ORDINARY DIFFERENTIAL EQUATIONS

Prerequisites & course information

Requisites: ( MATH 320 , 340 , 341 , 345 , or 375 ) and ( MATH 322 , 376 , 421 , or 521 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Spring 2026 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in ordinary differential equations (e.g., systems of differential equations, dependence on initial conditions, exponentials of matrices, Lyapunov functions, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., that a function is a solution to an ode, local and global stability of an equilibrium, that an initial value problem has a unique solution, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of ordinary differential equations (e.g., the existence and uniqueness theorem, Hartman-Grobman theorem). Moreover, recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use such theorems in the context of longer arguments by examining their premises (e.g., differentiable dependence upon initial conditions, checking stability via Lyapunov functions, etc.). Audience: Both Grad & Undergrad 5. Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, etc.). Audience: Both Grad & Undergrad 6. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 7. Identify applications of course content in current areas of research. Audience: Graduate Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in ordinary differential equations (e.g., systems of differential equations, dependence on initial conditions, exponentials of matrices, Lyapunov functions, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., that a function is a solution to an ode, local and global stability of an equilibrium, that an initial value problem has a unique solution, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of ordinary differential equations (e.g., the existence and uniqueness theorem, Hartman-Grobman theorem). Moreover, recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use such theorems in the context of longer arguments by examining their premises (e.g., differentiable dependence upon initial conditions, checking stability via Lyapunov functions, etc.). Audience: Both Grad & Undergrad 5. Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, etc.). Audience: Both Grad & Undergrad 6. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 7. Identify applications of course content in current areas of research. Audience: Graduate