General information 
Course unit name: Functional Analysis and Partial Differential Equations
Course unit code: 568175
Academic year: 20182019
Coordinator: María Jesús Carro Rossell
Department: Department of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface learning activities 
60 
 Lecture 
30 

 Lecture with practical component 
30 
Supervised project 
20 
Independent learning 
70 
Competences to be gained during study 


Learning objectives 
Referring to knowledge

Teaching blocks 
1. Hilbert spaces: orthogonality, duality and elementary spectral theory.
2. Banach and Frechet spaces. Boundedness of linear operators.
3. Fundamental theorems of Functional Analysis
* Fundamental theorem of Functional Analysis: Baire, Open mapping, Closed graph, Uniform boundedness principle and HahnBanach theorems.
4. Distribution theory.
* Weak derivatives, convolution, fundamental solutions, temperate distributions and Fourier transform.
5. Sobolev spaces: Regularity and compactness
6. Applications to PDE
* Existence of the fundamental solution, Regularity of the solutions, Application of the spectral theory.
Teaching methods and general organization 

Official assessment of learning outcomes 
This evaluation has 2 parts:
Examinationbased assessment Final exam with theoretical and practical questions. 
Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
Adams, R. A. Sobolev spaces. Amsterdam : Academic Press, 2003.
Brézis, H. Análisis funcional : teoría y aplicaciones. Madrid : Alianza, 1984.
Cerdà, J. Introducció a l’anàlisi funcional. Barcelona, Edicions UB, 2005.
Lax, P. Functional analysis. New York : Wiley, 2002.
Maz’ia, V. G. Sobolev spaces. Berlin : Springer, 1985.
Rudin, W. Functional analysis. New York : McGrawHill, 1991.