Mathematics and Climate is a timely textbook aimed at students and researchers in mathematics and statistics who are interested in current issues of climate science, as well as at climate scientists who wish to become familiar with qualitative and quantitative methods of mathematics and statistics. The authors emphasize conceptual models that capture important aspects of Earth's climate system and present the mathematical and statistical techniques that can be applied to their analysis. Topics from climate science include the Earth's energy balance, temperature distribution, ocean circulation patterns such as El NinoaEUR"Southern Oscillation, ice caps and glaciation periods, the carbon cycle, and the biological pump. Among the mathematical and statistical techniques presented in the text are dynamical systems and bifurcation theory, Fourier analysis, conservation laws, regression analysis, and extreme value theory. The following features make Mathematics and Climate a valuable teaching resource: Issues of current interest in climate science and sustainability are used to introduce the student to the methods of mathematics and statistics. The mathematical sophistication increases as the book progresses; topics can thus be selected according to interest and level of knowledge. Each chapter ends with a set of exercises that reinforce or enhance the material presented in the chapter and stimulate critical thinking and communication skills. The book contains an extensive list of references to the literature, a glossary of terms for the nontechnical reader, and a detailed index.
Maurizio Falcone is Professor of Numerical Analysis in the Mathematics Department of Sapienza University of Rome. He is an associate editor for the journal Dynamic Games and Applications and was a member of the scientific board of the CASPUR Consortium for Scientific Computing (2002-2012) and on the steering committee of the ESF Network ""Optimization with PDE Constraints""; (2008-2012). He has been an invited professor at ENSTA (Paris), the IMA (Minneapolis), Paris 6 and 7, PIMS (Vancouver and Banff), the Russian Academy of Sciences (Moscow), and UCLA and has coordinated international research projects with France, Russia, and the European Community (Marie Curie). He is the author of about 60 papers in international journals. His main research areas are numerical analysis, PDEs, control theory and differential games, and image processing. Roberto Ferretti is Associate Professor in Numerical Analysis at Roma Tre University. He has spent invited research periods at UCLA, IHP Paris, Goroda Pereslavlya University (Pereslavl-Zalessky, Russia),Technical University of Madrid, ENPC Paris, and ENSTA Paris. He is the author of about 35 research papers in international journals and in proceedings, most of which are on semi-Lagrangian schemes. His main research areas are numerical analysis, PDEs, control theory, image processing, and environmental fluid dynamics.
Preface; Notation; Chapter 1: Models and motivations; Chapter 2: Viscosity solutions of first-order PDEs; Chapter 3: Elementary building blocks; Chapter 4: Convergence theory; Chapter 5: First-order approximation schemes; Chapter 6: High-order SL approximation schemes; Chapter 7: Fluid Dynamics; Chapter 8: Control and games; Chapter 9: Front propagation; Bibliography; Index.
