
Course unit
FUNCTIONS THEORY
SCP3050963, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/05 
Mathematical Analysis 
8.0 
Mode of delivery (when and how)
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Practice 
4.0 
32 
68.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Start of activities 
02/10/2017 
End of activities 
19/01/2018 
Prerequisites:

Analysis courses of the first two years, and preferably the following courses
Real Analysis
Mathematical Methods
Functional Analysis 1 
Target skills and knowledge:

Methods of potential theory and of functional and harmonic analysis for the study of boundary value problems for integral and differential equations. 
Examination methods:

Partial tests and final oral exam 
Assessment criteria:

Evaluation of the knowledge of the candidate on each topic of the program 
Course unit contents:

Differential Calculus in Banach spaces, including analytic functions.
Schauder spaces. Potential theory.
Elliptic boundary value problems. Singular perturbation problems.
Topological degree and its applications to the analysis of nonlinear differential and integral equations. 
Planned learning activities and teaching methods:

Theoretical exposition with exercises and examples 
Additional notes about suggested reading:

The course content is entirely covered by handouts and or precise bibliographical references, which we list in part below. 
Textbooks (and optional supplementary readings) 

Cartan, Henri, Cours de calcul differentielHenri Cartan. Paris: Hermann, 1977.

Deimling, Klaus, Nonlinear functional analysisKlaus Deimling. Berlin <etc.>: SpringerVerlag, .

Nirenberg, Louis; Artino, Ralph A., Topics in nonlinear functional analysisLouis Nirenbergnotes by Ralph A. Artino. New York: Courant institute of mathematical sciences, Providence, American mathematical society, 2001.

Folland, Gerald B., Introduction to partial differential equationsby Gerald B. Folland. Princeton: N.J., Princeton University Press and University of Tokio Press, 1976.


