Courses 2010 Spring
MTH 132, Calculus I
Description: Application of partial derivatives, integrals, optimization of functions of several variables and differential equations.
MTH 133, Calculus II
Description: Applications of the integral and methods of integration. Improper integrals. Polar coordinates and parametric curves. Sequences and series. Power series.
MTH 234, Multivariable Calculus
Description: Vectors in space. Functions of several variables and partial differentiation. Multiple integrals. Line and surface integrals. Green's and Stokes's theorems.
MTH 829, Complex Analysis I
Description: Cauchy theorem, identity principle, Liouville's theorem, maximum modulus theorem. Cauchy formula, residue theorem, Rouche's theorem. CasoratiWeierstrass theorem, ArzelaAscoli theorem. Conformal mapping, Schwarz lemma, Riemann mapping theorem.
MTH 842, Boundary Value Problems II
Description: Methods for solving boundary and initial value problems for ordinary and partial differential equations.
MTH 849, Partial Differential Equations
Description: CauchyKowalewski theorem. Characteristics. Initialboundary value problems for parabolic and hyperbolic equations. Energy methods, boundary value problems for elliptic equations, potential theory. Green's function, maximum principles, Schauder's method.
MTH 920, Functional Analysis I
Description: Hilbert spaces: Riesz representation theorem, Parseval's identity, RieszFisher theorem, Fourier series operators. Banach spaces: HahnBanach theorem, open mapping and closed graph theorems, BanachSteinhaus theorem.
MTH 929, Complex Analysis II
Description: PhragmenLindelof method. Hadamard's theorem, Runge's thoerem, Weierstrass factorization theorem, MittagLeffler theorem, and Picard's theorem. Poisson integrals, Harnack's inequality, Dirichlet problem. Hpspaces and Blaschke products.
MTH 936, Complex Manifolds II
Description: Riemann surfaces, Serre duality, RiemannRoch theorem. Weierstrass points, Abel's theorem, Plucker formulas. Hermitian metrics, connections, curvature, Hodge theorem. Kaehler metrics, Kodaira vanishing theorem, Chern classes.
MTH 992, Special topics in Analysis
Description: Singular integrals, Hardy spaces and BMO, weighted inequalites, LittlewoodPaley theory, T1 theorem, and, time permitting, Tb theorems.
