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Unformatted text preview: 1 Introduction 1.1 The big picture 1.1.1 What is theoretical environmental analysis? Environment: the world around us, living and nonliving. Analysis: an investigation of the component parts of a whole and their rela tions in making up the whole ( http://wordnetweb.princeton.edu ). Theoretical: mathematical, guided by physical reasoning. 1.1.2 What sort of problems do we study? We focus on problems that • teach us about the interaction of the physical and biological worlds; • exhibit interesting principles of dynamics and selforganization; and • provide opportunities for learning widely useful mathematical tools and physical concepts. 1.1.3 Why focus on theoretical analysis? Observational data is hugely important in environmental science. But these data must be understood. We focus on problems for which understanding is not merely a matter of measurement. In this course, we consider that observed data are understood when trends in the data can be quantitatively predicted by a theoretical model dependent on no more than a few parameters. 4 We therefore use mathematics for two reasons: • to concisely describe complex phenomena; and • to develop insight (predictions) by deductive reasoning. In other words: the interplay of theory and observation is a major part of this course. 1.1.4 A broad overview The course is roughly divided into three parts: • Part I is loosely organized around Earth’s carbon cycle, with an emphasis on diffusive transport. • Part II focuses on climate cycles, their relation to celestial mechanics, and the analysis of periodic phenomena. • Part III features ecological organization and dynamics, and nonlinear dynamics more generally. We proceed to point out some of the highlights of the syllabus. 1.2 Earth’s carbon cycle It is conventional to consider two carbon cycles: biological and geochemical....
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 Fall '11
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 atmospheric CO2, Ecological Organization, theoretical environmental analysis, evolution atmospheric CO2

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