Competencies and objectives

Provisional information. Pending approval.

 

Course context for academic year 2026-27

The prerequisites for this course include knowledge of Real Analysis, both in one and several variables, as well as Point-Set Topology. The aim of the course is to provide students with a basic foundation in Complex Analysis, focusing on Cauchy theory, developed from the notion of line integrals along paths, Cauchy’s general theorem, and its applications to residue theory. Power series will also be studied as a fundamental tool in the development of the theory, together with the geometric interpretation of holomorphic functions and their relation to classical models in physics, infinite products, and an introduction to the theory of entire functions.

 

 

Learning outcomes / Course competencies (verified by ANECA in official undergraduate and Master’s degrees) for academic year 2026-27

Specific Competences (CE)

  • CE1 : Understand and use mathematical language. Acquire the capacity to enunciate propositions in different fields of Mathematics, to construct demonstrations and transmit the mathematical knowledge acquired.
  • CE10 : Communicate, both orally and in writing, mathematical knowledge, procedures, results and ideas.
  • CE11 : Ability to solve academic, technical, financial and social problems using mathematical methods.
  • CE14 : Solve qualitative and quantitative problems using previously developed models.
  • CE2 : Understand rigorous demonstrations of certain classical theorems in different fields of Mathematics.
  • CE3 : Assimilate the definition of a new mathematical object in terms of others already known and be able to use said object in different contexts.
  • CE5 : Propose, analyse, validate and interpret models of simple real-life situations, using the most appropriate mathematical tools for the purpose.
  • CE6 : Solve mathematical problems using basic calculus skills and other techniques, planning their resolution according to the tools available and any time and resource restriction.
  • CE9 : Use bibliographic search tools for Mathematics.

 

Specific Generic UA Competences

  • CGUA1 : Understand scientific English.
  • CGUA2 : Possess computer skills relevant to the field of study.
  • CGUA3 : Acquire or possess basic Information and Communications Technology skills and correctly manage the information gathered.

 

Generic Degree Course Competences

  • CG1 : Develop the capacity for analysis, synthesis and critical reasoning.
  • CG2 : Show the capacity for effective and efficient management/direction: entrepreneurial spirit, initiative, creativity, organisation, planning, control, decision making and negotiation.
  • CG3 : Solve problems effectively.
  • CG4 : Show capacity for teamwork.
  • CG5 : Commitment to ethics, the values of equality and social responsibility as a citizen and professional.
  • CG6 : Self-learning.
  • CG7 : Show the capacity to adapt to new situations.
  • CG9 : Show the ability to transmit information, ideas, problems and solutions to both specialist and non-specialist audiences.

 

 

 

Learning outcomes (Training objectives)

No data

 

 

Specific objectives stated by the academic staff for academic year 2026-27

This course has as its main objective the presentation of the principal topics in the Theory of Functions of a Complex Variable. To this end, students are expected to master basic operations with complex numbers, inequalities, geometric representations, as well as the computation of roots and logarithms. Knowledge of the exponential function and elementary functions is also required. Building on these foundations, the aim is to develop the notion of analytic function and the Cauchy–Riemann equations, leading to the study of Cauchy theory based on line integrals along paths. The applications of this theory, through the study of singularities, the Laurent expansion, and its application to residue theory, constitute an essential objective. Attention will also be given to the geometric interpretation of holomorphic functions and their main local properties, as well as to the most common transformations of this type. Finally, the study of basic properties of infinite products will lead to the representation of entire functions in product form, which constitutes another objective of the course.

 

 

General

Code: 25030
Lecturer responsible:
Sepulcre Martínez, Juan Matías
Credits ECTS: 6,00
Theoretical credits: 1,32
Practical credits: 1,08
Distance-base hours: 3,60

Departments involved

  • Dept: Mathematics
    Area: Mathematical Analysis
    Theoretical credits: 1,32
    Practical credits: 1,08
    This Dept. is responsible for the course.
    This Dept. is responsible for the final mark record.

Study programmes where this course is taught