Credits:
Total Credits:
Credits: 3 Lecture/Recitation/Discussion Hours:3
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.
Credits:
Total Credits:
Credits: 3 Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 847 or approval of department
Description:
Sobolev spaces and embedding theorems, weak solutions of second order elliptic equations in divergence form (existence, uniqueness, and regularity), Fredholm alternative, maximum principle, calculus of variations, Euler-Lagrange equations.
Credits:
Total Credits:
Credits: 3 Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 847 or approval of department
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Sobolev spaces and embedding theorems, weak solutions of second order elliptic equations in divergence form (existence, uniqueness, and regularity), Fredholm alternative, maximum principle, calculus of variations, Euler-Lagrange equations.