Mathematics and climate (Q2864118)

The main purpose of writing this textbook is to discuss current issues of climate science. Mathematical topics include dynamical systems, bifurcation theory, Fourier analysis, conservation laws, regression analysis, extreme value theory in order to pursue climate science. Climate science comprises earth's energy balance, temperature distribution, ocean circulation patterns, ice caps, carbon cycle, biological premps.NEWLINENEWLINE Exercises supplement theory. Some typical exercises are given below:{\parindent=5mm \begin{itemize}\item[1.] Discuss the dynamics of the equation \(\ddot x=x\). \item[2.] The strength of a preferred climate pattern is quantified by its index. Explain how these indices can be used to detect telecommunications. \item[3.] Find conditions for the parameters such that the velocity field is divergence free. \item[4.] Establish Rodrigués formula for Legendre polynomial. \item[5.] Show that \(\int^1_{-1} (P_n(y))^2 dy={2\over 2n+1}\), where \(P_n\) is the Legendre polynomial of degree \(n\).NEWLINENEWLINE\end{itemize}}