Analysis, PDE and Mathematical Physics at MSU

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. Casorati-Weierstrass theorem, Arzela-Ascoli 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: Cauchy-Kowalewski theorem. Characteristics. Initial-boundary 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, Riesz-Fisher theorem, Fourier series operators. Banach spaces: Hahn-Banach theorem, open mapping and closed graph theorems, Banach-Steinhaus theorem.

MTH 929, Complex Analysis II
Description: Phragmen-Lindelof method. Hadamard's theorem, Runge's thoerem, Weierstrass factorization theorem, Mittag-Leffler theorem, and Picard's theorem. Poisson integrals, Harnack's inequality, Dirichlet problem. Hp-spaces and Blaschke products.

MTH 936, Complex Manifolds II
Description: Riemann surfaces, Serre duality, Riemann-Roch 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, Littlewood-Paley theory, T1 theorem, and, time permitting, Tb theorems.