Nonlinear Dynamical Systems
Course Description
Summary
Differential equations are a powerful and pervasive mathematical tool in the sciences and are fundamental in pure mathematics as well. Almost every system whose components interact continuously over time can be modeled by a differential equation, and differential equation models and analyses of these systems are common in the literature in many fields including physics, ecology, biology, astronomy, and economics.
We will start by briefly studying the classical theory of ordinary differential equations and will spend most of our time learning dynamical systems approaches to understanding more complex non-linear systems. In this field, visual and analytical approaches are used to understand systems that cannot be solved explicitly. Students will be expected to understand concepts, engage productively in conversations about mathematical ideas, and apply the theory to problems – sometimes in ways requiring creativity and problem-solving skills.
Learning Outcomes
- Apply calculus, algebra, and graphing skills to analyze the dynamics of non-linear ordinary differential equations.
- Discuss mathematical concepts and work collaboratively to develop solutions to unfamiliar problems
- Participate in proving the core concepts covered in the course
- Communicate mathematics orally in and in writing
- Develop increasing levels of sophistication in analyzing and understanding complex systems, including developing a mathematical understanding of chaos
Prerequisites
Calculus. Strong algebra, graphing, and differentiation skills are helpful. To express interest in this course, fill out this form:
Please contact the faculty member : kmontovan@bennington.edu