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

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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.

[@jimpringle1634]

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]

E lvxe😢ce ussuit

[@onkeltschimi6923]

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]

Hello kindred soul

[@bad2infinity]

Ditto...right there w you.

[@dondonaldson1684]

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]

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]

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]

Me too.

[@user-hs1si2gr4s]

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

[@thescouselander5531]

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

[@felixyongco1168]

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

[@nicknike79]

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

[@deirdreberger1363]

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.

[@edvargas3105]

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!

[@henrychen9707]

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]

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]

What a stunning lesson, brilliant in its simplicity!

[@sebastiansalazar3553]

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.

[@vythinathanduraiswamy3430]

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

[@cluelessinky]

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

[@christophersmith2165]

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.

[@hemarajue2736]

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]

I agree!

[@harneksingh3207]

many thankd

[@harneksingh3207]

many thanks

[@kamalhameedbhatti8281]

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.

[@dennisclapp7527]

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.

[@ottofrank3445]

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

[@suyashprksh]

KZbin 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

[@DonaldWhiteIII]

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

[@ilkehureyiol1759]

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]

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

[@Miss_blizzard187]

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

[@tareksaid1623]

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

[@mohammedhafiz3137]

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]

Thank you. All your sessions are incredibly brilliant!

[@MathAndScience]

Thank you so much!

[@mathapelongwepe2652]

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]

Wow, thank you!

[@lucmarrouche71]

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

[@pekkagronfors7304]

Amazing tutor skills. Thank's.

[@danielnegussie4894]

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

[@terencewright2223]

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

[@nicanorrocamora794]

Industrious educator ,, a noble passion..

[@jackflash8756]

Fantastic intuitive , clear and concise video on e.

[@bushmanzanigaba3972]

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

[@kaili1094]

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

[@marnew1000]

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

[@hazelchong5111]

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.

[@stellaginger]

Thanks a lot for this marvelous lecture !

[@lazmotron]

Solid background explanations. Great channel

[@wilkyclergeot9416]

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!!!

[@wellyenas994]

Best teacher. Thanks for this. Appreciate your commitment.

[@hagosamear4665]

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.

[@jonnukisan9759]

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

[@roysmith3198]

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

[@ganeshjoshi6159]

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

[@alirezanabavian771]

He took the log and added or multiplied the results

[@bonilsson6349]

Wonderful lesson. TANK YOU!

[@nzarambafelicien9617]

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

[@MathAndScience]

Welcome!

[@meizhou2107]

beautifully done! much appreciated.

[@premakoya7939]

Beautiful teaching. Thank you

[@navindraarjunaabeyesekera7864]

Superb explanation. Really enjoyed listening to it

[@Jptoutant]

Thank you for another great lesson

[@williamwelmans8648]

An excellent lesson! Thanks!

[@sirousmohseni4]

Another excellent video. Thanks

[@guliyevshahriyar]

Very helpful video. Thank you very much.

[@joedasilva134]

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

[@MathAndScience]

Thanks!

[@joedasilva134]

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 . 😊😊😊

[@MavrikSoundsOfficial]

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

[@pboston6RR]

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.

[@johnmacmillan627]

A real gem! Thank you

[@lawrenceirvine8759]

Excellent simply excellent. You are passionate about e.

[@eduardor7301]

Thank you really helpful you lectures

[@jk3266]

You are a great teacher.

[@MathAndScience]

Thanks so much! So happy you liked it!

[@mnia8917]

Thanks a lot. You are the best. goodluck.

[@Saudivlog]

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

[@dbharathi2003]

Awesome and thanks for the tremendous energy

[@halwag]

Wish I had your lessons in High school. BRAVO.

[@collencekangaso8014]

Wow what a wonderful explanation

[@manu-jx5nc]

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

[@sriharitheerthagiri6196]

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

[@lprashant7325]

Best math teacher ever had

[@rkfm2012]

Beautiful teaching ....

[@smzakirhussain7604]

You are the best, Sir!

[@chinnachamykrishnasamy2010]

Very good explanation

[@roberthornbeck3831]

Love this presentation. I wish someone had done this for me in High School, before tech/eng school. Iam retired but enjoy math.

[@byronfuentes1281]

Thank you sir this is wonderful education

[@chadetrikrout]

Excellent explanation...

[@jjsmallpiece9234]

Excellent lesson

[@user-zp7xq9ft1d]

Thanks to explain

[@ronaldhofman1726]

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.

[@alfredthepatientxcvi]

This is phenomenal :D 😍😍😍😍

[@renatoberaldo2335]

aulas muito boas!!!!! obrigado!!

[@georgekoerner6591]

Beautiful presentation

[@augumentum]

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]

Awesome story. You are very welcome!

[@augumentum]

@@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?

[@tajbibishamim8085]

very beautifully explained

[@jeffreychavey4161]

Mind-blowing. Thank you

[@louisbatshone4754]

Best tutor thank you

[@mattdodgers9533]

Good job Jason

[@thandasibisi7534]

Good stuff.I only learned e when we did Calculus (differential calculus`. Specifically the derivative of a log function.

[@mnia8917]

Thanks a lot.

[@d34thcom3sripping]

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.

[@MathAndScience]

Wow thanks so much! I’m trying to do my part!

[@mohdsayeduzzaman]

Very nice explanation sir.

[@wonkyu1qlee66]

five-star lecture !

[@charlesabernathy1543]

Awesome. I always until now wonder how Euler got "e". Thanks soooe....much.

[@KMSINGH]

Good job!

[@leewheaton5257]

Thank you so much from Patten Maine

[@sydneydwoskin4950]

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

[@anaeleraph4278]

Dwoskin stop doing drugs

[@kallolbarmon1217]

Great. Thank u very much.

[@tresajessygeorge210]

THANK YOU... SIR...!!!