Introduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma. Stability of equilibria by Lyapunov's first and second methods. Feedback linearization. Application to nonlinear circuits and control systems. Alternate years. Description from course website: This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Introduction to theories of syntax underlying work currently being done within the lexical-functional and government-binding frameworks. Organized into three interrelated parts, each focused upon a particular area of concern: phrase structure; the lexicon; and principles and parameters. Grammatical rules and processes constitute a focus of attention throughout the course that serve to reveal both modular structure of grammar and interaction of grammatical components. This course is concerned with the concepts and principles which have been of central significance in the recent development of syntactic theory, with special focus on the "Government and Binding" (GB) / "Principles and Parameters" (P&P) / "Minimalist Program" (MP) approach. It is the first of a series of two courses (24.951 is taught during the Fall and 24.952 is taught in the Spring). This course deals mostly with phrase structure, argument structure and its syntactic expression, including "A-movement". Though other issues (e.g. wh-movement, antecedent-contained deletion, extraposition) may be mentioned during the semester, the course will not systematically investigate these topics in class until 24.952. The goal of the course is to understand why certain problems have been treated in certain ways. Thus, on many occasions a variety of approaches will be discussed, and the (recent) historical development of these approaches are emphasized.

LEARNING OBJECTIVE: Identify and distinguish between a parameter and a statistic.

LEARNING OBJECTIVE: Explain the concepts of sampling variability and sampling distribution.

This page collects together useful reference materials and examples for using Pencil Code. These are materials for an educator to use.

During the early days of the coronavirus pandemic, we all made sacrifices to slow the spread of the virus and to flatten the curve of infections.The curve itself appears in the susceptible-infected-recovered (SIR) model – a simple epidemiological model that explains some of the basic dynamics of infectious disease. Curve-flattening effects of mitigation measures such as social distancing, mask wearing, and hand washing can be seen in the dynamics of the SIR model as can the phenomenon of herd-immunity.In this activity, students are encouraged to derive the SIR model from scratch and to explore dynamical features of the model such as curve flattening and herd immunity.These resources were created by Dr. Robert Kipka of Lake Superior State University. They are intended for high school students and teachers. Calculus or familiarity with families of functions such as logarithms is not required. However, in spite of the relatively modest mathematical background called for, this activity may be challenging.It may help to complete the Three Weeks in March activity before beginning.

Three Weeks in March is a data-driven approach to modeling the spread of coronavirus cases in the United States.In this activity, students will use a difference equation to model day-to-day changes in the known cases of coronavirus within U.S. borders, as reported by the Centers for Disease Control and Prevention, during the first three weeks of March, 2020. The solution to this difference equation is an exponential model. The activity can serve as an introduction to exponential models.The main goals of this activity are to:Learn the idea of difference equation;Model exponential growth using a difference equation;Simulate exponential growth and estimate a parameter value using software.These resources were created by Dr. Rob Kipka of Lake Superior State University.