I'm given the following and I 'm asked to linearize around $x_1=0,x_2=0$$$x_1=x_2^2 \\ x_2=e^{x_1}+u$$ Only thing I know how to do is find the value for $u$ which is $-1$. The only problems I've faced are similar to this one I can't understand linearization in which no one has answered. But still, in this one I have two equations and I don't know how I should go about this.
The solution manual gives($\dot x_{1o}=\dot x_{2o}=0):$ $$x_{2o}=0\\u_o=-e^{x_{1o}}\\\dot x_1=x_2^2=>\dot x_{1o}+Δ\dot x_1=(x_{2o}+Δx_2)^2\\\dot x_2=e^{x_1}+u=>\dot x_{2o}+Δ\dot x_2=e^{x_{1o}+Δx_1}+u_o+Δu_1$$
I can understand how he produced the two last equations but why the dots on $x_1$ and $x_2$?