Ordinary differential equations (ODEs) arise in mathematics and the natural and social sciences. They describe dynamically changing phenomena, such as motion, growth, and decay, by relating differentials, derivatives, and functions. Essential in physics, biology, economics, chemistry, and engineering, ODEs are crucial for both theoretical and practical problem-solving. This course covers first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, existence and uniqueness theorems, and numerical solutions. Students will learn to formulate, solve, and interpret differential equations in various scientific and engineering contexts.
MATH 2400 or APPM 2350, along with MATH 2130/3130 or MATH 2135/3135, or instructor permission, is required.
Elementary Differential Equations and Boundary Value Problems by William E. Boyce, Richard C. DiPrima, Douglas B. Meade (11th Edition, 2017).
This course will follow a flipped classroom model, where students study core concepts before class, enabling deeper exploration and application during in-person sessions. Active engagement in small mathematics groups is central to this approach, reflecting research-backed best practices for effective learning. A meta-analysis of 225 studies demonstrates the benefits of active learning, with significant improvements in outcomes across science, engineering, and mathematics disciplines (see https://www.pnas.org/content/111/23/8410). Additional research on undergraduate STEM courses highlights the effectiveness of collaborative, small-group learning environments. This innovative pedagogical approach, successfully implemented over recent years, continues to deliver encouraging results.