Stability theory occupies a central role in the analysis of differential equations and wave equations, serving as the cornerstone for understanding the long‐term behaviour of dynamical systems. At its ...

Solve \(\sqrt 3 \cos x + \sin x = \sqrt 2\), for \(0 \le x \le 2\pi\). First of all we need to put \(\sqrt 3 \cos x + \sin x\) into the form \(k\cos (x - \alpha ...

The form you should use may be given to you in a question, but if not, any one will do. If in doubt, \(k\cos (x - \alpha )\) usually works. These worked examples show the processes you'll need to go ...