Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 ...

Linear Algebra Vector spaces, linear transformation, matrix representation, inner product spaces, isometries, least squares, generalised inverse, eigen theory, quadratic forms, norms, numerical ...

Abstract Using the axiom of choice, we prove a generalized converse of the well-known fact that if X is a finite-dimensional vector space, then any linear functional on X is continuous with respect to ...

Banach space theory, with its emphasis on complete normed vector spaces, provides the natural setting for addressing problems in functional analysis, differential equations and beyond.

Properties of the real numbers, infimum and supremum of sets. Numerical sequences and series. Limits of functions, continuous functions, intermediate value theorem, uniform continuity. Differentiation ...