14 - What is Euler's Number 'e', Ln(x) - Natural Log & e^x Functions?

Рет қаралды 222,568

Күн бұрын

View more at www.MathAndScience.com.
In this lesson, you will learn what Euler's number is and why it is important in math. We will learn that Euler's number comes from the exponential growth of money when the compounding period is allowed to get very, very small. Euler's number is then used to form the natural exponential function e^x and its inverse, the natural logarithm ln(x). The exponential function is special because it is the only function whose rate of change is equal to the value of the function itself and whose area under the curve is also equal to the value of the function itself.

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@jimpringle1634 2 жыл бұрын

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.

@maheenmubashir2932 6 ай бұрын

E lvxe😢ce ussuit

@onkeltschimi6923 3 жыл бұрын

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.

@edgepixel8467 2 жыл бұрын

Hello kindred soul

@bad2infinity Жыл бұрын

Ditto...right there w you.

@dondonaldson1684 2 жыл бұрын

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.

@defytyrantsofmississippi2198 4 жыл бұрын

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.

@TrinhNguyen-hc6pz 4 жыл бұрын

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.

@Daniel-OConnell 3 жыл бұрын

Me too.

@user-hs1si2gr4s Жыл бұрын

This is the finest teaching of maths that I have ever come across. Absolutely compulsive. Dr Ron Fitzgerald

@nicknike79 9 ай бұрын

I've been looking for this method of teaching math for like 3 years. I literally appreciate the effort.

@felixyongco1168 2 жыл бұрын

Thanks a lot and I am reminded of my days 58 YEARS ago. You are such a very , very good teacher.

@thescouselander5531 4 жыл бұрын

One of the best things I've seen on KZfaq. 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.

@deirdreberger1363 4 жыл бұрын

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.

@henrychen9707 2 жыл бұрын

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

@mikemullenix6956 3 жыл бұрын

This is one of the best examples and explanation of e and compound interest I've seen. So important for understanding the magic of compound interest.

@bandreon 3 жыл бұрын

What a stunning lesson, brilliant in its simplicity!

@sebastiansalazar3553 4 жыл бұрын

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.

@christophersmith2165 4 жыл бұрын

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.

@edvargas3105 3 жыл бұрын

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!

@vythinathanduraiswamy3430 3 жыл бұрын

The origin and importance of 'e' so well explained. You are an incredibly good and passionate teacher! Thank you very much.

@hemarajue2736 4 жыл бұрын

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.

@MathAndScience 4 жыл бұрын

I agree!

@harneksingh3207 4 жыл бұрын

many thankd

@harneksingh3207 4 жыл бұрын

many thanks

@cluelessinky Жыл бұрын

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

@ottofrank3445 2 жыл бұрын

Sir, you are saving the humanity! What an amazing explanation !

@dennisclapp7527 4 жыл бұрын

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.

@tareksaid1623 Жыл бұрын

When such explanations are simply done it only means that you master completely mathematics. Great job

@Miss_blizzard187 Жыл бұрын

Can't express how helpful this was. THANK YOU VERY MUCH!!!

@kamalhameedbhatti8281 2 жыл бұрын

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.

@lucmarrouche71 4 жыл бұрын

This teacher is simply amazing, his lessons are so well designed and easy to follow.

@DonaldWhiteIII 5 ай бұрын

What a great lesson. Some of the best teaching I have ever seen. The visualization and verbalization was incredible

@suyashprksh 3 жыл бұрын

KZfaq 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

@ilkehureyiol1759 3 жыл бұрын

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

@alirezanabavian771 2 жыл бұрын

He took the log and added the result or multiplied them....

@mohammedhafiz3137 6 ай бұрын

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

@kanitvi514 Жыл бұрын

Thank you. All your sessions are incredibly brilliant!

@MathAndScience Жыл бұрын

Thank you so much!

@danielnegussie4894 Жыл бұрын

The best teacher ever. I watch his videos a lot. Very talented person.

@jackflash8756 3 ай бұрын

Fantastic intuitive , clear and concise video on e.

@terencewright2223 3 жыл бұрын

Fascinating video , so brilliantly explained.Excellent video,thank you.

@pekkagronfors7304 4 жыл бұрын

Amazing tutor skills. Thank's.

@stellaginger 7 ай бұрын

Thanks a lot for this marvelous lecture !

@mathapelongwepe2652 Жыл бұрын

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.

@MathAndScience Жыл бұрын

Wow, thank you!

@hazelchong5111 2 жыл бұрын

Thank you so much for wanting to help us understand how the Euler's number come from. very interesting. Thank you for all your vids.

@bushmanzanigaba3972 2 жыл бұрын

Thank you Jason, you made my life easy. Now I can help my daughter in a very simple method that I learned from you.

@pboston6RR Жыл бұрын

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.

@nicanorrocamora794 3 жыл бұрын

Industrious educator ,, a noble passion..

@roysmith3198 3 жыл бұрын

I may never in my lifetime use this but it does my soul good to understand how and what it is.

@jonnukisan9759 2 жыл бұрын

fascinating! Always wondered about that mysterious e on the calculator - very logical teaching - thank you

@bonilsson6349 3 ай бұрын

Wonderful lesson. TANK YOU!

@meizhou2107 3 жыл бұрын

beautifully done! much appreciated.

@wellyenas994 9 ай бұрын

Best teacher. Thanks for this. Appreciate your commitment.

@williamwelmans8648 3 жыл бұрын

An excellent lesson! Thanks!

@marnew1000 2 жыл бұрын

Superb introduction to a complex topic. love your lessons, you're a brilliant teacher..

@wilkyclergeot9416 Жыл бұрын

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!!!

@augumentum 8 ай бұрын

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 8 ай бұрын

Awesome story. You are very welcome!

@augumentum 8 ай бұрын

@@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?

@johnmacmillan627 Жыл бұрын

A real gem! Thank you

@hagosamear4665 Жыл бұрын

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.

@premakoya7939 3 жыл бұрын

Beautiful teaching. Thank you

@Jptoutant 2 жыл бұрын

Thank you for another great lesson

@ganeshjoshi6159 4 жыл бұрын

I can't imagine how euler calculate such powers like 1000 or more. Really a great mathematician 🙏

@alirezanabavian771 2 жыл бұрын

He took the log and added or multiplied the results

@smzakirhussain7604 Жыл бұрын

You are the best, Sir!

@lazmotron 9 ай бұрын

Solid background explanations. Great channel

@sirousmohseni4 3 жыл бұрын

Another excellent video. Thanks

@dbharathi2003 Жыл бұрын

Awesome and thanks for the tremendous energy

@nzarambafelicien9617 2 жыл бұрын

Thank you very. The way you explained number e is incredible. None of my teachers was able to explain to me.

@MathAndScience 2 жыл бұрын

Welcome!

@kaili1094 Жыл бұрын

Another adult here keeps learning, and I really appreciate the clear explanation... I enjoy this lesson every minute. Thank you, Sir.

@eduardor7301 4 жыл бұрын

Thank you really helpful you lectures

@Saudivlog 2 жыл бұрын

You are a great teacher. Your explanation 👌 is very clear and interesting.

@lprashant7325 3 жыл бұрын

Best math teacher ever had

@guliyevshahriyar Жыл бұрын

Very helpful video. Thank you very much.

@MavrikSoundsOfficial Жыл бұрын

JASON I WANT TO GIVE YOU AN INFINITELY LARGE SMOOCH FOR YOUR GENIUS IN TEACHING THESE TOPICS!!! ♥♥♥

@navindraarjunaabeyesekera7864 2 жыл бұрын

Superb explanation. Really enjoyed listening to it

@renatoberaldo2335 2 жыл бұрын

aulas muito boas!!!!! obrigado!!

@jk3266 4 жыл бұрын

You are a great teacher.

@MathAndScience 4 жыл бұрын

Thanks so much! So happy you liked it!

@halwag Жыл бұрын

Wish I had your lessons in High school. BRAVO.

@mnia8917 8 ай бұрын

Thanks a lot. You are the best. goodluck.

@sydneydwoskin4950 3 жыл бұрын

"what we call, in advanced math, the limit..." omg i think i blushed. i was like....I DO ADVANCED MATH!???!?!!??!

@anaeleraph4278 3 жыл бұрын

Dwoskin stop doing drugs

@joedasilva134 2 жыл бұрын

The best explanation on Euler number I have ever had ! 👏👏👏👏

@MathAndScience 2 жыл бұрын

Thanks!

@joedasilva134 2 жыл бұрын

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 . 😊😊😊

@collencekangaso8014 2 жыл бұрын

Wow what a wonderful explanation

@user-zp7xq9ft1d 4 жыл бұрын

Thanks to explain

@mnia8917 8 ай бұрын

Thanks a lot.

@alfredthepatientxcvi 2 жыл бұрын

This is phenomenal :D 😍😍😍😍

@sriharitheerthagiri6196 Жыл бұрын

Thank you very much sir..!!! Student from India 🇮🇳❤️🙏

@manu-jx5nc 4 жыл бұрын

Hi, it's a beautiful lesson, well articulated.

@lawrenceirvine8759 3 жыл бұрын

Excellent simply excellent. You are passionate about e.

@talaalshareef6511 3 жыл бұрын

BEST OF THE BESTEST

@rkfm2012 3 жыл бұрын

Beautiful teaching ....

@mattdodgers9533 Жыл бұрын

Good job Jason

@kallolbarmon1217 3 жыл бұрын

Great. Thank u very much.

@byronfuentes1281 4 жыл бұрын

Thank you sir this is wonderful education

@louisbatshone4754 Жыл бұрын

Best tutor thank you

@wonkyu1qlee66 2 жыл бұрын

five-star lecture !

@ronaldhofman1726 Жыл бұрын

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.