Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 414 and MTH 421
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.
Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 847 or approval of department
Recommended Background:
MTH 828
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.
Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 847 or approval of department
Recommended Background:
MTH 828
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.