Competencies and objectives
Course context for academic year 2024-25
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) for academic year 2024-25
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 2024-25
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.
General
Code:
25030
Lecturer responsible:
Sepulcre Martínez, Juan Matias
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
-
DEGREE IN MATHEMATICS
Course type: COMPULSORY (Year: 3)
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DOUBLE DEGREE IN PHYSICS AND MATHEMATICS
Course type: COMPULSORY (Year: 3)