A Practical Course in Differential Equations and Mathematical Modelling: Classical and New Methods. Nonlinear Mathematical Models. Symmetry and Invariance Principles

The present textbook on ordinary and partial differential equations is tailored to develop analytic skills and "working knowledge'' in both classical and Lie's methods for solving linear and nonlinear equations. It is based on lectures delivered by the author at Moscow Institute of Physics and Technology, and Blekinge Institute of Technology. The prerequisites are linear algebra and mathematical analysis with one and several variables including elements of ordinary differential equations.