What is Euler's Number 'e' & Why is it SO Important?

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.

[finpas]

The Best Explanation Ever!!! Thank you 🙏🙏🙏

[DW-pqgw]

Since following your videos, I have learned the “why” of so many math concepts. Please continue your series as you have a gift that makes learning math fun and understandable.

[Mathwithbigfish]

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.

[stefanopogany]

This is so beautiful!…wonderful teacher

[rezamohamadakhavan_abdolla]

Thank you very much for such a clear explanation.

[surajshukla]

Really happy to learn from you ...

😊

[mtc-ji]

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

[chocolatemodelsofficial]

So if you compound by Planck time is the answer e or some rational number?

[wes]

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.

[joshcarlzunega]

Is the Euler's formula e^(iπ)+1=0? Then why if i input these numbers it equals to math error in my calculator? Please help
2.71828^(√-1×3.1415)+1=math error not 0😢

[kylesanders]

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

[michaelkurtz]

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.

[aram]

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.

[idolgin]

In my opinion e is much cooler than pi.

[americanexploring]

Euler was a great mathematician but only Kurt Gödel is the king of math who also shows math is broken.