what to do with it as a tool, and that's what engineers see math as.
@@pedrosantana3283 Leonard shows the derivation through his lectures. He spent an entire video explaining what exact solutions are and how they're derviaived. So I think hes a perfect blend of teaching theory and giving examples. Blessed we are to have this resource. I cannot find anything of this quality for real analysis or theoretical optimization. Im scared to attack abstract algebra and topology, since there isnt a professor leonard for those subjects... honestly.
At 36:55 I did the same technique but using property of square roots then exponents. Right away, I noticed \sqrt{xy}=\sqrt{x}\sqrt{y} since it was all over x I then used the property of exponents to simplify. Super cool to see how different brains process and think when working through problems. I am almost done with my BS in Pure math just going back to previous classes to not lose the skills. Thank you so much!
Thank you for warning us about anger! This is the first math class that I really was infuriated by it. I'll take your advice and take a break when I feel angry. :)
ya I'm glad he said it too because my professor for this course seems to enjoy us getting frustrated and angry. He actively pursues it and without Professor Leonard I would have given up on this class by now.
Man this is so much simpler and more understandable than the way I was taught in class. I went from tearing my hair out, to solving these problems rather quickly. Thanks Leonard. ps As an extra benefit I find myself not just more motivated to do math but also to hit the gym, I wonder why that is.
I think every professor should tell their students your speech about getting angry. I have noticed time and time again when I get angry, I am no longer taking in any information. I have to walk away!!! Thank you for always being so awesome Professor Leonard. I wish you'd come back and make more videos. I really could have used your help with Eulers method and then the improved Eulers method!
your teaching approach is so unique and wonderful. the last time I check no mathematics teacher would make this topic as easier has you have made it. I am so grateful professor keep doing this Good work for the world.
Thanks especially for the final segment concerning domain restrictions. It's not just nit-picking; over the years I've seen many practical cases where lack of attention to this detail have produced incorrect or incomplete results.
Absolutely, and I'm glad you enjoyed it. Lately, I've been of the mind to get the technique understood first and then, once that's mastered, to explain the finer points of what's really going on "behind the scenes" so to speak. Students seem to grasp the domain restrictions better once they have mastered what they are actually doing and why the are doing it. Thanks for watching!
Your approach does seem like the most effective plan. Even a quick mention early on that there are details to be examined later is enough to damp down a tendency to ignore them. Thanks again!
come teach at CSU PLEASE!!! my professor is so hard to follow that I watch your videos during class time rather than go to class and I gain SOOO much more comprehension. THANKYOU!!!
love this guy so much. I always feel dumb in my math lectures because all these professors have nothing on leonard... This is what education looks like^^
44:34 wow just when i was wondering if i skipped something or was at the wrong video a problem very similar to the one on my hw shows up lol, you're a god
Hey professor, First, I would like to thank you for teaching us. Second, I have only one problem with this method (I know I am the problem, not you). For example, the following problem is really difficult to solve using the method I learned from you. Or maybe I am doing something wrong? But when I searched for a solution, all the solutions I have found are using different methods for the specific problem I am facing. x dx + (y -2x) dy = 0 Would love to be able to solve it using the method I learned from you.
You can have a square root of 0 (which gives you 0). The only problem is with a square root of a negative number. Therefor you do need both x != 0 and xy >= 0.
Hello Professor Leonard, I know I'm late to the party, but I was wondering why you didn't completely solve for y (left it as y^2) during the first homogeneous example (somewhere around 33:00). If anyone wants to tune in and provide an explanation it would be greatly appreciated.
square root would make it + and -; we dont know if its positive or negative. Leaving it as y^2 is better when you have no values. He also kinda explains it 32:28
Why does the derivative of y=vx is dy=vdx+xdv in our book(dx is included). Tried solving the first problem with same approach on our book but i cant get it. Welp
I am confused. My teacher told me when I was doing the question x-y/x+y that the numerator and denominator have the same power, hence it's a homogeneous equation. Can anyone plz tell me if this approach is correct?
I switched to a Dual Major in Computer Science and Mathematics because of you. Classes I need you to teach please: Advanced Calculus I & II, Differential Equations II, Number Theory, Introduction to Proofs, and Statistics II.
