Competencies and objectives
- Course context for academic year 2021-22
- Course content (verified by ANECA in official undergraduate and Master’s degrees)
- Learning outcomes (Training objectives)
- Specific objectives stated by the academic staff for academic year 2021-22
Course context for academic year 2021-22
The prerequisites of this subject are: a course of real analysis of one and several variables and a course of topology. The objective is to provide to the student the basic training on complex analysis through the elementary theory of Cauchy, based on the notion of integral along a path, general Cauchy theorem and its applications to the theory of residues. Knowledge of the conformal mapping, infinite products, the theory of entire functions will be the topics to conceptualize this course.
Course content (verified by ANECA in official undergraduate and Master’s degrees)
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 knowledge related to the field of study.
- CGUA3 : Acquire or posses basic ICT (Information and Communication technology) skills and manage the information obtained appropriately.
Generic Degree Course Competences
- CG1 : Develop the capacity for analysis, synthesis and critical reasoning.
- CG2 : Show the ability for effective and efficient direction/management: entrepreneurial spirit, creativity, organisation, planning, control, decision making and negotiation.
- CG3 : Resolve problems effectively.
- CG4 : Show ability for teamwork.
- CG5 : Commitment to ethics, the values of equality and social responsibility as a citizen and as a professional.
- CG6 : Learn autonomously.
- CG7 : Show the ability to adapt to new situations.
- CG9 : Demonstrate 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 2021-22
This course aims primarily to present the main topics of the Theory of Complex Variable Functions. Therefore, you will need to master the basic operations with complex numbers, inequalities, geometric representations, and calculation of roots and logarithms. Knowledge of the exponential function and elementary functions are also specified. From here the aim is to assimilate the notion of analytic function and the Cauchy-Riemann equations, to pass to the study of Cauchy theory based on the integral along a path. The applications of this theory by studying the notion of singularity, the Laurent expansion and its final application to the residue theory is an essential goal. Knowing the notion of conformal transformation jointly with the most usual mappings of that kind is also a goal of our interest. The basic properties of infinite products to reach the representation as a product of an entire function is another objective pursued.
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