A study of analytic functions, power series, complex integration, conformal mapping, and the calculus of residues with applications to physical science. MATH210 and one mathematics course numbered 250 or above. Advanced calculus of functions of more than one variable. Topics include the geometry of Euclidean space, vector fields, line and surface integrals, curvature and differential geometry. Rigorous development of the topology of the real line, theory of metric spaces, and the foundations of calculus.
Attention is given to constructing formal proofs.
A course of varying content reflecting the needs and interests of students. Time permitting, topics in stochastic processes or statistics are introduced. A course of varying content reflecting the needs and interests of students. Attention is given to the construction of formal proofs. Selected topics in ordinary and partial differential equations including Sturm-Liouville problems, Fourier series, Laplace transforms, boundary value problems, and special functions of mathematical physics.