I know how much harder is to teach using this method, and I really appreciate the effort you have put in these lessons. I am an engineer. I have used calculus in my career many times, but I must admit I never really understood it on a gut level. Unfortunately I never had an instructor who took his job as seriously as you. Thank you.
Love these lessons. Im an adult that never really did well in school. In todays world its really helping keep up at work by learning from youtube and for maths I highly recommend this guy!! Thanks for creating this content that is free for me👍👍 respect.
I am an engineer and a keen lover of math. I was blessed to have a calculus teacher that explained this the same way that you did. I was also blessed to have a patient mother who drilled me in math so that I can do many complex calculations in my head by simplifying things back to first principles. My Dad was a mechanic who blessed me with the ingenuity to understand physics by asking questions that came from my curiosity. No wonder when I reached university the concepts of magnetism and electric fields helped me apply science and math to solve engineering problems. My favourite equation is the one you concluded with. e to the i*pi +1=0. It is so neat that the first derivative of the function (slope) is x and is the same as the integral (area under the curve) from - inf to x. Yes, Euler's number is indeed special.
Jason your videos have really helped me understand more complex mathematics than I thought I could ever grasp. You truly are a master and 2nd to none at teaching complex mathematical concepts. Thank you so much for what you do.
Nostalgia has brought a sixty something.here and it is quite amazing that something remaining in the dark for nearly half a century suddenly becomes clear, bright and simple. Thank you for your professional effort to simplify a complex subject.
First off, your videos are excellent. Clear and to the point. Moving between the different whiteboards and using the different colored markers is brilliant. With schools closed, my daughter is watching your videos to finish off her senior year in high school. She will continue with her transition to college. Hopefully schools are open by then.
Please set this lesson as the standard class and textbook lesson to all the 1st year senior highs kids. Now I have gotten it - why has the US been such a great nation? The instructor is the powerful answer!!!! Thank you so much
I received math lessons in my High school Education and in College. I am happy to tell you that your explanation of the Euler's number is the best and simple one I’ve seen. Many thanks for your time.
One of the best things I've seen on RU-vid. I've been using this stuff for years but nobody ever explained how it was derived or the meaning of the number. If only my maths lecturers were this good.
Brilliant explanation with simple language. I took math courses up to Differential equations and 'e' popped up everywhere, but I did not know why 'e' was so fundamental until now. Thanks a million!
It seems the Euler's number 'e' is an amazing discovery. Thanks, explain it so nicely. Curiosity is one of our basic instinct to know or learn(new) things. It is all around us if our mind opens to it. Without the curiosity we barely advance in our life.
Wish I had this instructor 60 years ago when I was studying calculus. It took me forever to understand the concept and he made it clear in ten minutes Well done and thank you
Didn't even noticed that 43 minutes of my life just passed by watching a lesson that had nothing to do with my life *BUT* it was the most interesting thing that I learnt today just for the sake of general knowledge.....thank you......bless you son.
Watched this explanation of "e" number first time, Understood it first time. Sir you are the Master we should have had in my school days,life would have been quite different. Thank you so much. It makes it lot easier for our children to enjoy Maths. Thanks
Thanks! That is very clear. If all instruction in mathematics were as well done, we would all be less likely to stop trying to get out of going to class.
This was really very interesting. I can see there is such a lot to think about here. I look forward to the next installments. As I do with all the other lessons on your website.
I remember receiving a loan in 1983. The banker had no clue how compound interest worked. 40 years later, I figured it out with your video. Also i calculated from your example n= 1 million Wow, it came out to exactly 6 digits of Euler‘s number. Jason, thank you for demystifying this formula. You remind me of my math teacher in high school with your contagious enthusiasm.
@@MathAndScience Jason, I just watched “09-Unit Circle” a couple of times several days ago. This was the 1st time I have ever heard of a unit circle. You explained it very well. In the 30º, 60º, 90º right triangle the x,y coordinates were ( √3/2,½) . The sine of 30º = ½ (y axis) is permanently etched in my brain with the flashlight analogy . Then √3/2 = x-axis (cos.). Next some calculations were done to understand this more fully. √3/ 2 =1.7305/ 2 = .866025. Then the Cos 30º = .866025 on the calculator. This is also true for the Isosceles right triangle at 45º( √2/2). So, being new to the “Unit Circle", I am puzzled!! Why deal with a √3 divided by 2 when 2 clicks of the Construction Master calculator gives the exact same number (.866025 for the cos of 30º) Is this because it is easier to remember the simple square roots rather than a 6 digit decimal and plug them into the other 3 quadrants of the circle?
RU-vid inspires own generation of creativity and budding minds! Thanks! We were about to be misguided but youtube comes to the rescue. Greatest invention of all time
I can't underestimate how thankful I am to you for this amazing explanation of the Euler's number. It really helped me with my math project. Thank you so much one more time
Very well done!!! I’m 83 years old and remember in a graduate chemistry class the prof was using “e” in his equations and told us it was easy to remember because it was 2.7 Andrew Jackson squared. WHAT??? Andrew Jackson was elected in 1828 so “e” was 2.718281828 . But I didn’t appreciate the derivation of “e” until viewin your presentation. Before it was just a number to me. Now it makes sense. Oh, and I liked your inclusion of the area under the curve. Very neat! Thanks, Paul Boston, former chemistry teacher.
This is the most beautiful mathematical video I've seen this year, thank you. I've just fallen in love with maths and it might change the entire course of my life.
I truly considering that incredible teacher is the most famous teacher i've seen in my whole life for real and then thank you so much incredible teacher!!!
perfectly explained , i now get the charging formula of a capacitor Uc=Uv* (1-^e^(1/rc)), it's perfect., it 1/rc from the addition to inifinity of what you can get, it maps to your annual growth where it's 1/rc , really love your video's, studyd electronics in the past but learned some stuf out of my head and never got the gut feeling with it m just implemented it.
Thank you for the incredible explanation. I have understood the basic concept of e , it’s function and it’s properties which I couldn’t understand it from other books or lectures.
Just a minor correction, e^iπ+1=0 (or e^iπ=-1) is not Euler’s formula. This is called Euler’s Identity. Euler’s formula is e^ix= cos (x) + isin(x). Awesome video!
Well, while thinking about the area under the e^x curve, you still need to keep in mind, that the graph never touches the x axis, so it's still more of a "limit" conceptually.
I have been binging in all of your videos . Today I covered 3 . They r awesome !!! Keep them coming . I would love to watch one Riemann Zeta Function . Thanks n may the forth b with u . 😊😊😊
Narutal log of 2, or 'e' is a great number. I like to play with '1/e' or .36787... this to me would be the experiential growth rate of the speed of light as the gravitational effects change as it moves from objects or towards an object in relation to it's distance. So as lights hits Murcery it moved a shorter distance but took longer to escape the pull of the sun gravity, but as it passes Murcery heading to Earth it speeds up.
There is a trick here: Banks quote annual interest rates but they compound interest on your min/max daily or monthly balance. Because of this formula it is misleading to say 10% pa interest compounded monthly unless you mean the interest rate is that, which if you compounded it monthly, would produce 10% pa interest. That rate is not 10% / 12 = 0.8333...% but (1+10%)^(1/12) -1 = 0.797414...%
I think it would be worth while to answer “why does in converge to 2.72?” The exponent is getting bigger so that should give you a large result. Nevertheless what you are adding to the one in the parenthesis is getting smaller and smaller. So, if you compound every nanosecond the compounding is great, but what is being compounded becomes neglectible beyond a certain value. It does grow, but you will see the growth very very far to the right of the period in 2.7182…….
In the last, the Euler’s formula is beautiful because “how beautifully the irrational numbers pi & e which are hidden in the nature or geometry of the universe are connected to imaginary number i” In my opinion, one day this equation will open some big door in science or nature in front of us. Currently it’s like we have the key in hand, but we don’t know yet where is that door?
Sir, who was your teacher or, i should better say, what are the sources that has created your base? Because, you explain the root cause and thus things (maths) no more remains some abstract numbers but, we can relate to real life situations. More i see your videos, your source of knowledge intrigues me more and more. Regards
dude, you're the best. MORE, ALWAYS MORE. i just wish I could pick you're brain. also, you should have a Saturday morning science show; you'd save our youth.
