The Exponential Function

[@niceonedelboy]

Prof Strang, I hope you read these comments: I've done two engineering degrees and maths at school and you are the first person who has ever been able to explain this function to me in a manner I could understand! Outstanding. Thank you.

[@areebahmad1484]

9 years ago you posted this comment what are you doing now

[@rommul1389]

@@areebahmad1484 Lol.

[@elonmusk2315]

what are you doing now really

[@powerenergy3480]

Indians - bhaiya iit nikla ? :)

[@bullymaguiresdirtsupplier]

@@powerenergy3480 Lmao JEE simplified se aaya na?😂

[@BewilderedBird]

This is like poetry. I completely understand e now. I understand where it comes from and what the exponential function is. Jesus, this guy’s good.

[@MiladKiaeeDreamTheater]

I really admire him and MIT for contribute these valuable videos. I think he will remain in the history of math forever.

[@bayesian7404]

Gil, I am totally hooked on your lectures. After your explanation of e and the power of e to the x. Wow! I looked around and came across a series of videos covering linear algebra. I'm just turning70 and decided to return to my of mathematic. With you as my guide, this will be a wonderful journey. Thank you.

[@shadoninja]

This man got me through my Linear Algebra class so I applaud him. Came here just by seeing that tiny picture of this video and remembering how much he helped. Thank you Mr. MIT guy!

[@suyashmuley9096]

I seriously can't understand why would anybody want to dislike such a lecture video.

[@menecross]

lack of boobs - that's why the dislikes... I run into "e^x" in my work for some time, but now I can say I've been properly introduced to it.

[@SameerAman]

One of the most elegant explanations I've ever seen.

[@henarki]

Professor Strang, thank you. You have a kindness in your explanation, a delight in your voice, energy that overflows and intelligence that beams into the edges of space-time. Your teaching methods are unique and easily absorbed. Thank you again.

[@upmperthay]

+henarki AMEN!!!

[@aseefzahir8789]

You are the real superhero Prof. Strang. Thank you for everything.

[@lfalfa8460]

No words to express how grateful I am. Prof. Strang, you are an inspiration.

[@mayur_krishna_devotee]

Professor Strang has explained the beauty of this function e^x in this video in an amazing way, a must-watch video for the math enthusiasts.

[@primajump]

He is an amazing teacher. For the first time, I can really appreciate the exponential function. Thanks for making these lectures available to all.

[@rakeshramadas1934]

The best explanation i have seen so far about "e"

[@bas3995]

What a mesmerizing video explaining the exponential function in a manner no one in my college had dared to touch. Students of this institution are really blessed to have such genius in their faculty and once heard will never be forgotten. Thank you sir Live from Tamil Nadu India

[@uselesvideo]

Man i love this professor from MIT, i was searching for Exponential distributions but youtube showed this video on suggested and i just clicked on to it for this professor..now i am following this course...this guy is amazing

[@Ex-Navodayan]

I have never seen such a great explanation about the exponential function "e"...... Thanks Professor Gilbert Strang for such a great explanation......

[@g0rgth3b0rg]

I love the way he derives the power series for e^x at 7:24. I have never seen it done exactly like that before.

[@Ray1tx]

The most didactic explanation of exponential function properties I have ever seen in my life. Thanks MIT and thanks Dr. Strang.

[@PedroGuilhermeSiqueiraMoreira]

Wow! That demonstration of the infinite summation was beautiful.

[@Zonnymaka]

Frankly speaking, i knew everything prof Strang (MIT) published about (thank you for that!), yet i found the "angles" and his explanations crystal clear and amazingly instructive, especially for ppl who cope with the matter for first time! Strang is a MUST WATCH! Period.

[@13bionia]

Enlightening. Thank you. A personal expression and explanation from a live human being who is as naturally interested in the subject as prof. Strang inspires insight as no book can.

[@kevinprinceofdarkne]

I think I'm in love. For the past thirty years I have been coming up to the same old hurdle ( with Bundey and Mulholland ) and failing to see any relevance but this man's explanation does it. Thank You.

[@evasuser]

I wish Prof. Strang's lectures were publicly available 40 years earlier. We are lucky that MIT has uploaded them here.

[@smrd0110]

I love this professor. He is a national treasure.

[@ArthurMcGDM]

I'm a math masters student and he gave the best explanation of e that I've ever heard.

[@PHRANQ2K2]

I never imagined that i could _ever_ attend to a class at MIT with such a great professor.

[@kapil4497]

Dear professor Strang... I wish I could have every moment spent with you. Like the calculus that works continuously to make e what it is... An exponential. You are a real joy to watch. Thanks is such a trivial expression to express my gratitude.

[@userangelanameangela7322]

He is the greatest math teacher ever. A real wizard.

[@hankyje117]

This is the level of energy that I wish my math teacher had

[@takaokutsu2980]

Great example of first class education and real learning experience! I enjoyed the video very much. Thank you very much Dr. Strang and MIT!

[@yucelozyazgan]

Thanks for this amazing lesson Mr Strang and MIT. It was really helpful for me to understand the concept of Euler number e ... Unfortunately most of teachers are not taking care of simplicity in their lessons.

[@fernandogomes4512]

What a brilliant class! The best explanation about exponentials that I'd ever seen in life

[@Ceorolus]

I found this video very entertaining. Professor Strang does his usual to make sure we get the message.

[@ripperduck]

Where was this guy when I was in second year physics? He makes more sense than any prof/teacher I've had...

[@nynmlg2299]

I’m from Germany and I wished The professors were as good as you! Thank you

[@georgesadler7830]

This lecture helps me understands the number "e" and it's importance in mathematics.

[@bedwarri0r333]

Sir, I want to thank you for enlightening me with all your videos and giving me more opportunity for higher learning.

[@sidaie2876]

wow! what an insightful lecture. This is the where MIT makes a difference. I could never get this level of intuition of an exponential function from anywhere else.

[@leifeng234]

As usual, Strang is the man.

[@celesteadeanes4478]

if one can explain simply ,that demonstrates mastery. well done,refreshing

[@anusharma6854]

Prof. Gilbert Strang explained in a very well-organized manner the properties and applications of the exponential function in the real world.

[@elamvaluthis7268]

How hard and sincere explanation he excels in this from others.

[@Deuterium52]

"Suppose you're getting 100% interest...generous bank...okay." lol! Professor Strang is awesome

[@skoolwal3874]

Beautiful... No other word can describe maths and the way he teaches it.

[@vijaykumar-gv1dg]

his teaching creates exponential understanding i should say......great upload thanks for that

[@Narendraprsd21]

I tried hard to understand exponential by reading book, and got nothing. But this video gives me enough to understand it. Thank you very much Sir

[@twicecookedporkins3235]

Thank you, Professor Strang. Excellent demonstration.

[@dr28kumar]

Very good lecture Professor Strang. Thank you

[@phillycheeseman]

This is exactly what I have been looking for for years. Thanks so much...

[@thathirteenth]

Loving this professor in everything he does

[@rjaph842]

Priceless, Prof Strang. Stunned by that multiplication technique(stacking the two polynomials side by side and multiplying them). Hw is it done, anyone?

[@rreddy20]

One of the Best explanations of Fundamentals of Calculus.

[@Sandro6080]

- The mathematics is fascinating, even a subject that can seem simple, it deserves a lot of respect because there are more things submerged that we can imagine, teacher has been attending their classes and I have been amazed, me secondary teacher and I notice that the students possess a lot of difficulty, and these videos has been of stimulant, thank you. (Excuse the mistakes) Brazil.

[@ajethmoolayil3594]

This is gem from Professor Strang!

[@mohfa1806]

YOU......YOU......YOU are big time prof.....i salute you

[@distopiadnb]

14:04 obviously reveals a passion for a renowned strategy PC game from the Nineties.

[@fabianhaglund5792]

Stroke me instantaneously when he said that as well. Was waiting for "insufficient funds" in the end at the Bank example.

[@distopiadnb]

lol, that's right.

[@gaurav.raj.mishra]

distopiadnb Which one?

[@michaelgray7717]

Gaurav Mishra Age of Empires

[@noname_whatsoever]

distopiadnb Always played House Harkonnen as a kid :)

[@anumali5907]

Wonderful!!!!!! The professor is amazing. The video was amazing. Good work!

[@amysadler6015]

Thank you Professor Strang... Seriously, thank you!

[@swapgs3427]

mind blowing...really wish we were taught maths during our school/college time... :( better late than never, thanks MIT for these lectures. love you professor strang :)

[@johnnycovington3761]

Prof Strang is awesome!

[@gokulnair370]

I think it is best way to teach students. Reason I can say that in this there is interaction between student and teacher and increasing concentration.

[@wassilijstrugalski934]

WOW! Wow! wow.. wow.. Thank You Thank You Thank You! I think I finally got it) Clear, beautiful. The nature is sooo elegant!) And God is soooo witty)

[@fazlanpera]

This is why MIT shines

[@jmguevarajordan]

This video is correct, the way to explain the exponential is with the differential eq, which gives the connection with the logarithms and the series in a natural way. I am pretty sure that the important number 'e' was discovered by solving differential eq. Without the differential equation it is not possible to explain why 'e' is such a notable number and its connection with trigonometric functions.

[@MichelLongtin]

what a passionnate teacher!!! What a great math professor!! Michel

[@CrystalFeatherstone]

this was so simple to follow and made sense...I love the presentation and I am in love with calculus..

[@MrSupernova111]

This dude must be wicked smart. He almost made me like math after a love hate relationship with the subject over a lifetime. haha

[@krozareq]

I hated it in school but now I love it. Rocket calculations and orbital trajectories turned me on to math in a new way. "e" is also used in rocketry, since the weight of fuel is constantly decreasing and thus the thrust-to-weight ratio is always increasing with an engine at a fixed specific impulse. The Tsiolkovsky rocket equation is simply: deltaV = Ve * ln(total mass/dry mass). Ve is V sub e and is the product of the acceleration of gravity (earth = 9.81m/s^2) and the specific impulse (I sub sp, or often written as Isp). Of course ln is a logarithm with the base of e. It's amazing how technology, easy access to fun new ways to learn, can have such an impact on how we see things in a new light.

[@krozareq]

Forgot to mention: Kerbal Space Program FTW.

[@jstarks123]

@@foobarmaximus3506 except most of the people in this comments section do think he’s a good math teacher, so for most I guess he has the desired effect that you’ve described.

[@emreozgun3846]

@@foobarmaximus3506 why not this person ?

[@jstarks123]

@Noah dean and that emotional relationship will be different from student to student. Some will be able to relate to this teacher while others will not.

[@cablaze1]

i'm loving this guy more everyday!

[@MrBorceivanovski]

This lecture is also spiritual motivation of mathematics way of thinking!

[@yashj1072]

Marvellous. This e always baffled me even after so many readings.

[@user-or7ji5hv8y]

His erudition is amazing.

[@emman1927]

That was wonderful. Thank you Prof. Strang.

[@akshayv2849]

Lovely teaching. I'm really glad I saw this video 😄.Hope Sir Gilbert is fine.

[@HK-yg4fd]

I've noticed how poor my high school text book was. He gave me the clear and intuitive definition of exponential function.

[@aabp2317]

Most math teachers need to watch Professor Strang's lectures so that they can see how it is done right.

[@gregg4]

The growth (or derivative) of 100^x is equal to: dy/dx = 100^x * ln 100 ln is a log with base e. So e is fundamental to any fully maxed out growth.

[@Eternaldream00]

I think this is some kind of introductory lesson so he's taking his time.

[@EclecticSceptic]

I live off these videos. Gil Strang is such a good teacher.

[@klam77]

a most beautiful lecture. wish i had learnt like this from the get go!

[@nageshg.s.6983]

awesome lecture the best i have ever heard thanks for the upload

[@aplacefaraway]

exp function is probably the most fundamental pattern in all of math and physics. my best intuitive understanding of what it is doing is transforming space between Cartesian and wave (cyclic)

[@fragnar]

this is a great explanation, I don't remember our teacher doing this for us in Calculus...

[@mohammadpourheydarian5877]

such a valuable asset to our nation.

[@MohAku-f]

9:43 i like how the Proffesor explain what e number really, is the slope is same as the function. That e is in Mac Lauin series. Correct me if i wrote those wrong. But i do love how he explain this completely not making any sense thing become simply make sense. An Experienced Tutor.

[@gat0tsu]

this explanation is amazing

[@gregg4]

The point about e is that it's all about growth. The example is given about interest. If you let the interest you get every year compound then your money will grow. If you could get your interest every month and let that compound it would grow even faster.The smaller the time intervals (every day, every hour, ...) the faster the growth. So if you take the limit to infinitely small time intervals lim n->infinity as (n + 1/n)^n you get as extreme a growth as you can get.

[@Chill197]

Thank you MIT I was woried that my education would be cut short due to not having any money.

[@CanadianMathMagician]

As an added piece of information to my previous post, I would like to say that some calculators will return a 1 only because they return the right hand limit of the function f(x) = (x to the power of x). The left hand limit however should be -1. If you consider both the left and right hand limits, the entire limit will not exist and hence 0 to the power of 0 is considered non-existent (or sometimes people will say indeterminate/undefined).

[@Amine-gz7gq]

Best math teacher !

[@exlife9446]

thanks for the lecture, make things more clearly about e.

[@fabianhaglund5792]

What a joyful video to watch

[@csikjarudi]

You can think of the exponential function in a more fundamental way; as it is defined by the functional equation f(x+y)=f(x)f(y) for all real x,y. If, in addition, we assume that f is continuous and monotone then everything else follows, even the differential equation thing.

[@Krsnee]

Excellent explanation....

[@musa78692]

professor strang you are just amaizing!

[@حسينالقطري-ب8ص]

I appreciate this man for his nice explination

[@goeatbobby]

Awesome! I cant wait to use this knowledge once I leave my College. Oh wait hang on a second....

[@احمدحميد-م6ط]

Wonderful!!!!!! The professor is amazing

[@donaldmaase776]

Very good lecture. Even a dolt like me got it. Thank you for not using gizmos and gadgets.

[@vozedale]

14:39 - Check.. Multi-Uh,.. Well, I've asked you... ! Ha! Cracks me up every time.

[@zerroukafaf7846]

Beautiful explanation 😍😍😍