This is a graduate mathematics course for subsea engineers covering linear algebra, ordinary differential equations, Laplace Transforms, Fourier series, linear systems analysis, partial differential equations, analytical and computational solutions to PDEs.
Linear Algebra and Matrix Analysis: A quick review and summary of linear algebra and matrix analysis will be covered in this unit. Vector spaces, linear operators, basic matrix algebra and function are some of the topics to study.
Ordinary Differential Equations: In this unit, solution to ODE using separation of variables and derivation of the Laplace transform, Laplace transform of signal and systems will be extensively explained. Introduction to transfer functions, definition and applications of poles and zeros and solutions to ODE using Laplace transforms will be covered. Connections between time domain and frequency domain, including forward and backward Fourier transforms will be presented.
Partial Differential Equations: In this section, the solution of differential equation typically encountered in the physical sciences and engineering is extended to situations involving more than one independent variable. The discussion of this unit will include analytical and computational solutions to partial differential equations (PDE).