APPLIED MATHEMATICAL ANALYSIS 1: VECTOR AND COMPLEX CALCULUS

Prerequisites & course information

Requisites: ( MATH 234 and 320 ), ( MATH 234 , 319 , and 340 ), ( MATH 234 , 319 , and 345 ), ( MATH 319 and 341 ), MATH 376 , or graduate/professional standing Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Honors - Accelerated Honors (!) Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the formal definitions, properties, and theorems associated to elementary vector calculus including complex calculus. Audience: Undergraduate 2. Verify if a mathematical object has a given property used in complex and vector calculus (e.g., that a matrix is invertible, that a set of vectors is linearly independent, that a vector field is conservative, etc.) Audience: Undergraduate 3. Check the premises of theorems used in complex and vector calculus in order to apply their conclusions (e.g., that a vector field is conservative and so one can apply the fundamental theorem of path integrals). Audience: Undergraduate 4. Resolve algebraic statements and perform standard computations related to vector and complex calculus (e.g., compute residues, perform basis changes, use multivariate substitution in integrals, compute surface areas, etc.). Audience: Undergraduate 5. 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 elementary vector calculus including complex calculus. Audience: Undergraduate 2. Verify if a mathematical object has a given property used in complex and vector calculus (e.g., that a matrix is invertible, that a set of vectors is linearly independent, that a vector field is conservative, etc.) Audience: Undergraduate 3. Check the premises of theorems used in complex and vector calculus in order to apply their conclusions (e.g., that a vector field is conservative and so one can apply the fundamental theorem of path integrals). Audience: Undergraduate 4. Resolve algebraic statements and perform standard computations related to vector and complex calculus (e.g., compute residues, perform basis changes, use multivariate substitution in integrals, compute surface areas, etc.). Audience: Undergraduate 5. Express informal mathematical arguments in English using appropriate mathematical terminology and notation. Audience: Undergraduate