The course is held in two parts. The first part of the course covers
review of the differential equations and linear algebra undergraduate topics: First-order
and second order ordinary differential equations and their solutions. Laplace
transforms and power series solutions. The linear algebra topics (the system
solutions, vectors etc.), as well as their examples of applications in the
field of engineering. In the second part, the
higher order linear
differential equations with variable coefficients, higher order nonlinear
differential equations, Laplace Transforms, inverse Laplace transforms,
Convolution and integral equations, solution of differential equations systems
with Laplace transform, initial value series solutions of differential
equations are discussed.