TECHNIQUES IN ORDINARY DIFFERENTIAL EQUATIONS

Prerequisites & course information

Requisites: MATH 222 or graduate/professional standing Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the formal definitions, properties, and theorems associated to ordinary differential equations (e.g. systems of linear ODEs, homogeneous/inhomogeneous ODEs, series solutions, Laplace transform, equilibria, etc.). Audience: Undergraduate 2. Verify if a mathematical object has a given property used in ODEs (e.g. that a problem is well-posed, that a given function is a solution, etc.). Audience: Undergraduate 3. Apply algorithms to describe the solutions to various types of ODEs (e.g. separable equations, linear systems, boundary value problems, etc.). Audience: Undergraduate 4. Check the premises of theorems used in elementary ODEs in order to apply their conclusions (e.g., that a given equation satisfies conditions which guarantee the existence of a solution). Audience: Undergraduate 5. Apply the presented techniques for solving ODEs to solve problems from physics (e.g. spring problems, pendulum problems, etc.). Audience: Undergraduate 6. Express informal mathematical arguments in English using appropriate mathematical terminology and notation. Audience: Undergraduate Learning Outcomes: 1. Recall and state the formal definitions, properties, and theorems associated to ordinary differential equations (e.g. systems of linear ODEs, homogeneous/inhomogeneous ODEs, series solutions, Laplace transform, equilibria, etc.). Audience: Undergraduate 2. Verify if a mathematical object has a given property used in ODEs (e.g. that a problem is well-posed, that a given function is a solution, etc.). Audience: Undergraduate 3. Apply algorithms to describe the solutions to various types of ODEs (e.g. separable equations, linear systems, boundary value problems, etc.). Audience: Undergraduate 4. Check the premises of theorems used in elementary ODEs in order to apply their conclusions (e.g., that a given equation satisfies conditions which guarantee the existence of a solution). Audience: Undergraduate 5. Apply the presented techniques for solving ODEs to solve problems from physics (e.g. spring problems, pendulum problems, etc.). Audience: Undergraduate 6. Express informal mathematical arguments in English using appropriate mathematical terminology and notation. Audience: Undergraduate