Establish the fundamentals on advanced mathematical operations and topics, such as series expansion, Leibniz' rule, averaging, special functions and distributions.

Develop a mathematical toolbox for solving linear initial and boundary value problems, along with partial differential equations, analytically.

Apply the methods of analysis for nonlinear equations, such as perturbation methods, numerical root solving and numerical integration for IVPs, BVPs and PDEs.

Obtain information about advanced mathematical topics, such as integral transforms, discrete systems and inverse problems.

Ability to read and reproduce reports and analyses in literature related to engineering mathematics.