ACM702 Ordinary and Partial Differential Equations

[3–0, 3 cr.]

Topics in ODEs are: Linear systems (exponential of operators, diagonalization, Jordan forms, stability theory, etc.), non-linear systems (existence and uniqueness theorem, continuous dependence on initial conditions and parameters, linearization, stability and Lyapunov functions, etc.), and boundary-value problems. Topics in PDEs include: Boundary and initial-value problems, types of PDEs, well-posed and ill-posed problems, the Sturm-Liouville theory, Green’s functions, solutions of parabolic, elliptic, and hyperbolic equations.