TOPICS IN MULTI-VARIABLE CALCULUS AND DIFFERENTIAL EQUATIONS

Prerequisites & course information

Requisites: MATH 375 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: Spring 2026 Learning Outcomes: 1. Identify the formal definitions of mathematical objects and their properties used in integral multivariable calculus and elementary ordinary differential equations (e.g., multivariate integrals, line and surface integrals, systems of linear ODEs, etc.). Audience: Undergraduate 2. Understand and use the standard methods and tools of mathematical argument in the context of integral multivariable calculus and elementary ordinary differential equations (e.g direct and indirect methods, the construction of examples and counterexamples, induction arguments, first-order logic, set theory, and quantifiers). Audience: Undergraduate 3. Distinguish if a mathematical construct does or does not have the condition of having a particular property formally (e.g., that a vector field is conservative, that a given function is a solution, etc.). Audience: Undergraduate 4. Identify standard theorems in integral multivariable calculus and elementary ordinary differential equations (e.g., Green's theorem, the Divergence theorem, Stokes' theorem, existence and uniqueness theorem for ODEs, etc.) and recall arguments for these theorems and the underlying logic of their proofs. Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of integral multivariable calculus and elementary ordinary differential equations using the techniques of mathematical argument. Audience: Undergraduate 6. Perform standard computations in the context of integral multivariable calculus and elementary ordinary differential equations (e.g. evaluate surface and line integrals, solve simple ordinary differential equations, etc.). Audience: Undergraduate 7. Write mathematical proofs and concepts in logical, reasonable, and concise ways. Audience: Undergraduate Learning Outcomes: 1. Identify the formal definitions of mathematical objects and their properties used in integral multivariable calculus and elementary ordinary differential equations (e.g., multivariate integrals, line and surface integrals, systems of linear ODEs, etc.). Audience: Undergraduate 2. Understand and use the standard methods and tools of mathematical argument in the context of integral multivariable calculus and elementary ordinary differential equations (e.g direct and indirect methods, the construction of examples and counterexamples, induction arguments, first-order logic, set theory, and quantifiers). Audience: Undergraduate 3. Distinguish if a mathematical construct does or does not have the condition of having a particular property formally (e.g., that a vector field is conservative, that a given function is a solution, etc.). Audience: Undergraduate 4. Identify standard theorems in integral multivariable calculus and elementary ordinary differential equations (e.g., Green's theorem, the Divergence theorem, Stokes' theorem, existence and uniqueness theorem for ODEs, etc.) and recall arguments for these theorems and the underlying logic of their proofs. Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of integral multivariable calculus and elementary ordinary differential equations using the techniques of mathematical argument. Audience: Undergraduate 6. Perform standard computations in the context of integral multivariable calculus and elementary ordinary differential equations (e.g. evaluate surface and line integrals, solve simple ordinary differential equations, etc.). Audience: Undergraduate 7. Write mathematical proofs and concepts in logical, reasonable, and concise ways. Audience: Undergraduate