First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
FUNCTIONS THEORY
SCP3050963, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination FUNCTIONS THEORY
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA

Lecturers
Teacher in charge MASSIMO LANZA DE CRISTOFORIS MAT/05

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

Syllabus
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 hand-outs 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.>: Springer-Verlag, --.
  • 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.