Foundational Methods in Applied Mathematics

4 Credits.

Key mathematical techniques and formalism in multivariable calculus, linear algebra, and real analysis essential to advanced AMS courses. Basics of convergence and limits; differentiability of vector-valued functions; multiple integrals and applications; implicit and inverse function theorems; interchanges of limits; change of variables. Linear algebraic methods, including matrix operations, factorizations, and spectral and Jordan decompositions; determinants; special matrices. Constrained optimization. Emphasis is on proof, interpretation of results, and mathematical applications. Note: multivariable calculus and linear algebra are prerequisites for this course.