CALCULUS--FUNCTIONS OF SEVERAL VARIABLES

Prerequisites & course information

Requisites: MATH 222 Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Intermediate L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Analyze the behavior of functions of several variables, including their asymptotic behavior, local behavior, and existence of extrema with the tools of calculus (e.g., limits and continuity of multidimensional functions, derivatives and integrals of vector valued functions, arc length and curvature, partial derivatives, tangent planes, etc.). Audience: Undergraduate 2. Describe and analyze motion in space with the tools of calculus (velocity vector and acceleration, directional derivatives and the gradient vector, etc.). Audience: Undergraduate 3. Represent and compute areas and volumes by means of multiple integrals (e.g., integration over rectangles and more general spaces, average values, integration with polar, cylindrical, and spherical coordinates, general changes of variables, etc.). Audience: Undergraduate 4. Derive relations between different physical phenomena and their integral representations (e.g., using Green's theorem, the Divergence theorem, and Stokes' theorem). Audience: Undergraduate 5. Describe physical, biological, and/or economic phenomena using mathematical models (e.g., topographical maps and level curves, Lagrange multipliers, etc.). Audience: Undergraduate 6. Offer informal mathematical arguments and formal computations in English using appropriate mathematical terminology, notation, and grammar. Audience: Undergraduate Learning Outcomes: 1. Analyze the behavior of functions of several variables, including their asymptotic behavior, local behavior, and existence of extrema with the tools of calculus (e.g., limits and continuity of multidimensional functions, derivatives and integrals of vector valued functions, arc length and curvature, partial derivatives, tangent planes, etc.). Audience: Undergraduate 2. Describe and analyze motion in space with the tools of calculus (velocity vector and acceleration, directional derivatives and the gradient vector, etc.). Audience: Undergraduate 3. Represent and compute areas and volumes by means of multiple integrals (e.g., integration over rectangles and more general spaces, average values, integration with polar, cylindrical, and spherical coordinates, general changes of variables, etc.). Audience: Undergraduate 4. Derive relations between different physical phenomena and their integral representations (e.g., using Green's theorem, the Divergence theorem, and Stokes' theorem). Audience: Undergraduate 5. Describe physical, biological, and/or economic phenomena using mathematical models (e.g., topographical maps and level curves, Lagrange multipliers, etc.). Audience: Undergraduate 6. Offer informal mathematical arguments and formal computations in English using appropriate mathematical terminology, notation, and grammar. Audience: Undergraduate