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

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  • Опубликовано: 6 сен 2024

Комментарии • 253

  • @jimpringle1634
    @jimpringle1634 2 года назад +55

    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.

  • @onkeltschimi6923
    @onkeltschimi6923 3 года назад +82

    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
      @edgepixel8467 2 года назад +4

      Hello kindred soul

    • @bad2infinity
      @bad2infinity Год назад +2

      Ditto...right there w you.

    • @donaldeaston9564
      @donaldeaston9564 2 дня назад

      Thank you for calling it MATHS, and not MATH. It’s one thing that grates on me. Destroying my language all for one letter, that Americans seem to have problem with.

  • @dondonaldson1684
    @dondonaldson1684 2 года назад +10

    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.

  • @TrinhNguyen-hc6pz
    @TrinhNguyen-hc6pz 4 года назад +17

    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.

  • @defytyrantsofmississippi2198
    @defytyrantsofmississippi2198 4 года назад +23

    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.

  • @deirdreberger1363
    @deirdreberger1363 4 года назад +14

    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.

  • @user-hs1si2gr4s
    @user-hs1si2gr4s Год назад +3

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

  • @thescouselander5531
    @thescouselander5531 4 года назад +5

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

  • @bandreon
    @bandreon 3 года назад +22

    What a stunning lesson, brilliant in its simplicity!

  • @henrychen9707
    @henrychen9707 2 года назад +1

    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

  • @sebastiansalazar3553
    @sebastiansalazar3553 4 года назад +18

    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.

  • @mikemullenix6956
    @mikemullenix6956 4 года назад +6

    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.

  • @felixyongco1168
    @felixyongco1168 2 года назад +2

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

  • @hemarajue2736
    @hemarajue2736 4 года назад +17

    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.

  • @edvargas3105
    @edvargas3105 3 года назад +4

    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!

  • @nicknike79
    @nicknike79 11 месяцев назад +1

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

  • @vythinathanduraiswamy3430
    @vythinathanduraiswamy3430 3 года назад +4

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

  • @cluelessinky
    @cluelessinky Год назад

    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

  • @kamalhameedbhatti8281
    @kamalhameedbhatti8281 3 года назад

    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.

  • @christophersmith2165
    @christophersmith2165 4 года назад +17

    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.

  • @mohammedhafiz3137
    @mohammedhafiz3137 7 месяцев назад

    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

  • @dennisclapp7527
    @dennisclapp7527 4 года назад +3

    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
    @ottofrank3445 2 года назад +2

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

  • @lucmarrouche71
    @lucmarrouche71 4 года назад +6

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

  • @roysmith3198
    @roysmith3198 4 года назад +3

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

  • @pboston6RR
    @pboston6RR 2 года назад

    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.

  • @nitinbhalla3391
    @nitinbhalla3391 3 года назад +1

    9:25 - Compound Interest
    20:56 - Continuous Compounding

  • @aram5642
    @aram5642 7 месяцев назад

    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.

  • @augumentum
    @augumentum 10 месяцев назад

    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
      @MathAndScience  10 месяцев назад

      Awesome story. You are very welcome!

    • @augumentum
      @augumentum 10 месяцев назад

      @@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?

  • @sydneydwoskin4950
    @sydneydwoskin4950 3 года назад +6

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

  • @tareksaid1623
    @tareksaid1623 Год назад

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

  • @DonaldWhiteIII
    @DonaldWhiteIII 7 месяцев назад

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

  • @ilkehureyiol1759
    @ilkehureyiol1759 3 года назад +1

    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
      @alirezanabavian771 2 года назад

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

  • @ganeshjoshi6159
    @ganeshjoshi6159 4 года назад +4

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

  • @ronaldhofman1726
    @ronaldhofman1726 Год назад

    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.

  • @suyashprksh
    @suyashprksh 3 года назад

    RUclips 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

  • @danielnegussie4894
    @danielnegussie4894 Год назад

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

  • @hagosamear4665
    @hagosamear4665 Год назад

    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.

  • @mathapelongwepe2652
    @mathapelongwepe2652 Год назад

    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.

  • @oshafactcheckerexposethepl9245
    @oshafactcheckerexposethepl9245 2 года назад

    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.

  • @jefferygreene8538
    @jefferygreene8538 2 года назад +1

    Euler number was used in the movie “Hidden Figures” when changing from a elliptical to parabolic orbit for NASA space capsule to return to earth.

  • @wilkyclergeot9416
    @wilkyclergeot9416 Год назад

    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!!!

  • @nzarambafelicien9617
    @nzarambafelicien9617 2 года назад

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

  • @jackflash8756
    @jackflash8756 5 месяцев назад

    Fantastic intuitive , clear and concise video on e.

  • @bushmanzanigaba3972
    @bushmanzanigaba3972 2 года назад

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

  • @Davionious
    @Davionious Месяц назад

    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...%

  • @kanitvi514
    @kanitvi514 Год назад +1

    Thank you. All your sessions are incredibly brilliant!

  • @kaili1094
    @kaili1094 2 года назад

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

  • @JavierBonillaC
    @JavierBonillaC 7 месяцев назад

    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…….

  • @redsix5165
    @redsix5165 Год назад

    15:57 You are not getting 2.25 because the interest will compound in the second period. You need to find the effective 6m rate to make this math work

  • @arturogonzalez6232
    @arturogonzalez6232 27 дней назад

    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!

  • @Miss_blizzard187
    @Miss_blizzard187 Год назад

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

  • @guliyevshahriyar
    @guliyevshahriyar Год назад

    All students should subscribe to this Foundational Scientific channel, thanks teacher.

  • @davidgari3240
    @davidgari3240 Год назад

    Yelp review: e ^ - lazy 8 * (what the ...)
    Love the term "negative infinity" SO MUCH.

  • @joedasilva134
    @joedasilva134 2 года назад

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

    • @MathAndScience
      @MathAndScience  2 года назад +1

      Thanks!

    • @joedasilva134
      @joedasilva134 2 года назад

      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 .
      😊😊😊

  • @roberthornbeck3831
    @roberthornbeck3831 2 года назад

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

  • @DavidRodriguez-er4rq
    @DavidRodriguez-er4rq Год назад

    This lecture was very interesting. This content is on par with Khan academy.

  • @nicanorrocamora794
    @nicanorrocamora794 4 года назад

    Industrious educator ,, a noble passion..

  • @wellyenas994
    @wellyenas994 11 месяцев назад

    Best teacher. Thanks for this. Appreciate your commitment.

  • @hazelchong5111
    @hazelchong5111 2 года назад

    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.

  • @marnew1000
    @marnew1000 2 года назад

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

  • @pjarina
    @pjarina 4 года назад +1

    It also works using google sheets FV function graphed line chart.

  • @stellaginger
    @stellaginger 9 месяцев назад

    Thanks a lot for this marvelous lecture !

  • @MavrikSoundsOfficial
    @MavrikSoundsOfficial Год назад

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

  • @gautamroychoudhury2735
    @gautamroychoudhury2735 3 месяца назад

    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

  • @user-zp7xq9ft1d
    @user-zp7xq9ft1d 4 года назад +2

    Thanks to explain

  • @halwag
    @halwag 2 года назад

    Wish I had your lessons in High school. BRAVO.

  • @lprashant7325
    @lprashant7325 3 года назад

    Best math teacher ever had

  • @sriharitheerthagiri6196
    @sriharitheerthagiri6196 Год назад

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

  • @manu-jx5nc
    @manu-jx5nc 4 года назад +7

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

  • @bonilsson6349
    @bonilsson6349 5 месяцев назад

    Wonderful lesson. TANK YOU!

  • @jk3266
    @jk3266 4 года назад +2

    You are a great teacher.

    • @MathAndScience
      @MathAndScience  4 года назад +1

      Thanks so much! So happy you liked it!

  • @jonnukisan9759
    @jonnukisan9759 2 года назад

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

  • @commentfromnitya
    @commentfromnitya Год назад

    Great learning for beginners. Though i also comes from geometry just as we step into complex plane

  • @mnia8917
    @mnia8917 10 месяцев назад

    Thanks a lot. You are the best. goodluck.

  • @Saudivlog
    @Saudivlog 2 года назад

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

  • @pekkagronfors7304
    @pekkagronfors7304 4 года назад +2

    Amazing tutor skills. Thank's.

  • @commentfromnitya
    @commentfromnitya Год назад

    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?

  • @lazmotron
    @lazmotron 11 месяцев назад

    Solid background explanations. Great channel

  • @mnia8917
    @mnia8917 10 месяцев назад +1

    Thanks a lot.

  • @leewheaton5257
    @leewheaton5257 4 месяца назад

    Thank you so much from Patten Maine

  • @louisbatshone4754
    @louisbatshone4754 Год назад

    Best tutor thank you

  • @dimorvanerkel2025
    @dimorvanerkel2025 7 месяцев назад

    Holy smokes man this is what learn from you mister awesomr😂🎉👍🏆wow lots of things are alot clearder now great 🎉

  • @paganimarker1898
    @paganimarker1898 Год назад

    what amazing explenation
    can you explain lke that and for Trigonometry???

    • @MathAndScience
      @MathAndScience  Год назад

      Yes! Look for my trig videos it’s all there

  • @terencewright2223
    @terencewright2223 3 года назад

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

  • @navindraarjunaabeyesekera7864
    @navindraarjunaabeyesekera7864 2 года назад

    Superb explanation. Really enjoyed listening to it

  • @thandasibisi7534
    @thandasibisi7534 3 года назад

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

  • @d34thcom3sripping
    @d34thcom3sripping 4 года назад

    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
      @MathAndScience  4 года назад

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

  • @chinnachamykrishnasamy2010
    @chinnachamykrishnasamy2010 4 года назад

    Very good explanation

  • @eduardor7301
    @eduardor7301 4 года назад +1

    Thank you really helpful you lectures

  • @wonkyu1qlee66
    @wonkyu1qlee66 2 года назад

    five-star lecture !

  • @georgekoerner6591
    @georgekoerner6591 Год назад

    Beautiful presentation

  • @tresajessygeorge210
    @tresajessygeorge210 9 месяцев назад

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

  • @idreeskhan6652
    @idreeskhan6652 3 года назад

    here i got the whole concept of e formula is investing 1 dollar,, so in final result we get 2.000000 something, which the format looks like the "e".
    But what about if we put the invest digit more than 1 in the formulat, still would get 2.0000 something format?

  • @lawrenceirvine8759
    @lawrenceirvine8759 4 года назад

    Excellent simply excellent. You are passionate about e.

  • @Amitavac
    @Amitavac 11 месяцев назад

    Hat's off to you Sir🙏

  • @boomersooner535
    @boomersooner535 4 года назад +2

    I'm glad I bought your dvds years ago to help this project

  • @from-you-65
    @from-you-65 7 месяцев назад

    Thank you teacher

  • @kamalhameedbhatti8281
    @kamalhameedbhatti8281 3 года назад

    WOW......never thought mathematics was so interesting.

  • @smzakirhussain7604
    @smzakirhussain7604 2 года назад

    You are the best, Sir!