Cambridge Maths Academy

수학 모음 (Maths collection) 전체보기 For a function which depends on two variables $(x,y)$, $$ \textrm f = \textrm f(x,y) $$ we find the critical points by considering 2-dimensional gradient and second-order derivatives. (In 1D, the critical points are usually called the stationary points.) (i) Critical points: $$ \begin{align} \nabla \textrm f = \left( \frac{ \partial \textrm f }{ \partial x }, \frac{..

수학 모음 (Maths collection) 전체보기 This little investigation has been motivated by Exercise 7B, Challenge in CP2 §7.2 Second-order homogeneous differential equations. Question 1. What happens with a first-order differential equation with complex constant coefficients? $$ \begin{align} (a_1 + ia_2) \frac{ \textrm{d} y }{ \textrm{d}x } + (b_1 + ib_2) y &= 0 \end{align} $$ Method 1. Using matrix notatio..