A three-quarter sequence covering advanced linear algebra and matrix analysis, ordinary differential equations (existence and uniqueness theory, linear systems, numerical approximations), Fourier analysis, introductions to functional analysis and partial differential equations, distribution theory.

Prerequisite: MATH 426 and familiarity with complex analysis at the level of 427 (the latter may be obtained concurrently).

Texts:

Autumn:

Horn and Johnson, Matrix Analysis
Coddington and Levinson, Theory of Ordinary Differential Equations
Birkhoff and Rota, Ordinary Differential Equations

Winter:

Jones, Lebesgue Integration on Euclidean Space
Riesz and Sz.-Nagy, Functional Analysis

Spring:

Friedlander, Theory of Distributions