数学 The Binomial and Multinomial Theorems: Proofs and Examples
IntroductionThe Binomial Theorem is a highly versatile theorem that appears in various contexts. In this article, we wil...
数学 
数学 The mechanism of Helmholtz resonance and a simple proof of the resonance frequency theory
IntroductionWhen you blow air across the mouth of an empty bottle, you hear a "booo" sound. This phenomenon is called He...
数学 Taylor Expansion of Two-Variable and Multivariable Functions: Theory and Simple Proof
IntroductionIn a previous article, we discussed the Taylor expansion of a single-variable function $f(x)$.So, how can we...
数学 Maclaurin Series Examples: Expanding exp, sin, cos and Deriving Euler’s Formula
IntroductionLast time, I wrote an article about Taylor series expansion.To recall the Taylor series expansion:Taylor Ser...
数学 Understanding Taylor Expansion Theory: Why Can Functions Be Expressed as Polynomials?
IntroductionI believe the beauty of Taylor expansion lies in the fact that functions can be expressed as polynomials.Whe...
