MATH 216 - Introduction to Analysis

3 units (fi 6)(EITHER, 3-0-0)

Sets and functions. Induction. Axiomatic introduction of the real numbers. Sequences and series. Continuity and properties of continuous functions. Differentiation. Riemann integral. Corequisite: One of MATH 101, 115, 136, 146, 156 or SCI 100. Note: This course may not be taken for credit if credit has already been obtained in MATH 117. Credit can only be obtained in one of MATH 216 or MATH 314.

MATH 539 - Applied Functional Analysis

3 units (fi 6)(EITHER, 3-0-0)

Linear part:structure of function spaces, Sobolev spaces, embeddings, topologies, linear operators, adjoint and inverse operators, spectra, distributions, semigroup theory, integral equations, well-posedness and the notion of a solution. Nonlinear part: inequalities, Frechet and Gateaux derivatives, fixed point theorems. Applications from mechanics, reaction-diffusion equations, the Navier-Stokes equations, nonlinear Schrödinger equation. Prerequisite: MATH 438 or equivalent.