Applications of differential equations (including ODEs) are the main objective of the course; however, accordingly the following are included to a certain extent:

• Linear and nonlinear partial differential equations of mathematical physics.
• Dimensional analysis, dimensionless quantities, reduction of models.
• Classification of linear second-order partial differential equations.
• Separation of variables for linear problems. Sturm-Liouville theory and its applications.
• Method of characteristics for linear and quasilinear PDEs.
• Method of Green’s functions and its applications.
• Method of conformal mappings and its applications.
• Travelling wave solutions of time dependent PDEs. Reductions of PDE problems to lower-dimensional and ODE problems.
• Asymptotic analysis: basic ideas, regular and singular perturbations, boundary layers.