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.
Remote students can contact the instructor to discuss whether the class can be taken remotely in a way that makes sense for them.
Learning Outcomes:
In this course, you will:
• 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
• Help develop proofs for 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
Delivery Method: Fully in-person
Prerequisites: To be ready for this course you must have taken calculus (AP/IB credit from high school is acceptable) and taken at least one math class at Bennington. Strong algebra, graphing, and differentiation skills are helpful. Students who take Differential Equations in the fall will find this a natural follow-up course but it is not a required prerequisite. To express interest in the course email Katie (kmontovan@bennington.edu) on the day of 4000-level registration. Students will be chosen for the course based on satisfactory prerequisite skills and preference will be given to students who email on a first come first serve basis.
Course Level: 4000-level
Credits: 4
M/Th 10:00AM - 11:50AM (Full-term)
Maximum Enrollment: 18
Course Frequency: Every 2-3 years
Categories: All courses , Fully In-Person , Mathematics
Tags: applications , chaos , non-linear systems , problem solving