Syllabus

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Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Course Description

Analysis of cooperative processes that shape the natural environment, now and in the geologic past. Emphasizes the development of theoretical models that relate the physical and biological worlds, the comparison of theory to observational data, and associated mathematical methods. Topics include carbon cycle dynamics; ecosystem structure, stability and complexity; mass extinctions; biosphere-geosphere coevolution; climate change. Employs techniques including stability analysis; scaling; null model construction; time series and network analysis.

Objectives

The principal objectives of this course are twofold. First, it provides students with an understanding of the mechanisms that underly the organization of the natural environment; i.e., how nature works. Second, it introduces students to methods of quantitative analysis that are useful for investigating how any system works. The course teaches students how to identify fundamental phenomena, how to formulate theoretical models, and how to quantitatively test models by comparison to observations. Students are provided with real datasets so that they can engage in these processes independently and creatively.

A secondary but no less important objective is to provide students with a unified view of environmental science. The unification is made possible by emphasizing aspects of earth, atmospheric, and planetary sciences that collectively act to create the natural environment, both physical and biological. We feature several of the great advances of 20th-century science (e.g., plate tectonics, climate cycles, and chaos theory) and introduce modern mathematical models of complex phenomena that remain to be understood. In so doing, we teach methods of analysis that are applicable throughout science and engineering.

Prerequisites and Corequisites

The course requires elementary physical reasoning, and therefore 18.01 Single Variable Calculus is a prerequisite. The course also requires mathematical experience at the level of 18.03 Differential Equations. However, because all relevant 18.03-type concepts will also be developed here, 18.03 is a co-requisite rather than a pre-requisite.

Requirements

There are quasi-weekly problem sets, a take-home midterm exam, and a final project due on the last day of classes. Whereas the problem sets will be directed towards developing specific skills, the mid-term and final project will ask that you use tools developed previously to perform independent analysis of your own design.

Overview and Calendar

The first part of the course (topics 2–4) is loosely organized around Earth's carbon cycle: the injection of CO₂ into the atmosphere and oceans by volcanoes and other tectonic processes, the exchange CO₂ between the atmosphere and oceans, and the runoff of dissolved carbon from rivers into the oceans. In each case, we emphasize the role of diffusion, perhaps the simplest and most important mode of transport in the natural environment.

In the second part of the course (topics 5-6) we focus on climate cycles, their foundation in orbital dynamics, and methods for the analysis of periodic phenomena in general. We learn how to compute and interpret power spectra, one of the most important tools used in the analysis of any system that evolves with time.

In the final part of the course (topics 7–8) we discuss the physical basis of ecological organization, the dynamics of ecological communities, and nonlinear dynamics in general. Here we meet concepts of scaling, stability, and the geometry of natural networks. The course ends with an introduction to the greatest intellectual achievement arising from the study of environmental dynamics: the theory of chaos.

Grading