A comprehensive examination of various methods for determining whether a series converges or diverges.

We examine fundamental concepts of calculus such as the definition of sequences and series, convergence and divergence of sequences, convergence and divergence of series, and the definition of e, t...

We explore Newton's laws of motion, the meaning of these three laws, and the definitions of inertial mass and gravitational mass, as well as the principle of equivalence, which holds significant im...

We examine how the general solution of homogeneous linear ODEs with constant coefficients takes different forms depending on the sign of the discriminant of the characteristic equation.

Learn about the definition and characteristics of second-order linear differential equations, and understand the important theorem of the superposition principle and the resulting concept of basis ...

Calculate the energy transfer rate due to particle collisions for both elastic and inelastic collisions, and compare the magnitude of energy transfer rates for cases when the masses of the two coll...

We set up the Schrödinger equation for the harmonic oscillator in quantum mechanics and explore its analytical solution method. We solve the equation by introducing the dimensionless variable 𝜉, an...

We set up the Schrödinger equation for the harmonic oscillator in quantum mechanics and explore its algebraic solution method. We derive the wave function and energy levels of any stationary state ...

This post introduces the process of implementing multilingual support by applying the Polyglot plugin to a Jekyll blog based on 'jekyll-theme-chirpy'. This is the second post in the series, coverin...

This post introduces the process of implementing multilingual support by applying the Polyglot plugin to a Jekyll blog based on 'jekyll-theme-chirpy'. This is the first post in the series, covering...