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Mathematics and climate. (English) Zbl 1285.86001

Other Titles in Applied Mathematics 131. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-611972-60-3/pbk). xx, 295 p. (2013).
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.
Exercises supplement theory. Some typical exercises are given below:
1.
Discuss the dynamics of the equation \(\ddot x=x\).
2.
The strength of a preferred climate pattern is quantified by its index. Explain how these indices can be used to detect telecommunications.
3.
Find conditions for the parameters such that the velocity field is divergence free.
4.
Establish Rodrigués formula for Legendre polynomial.
5.
Show that \(\int^1_{-1} (P_n(y))^2 dy={2\over 2n+1}\), where \(P_n\) is the Legendre polynomial of degree \(n\).

MSC:

86-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
00A79 Physics
00A69 General applied mathematics
00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
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