Complex Variable and Transforms

Theorethical hours: 20 h.
Exercises hours: 20 h.
Personal working hours: 70 h.

PRERREQUISITES AND RECOMMENDED PREVIOUS KNOWLEDGE

Linear Algebra, Differential Calculus, Integral Calculus, Vector Calculus.

GENERAL DESCRIPTION OF THE COURSE

An introductory course to the theory of Complex Variable and Transforms Theory (Fourier series, Fourier transform, Laplace transform and Z-transform), with applications.

OBJECTIVES: KNOWLEDGE AND SKILLS

• To introduce the student in the study of Complex Analysis, in particular, complex series and integrals.
• To know the Theory of Transforms, in particular Fourier series, Fourier transform, Laplace transform and Z-transform. 
• To apply these tools to the solution of differential and difference equations.

TEACHING MATERIAL

The students receive course notes including the mathematical concepts and the theorems needed to solve the exercises. They also have basic reference texts to facilitate the understanding of the concepts. A list of complementary bibliography completes the reference texts. A list of exercises is provided with some hints for the more difficult problems. Finally, the students have the solutions of almost all problems in a separate list.

 PRACTICAL ASSIGMENTS AND ASSESSMENT ACTIVITIES

The students have several assessment tests with its solutions in order to check that they have acquired the necessary capabilities.