Checking date: 19/03/2019


Course: 2019/2020

Advanced Mathematics
(15943)
Study: Bachelor in Telematics Engineering (215)


Coordinating teacher: MOLINA MEYER, MARCELA

Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS

Course:
Semester:

Branch of knowledge: Engineering and Architecture



Students are expected to have completed
Calculus I, Calculus II and Linear Algebra
Competences and skills that will be acquired and learning results. Further information on this link
The student should be familiar with the most important techniques in complex variable functions. Specifically, he/she should understand and manage the following basic concepts: 1. Elementary functions of one complex variable 2. Integration in the complex plane 3. Power series expansions 4. Apllications of the residue theorem The course is complemented with some basic topics in ordinary differential equations: 1. Solution of first order differential equations. 2. Solution of higher order linear differential equations. 3. Use of Laplace transform to solve linear equations with constant coefficients.
Description of contents: programme
1. FUNCTIONS OF ONE COMPLEX VARIABLE: Complex numbers. Analytic functions. Cauchy-Riemann equations. Harmonic functions. Power series and elementary functions. Complex integration. Cauchy's theorem and applications. Laurent series and calculus of residues. The residue theorem and applications. 2. ORDINARY DIFFERENTIAL EQUATIONS: Initial and boundary value problems. Existence and y unicity. Elementary solution methods. Linear equations and systems. Laplace Transform and applications.
Learning activities and methodology
The docent methodology will include: 1. MASTER CLASSES, where the knowledge that the students must acquire will be presented. To make easier the development of the class, the students will have written notes and also will have the basic texts of reference that will facilitate their subsequent work. 2. RESOLUTION OF EXERCISES by the student that will serve as self-evaluation and to acquire the necessary skills. 3. PROBLEM CLASSES, in which the proposed problems are discussed and developed. 4. PARTIAL CONTROLS. 5. FINAL EXAM. 6. TUTORIALS.
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Basic Bibliography
  • LEVINSON, N., REDHEFFER, R. M., . Curso de Variable Compleja. Ed. Reverté, Madrid. 1990
  • PESTANA, D., RODRÍGUEZ, J. M., MARCELLÁN, F.. Curso Práctico de variable compleja y teoría de transformadas. Pearson Educación. 2014
  • SIMMONS, G.F Y S.G. KRANTZ. Ecuaciones Diferenciales, Teoría, técnica y práctica. Ed. McGraw-Hill, México. 2007
Recursos electrónicosElectronic Resources *
Additional Bibliography
  • CHURCHILL, R.V. y BROWN, J.W.. Variable Compleja y Aplicaciones. Ed. McGraw-Hill, N.Y.. 1992
  • EDWARDS, C. H. Jr., PENNEY, D. E.. Ecuaciones Diferenciales Elementales y Problemas con Condiciones en la Frontera, tercera edición. Ed. Prentice Hall México. 1993
  • MARCELLÁN, F., CASASÚS, L., ZARZO, A.. Ecuaciones Diferenciales, Problemas de Contorno y Aplicaciones. Ed. McGraw-Hill, Madrid. 1990
  • NAGLE, R.K. Y SAFF, E.B.. Fundamentos de ecuaciones diferenciales, segunda edición. Ed. Addison-Wesley. 1992
  • PESTANA, D., RODRÍGUEZ, J. M., MARCELLÁN, F.. Variable compleja, un curso práctico. Ed. Síntesis. 1999
  • SPIEGEL, M.R.. Variable compleja. Ed. McGraw-Hill, México. 1971
  • VOLKOVYSKII, L.I., LUNTS, G.L. y ARAMANOVICH, I.G.. A collection of problems in complex analysis. Ed. Dover, N.Y. 1991
  • WUNSCH, A. D.. Variable Compleja con Aplicaciones, segunda edición. Ed. Pearson Educación, México. 1999
  • ZILL, D. G.. Ecuaciones Diferenciales con Aplicaciones de Modelado, sexta edición. Thomson Editores, México. 1997
(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN


The course syllabus and the academic weekly planning may change due academic events or other reasons.