MATH 432 - Intermediate Differential Equations

3 units (fi 6)(EITHER, 3-0-0)

Elementary existence and uniqueness theorems. Systems of equations, stability, perturbation theory. Introduction to numerical methods. Introduction to phase plane analysis. Prerequisite: One of MATH 201, MATH 334, MATH 336, or MA PH 251

MATH 436 - Intermediate Partial Differential Equations

3 units (fi 6)(FIRST, 3-0-0)

Partial differential equations as physical models. Introduction to basic generalized functions. Theory of linear and quasi-linear first-order equations: general solution, initial value problem, generalized solutions and propagation of singularities, characteristic surfaces, shock formation. Theory of fully nonlinear first order equations: complete solution and the initial value problem. Hamilton-Jacobi equation and its applications. Second order linear equations in n dimensions: classification, canonical form, characteristic surfaces and shock formation, initial and boundary value problem. Prerequisite: MATH 300 or MATH 337.