Differential Equations

Differential equations arise as common models in the physical, mathematical, biological and engineering sciences. This subject covers linear differential equations, both ordinary and partial, using concepts from linear algebra to understand the structure of the general solutions. It balances basic theory with concrete applications. Topics include: - linear ordinary differential equations and initial-value problems, including systems of first-order linear ordinary differential equations; - Taylor series solutions of linear ordinary differential equations; - Laplace transform methods for solving dynamical models with discontinuous inputs; - boundary-value problems for linear ordinary differential equations and their interpretation in terms of eigenvalues and eigenfunctions; - Fourier series solutions of certain linear partial differential equations on spatially bounded domains using separation of variables and eigenfunction expansion; - Fourier transform solutions of certain linear partial differential equations on unbounded spatial domains.