What is Euler's Number?

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  • čas přidán 29. 04. 2024
  • In this video, discover the essence of Euler's number, denoted as "e," a fundamental constant in mathematics. Euler's number is an irrational and transcendental constant that arises in various mathematical contexts, including calculus, analysis, and probability theory. Originating from the study of compound interest, "e" emerges as the base of the natural logarithm, offering profound insights into exponential growth and decay phenomena.
    Through clear explanations and illustrative examples, delve into the significance of Euler's number in calculus, where it serves as the foundation for understanding exponential functions and their derivatives. Explore its applications in solving differential equations and modeling continuous processes in science and engineering.
    Unlock the mysteries behind Euler's number as you grasp its role in complex analysis, where it serves as a cornerstone in the study of complex numbers and functions. Understand its connection to trigonometry, probability, and the Riemann zeta function, showcasing its ubiquitous presence across diverse mathematical domains.
    Join us on an enlightening journey to unravel the mysteries of Euler's number, gaining a deeper appreciation for its significance in mathematical theory and practical applications alike. Whether you're a student, educator, or math enthusiast, this video offers valuable insights into the beauty and elegance of one of mathematics' most profound constants.
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Komentáře • 15

  • @Christopherbigfish
    @Christopherbigfish Před měsícem

    I hold HND in Electrical Engineering and a Bachelor's degree in physics...I have watched videos of the best physicist of the modern era but non can be compare to the way you teach... I really enjoy watching your videos... Thanks for the good job.

  • @rezamohamadakhavan_abdolla8627

    Thank you very much for such a clear explanation.

  • @BG-wm2tw
    @BG-wm2tw Před měsícem +2

    Thank you for this video.

  • @kylesanders8276
    @kylesanders8276 Před měsícem +1

    My math teacher in high school had a sign that read, "Euler: pronounced like "oiler" not like '"ruler" " lol

  • @drumtwo4seven
    @drumtwo4seven Před měsícem +1

    Nice 👍

  • @surajshukla1787
    @surajshukla1787 Před měsícem

    Really happy to learn from you ...
    😊

  • @miriamcollins7587
    @miriamcollins7587 Před měsícem

    That is really cool about the slope of e^x at every function value!

  • @roger7341
    @roger7341 Před měsícem +1

    e would appear to be the limit of (1+ε)^(1/ε) as ε→0
    For ε=1.0e-16, (1+ε)^(1/ε) on my pocket calculator gives E=2.718281828459045..., while it gives e=2.718281828459045... when I press the e button.
    Subtracting e, according to my calculator, from E gives E-e=1.018986660018517e-16, indicating that 1^∞ has a good chance of reaching e.

  • @joetandingan6328
    @joetandingan6328 Před měsícem

    Best teacher

  • @kenlamb5697
    @kenlamb5697 Před měsícem

    Great pre calculus set up.

  • @aram5642
    @aram5642 Před měsícem

    While the slope is quite straightforward, with the area under the curve is not. The area is actually infinite because the curve never touches the X axis.

  • @idolgin776
    @idolgin776 Před měsícem +3

    In my opinion e is much cooler than pi.

  • @michaelkurtz1967
    @michaelkurtz1967 Před měsícem

    Euler was born April 15, 1707 Switzerland and died September 18, 1783 Russia. The last seventeen years of his life he was almost totally blind and died from what they believe was a brain hemorrhage. He was quoted to have said there "fewer distractions" since loosing his sight.

  • @o0QuAdSh0t0o
    @o0QuAdSh0t0o Před měsícem

    Discrete Maths