The mathematical sub-discipline of differential equations is foundational in the study of applied mathematics for engineers. Differential equations arise in a variety of contexts, some more theoretical and some of practical interest. The qualitative and quantitative study of differential equations incorporates an elegant mixture of linear
algebra and advanced calculus. For this reason, it is expected that the student has already completed courses in (i) linear algebra; (ii) multivariable calculus; and (iii) introductory differential equations.
The course will cover advanced topics of first order and second order ODEs like initial and boundary value problem and stability of solutions and phase portrait of them. A classification will be provided of the various existing types of methods for exploring solutions in connection with the various types of scientific and technological mathematical models that utilize them. The content of the course includes power series techniques as well as the Laplace transformation method for acquiring solutions of ODEs.
Furthermore, PDEs will be studied to model problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. PDEs categories will be connected with a wide variety of interesting and important phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. All these seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. The content of the course will cover techniques that refer to Elliptic, Parabolic Partial Differential Equations and Hyperbolic Partial Differential Equations as well as Initial and Boundary Conditions. The course will be delivered with lectures that will deliver the necessary theoretical background. However, all the lectures and the tutorials will encapsulate many examples with a software capable to perform symbolical calculations in order to capture the interest and motivate engineers.