Differential Equations

This course introduces the fundamental concepts and methods of ordinary differential equations used to model and analyze dynamic systems.

Students develop quantitative reasoning and problem-solving skills through the study of first- and higher-order differential equations, initial-value problems, qualitative methods, Laplace transforms, and systems of linear differential equations.

Topics include separable, linear, and exact equations; direction fields; equilibrium and stability; second-order linear and nonhomogeneous equations; and systems of differential equations.

By the end of the course, students will understand how differential equations represent changing systems, select appropriate solution methods, and interpret the behavior of solutions.

Emphasis is placed on applications in mathematics, engineering, physics, biological sciences, computer science, economics, and other quantitative fields.