Explore three different mathematical methods for solving the simple harmonic oscillator, one of the most important models in physics and applied mathematics. This guide compares the approaches step by ...

A series of unsolved puzzles in number theory called Diophantine problems date back to 3,700 years ago. Over the years mathematicians have whittled away at them, and recent work has made significant ...

For millennia, humanity has observed the changing phases of the Moon. The rise and fall of sunlight reflected off the Moon, as it presents its different faces to us, is known as a “phase curve”.

Most mathematical models do not admit exact solutions. Asymptotic and perturbation methods provide powerful techniques for obtaining approximate solutions, which allow one to draw physical conclusions ...