First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
SCP3050960, 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 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
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
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge FABIO ANCONA 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: Differential and integral calculus.
Elementary theory of ordinary differential equations.
Basic theory of complex analysis (functions of complex variables, holomorphic and analytic functions).
Target skills and knowledge: Basic notions of the theory of linear partial differential equations. It's a fundamental course suggested to students with interests both in pure and in applied mathematics, and in particular to students with a curriculum in analysis.
Examination methods: The exam consists of a final oral examination on the topics treated in class. There will be both theoretical questions and the discussion of some exercise to solve.
Assessment criteria: The evaluation criteria will be the following:
- coherence and rigor in the exposure of statements and theorems
- thoroughness and adherence to the topics of discussion
- ability to use the acquired knowledge to solve problems and exercises.
Course unit contents: Didactic plan:
- First order PDEs: transport equation with constant coefficients, conservation laws (classical and weak solutions, Rankine-Hugoniot conditions, Riemann problem).
- Wave equation: existence of solutions, D'alembert formnula, method of spherical means, Duhamel's principle, uniqueness, finite speed of propagation.
- Laplace equation: fundamental solution, harmonic functions and main properties, mean value formulas, Harnack's inequality, maximum principle. Poisson equation. Green's function and Poisson's representation formula of solutions.
- Heat equation: fundamental solution, existence of solutions for the Cauchy problem and representation formula. Uniqueness and stability of solutions. Mean value formulas, maximum principle, Hopf's maximum principle.
Planned learning activities and teaching methods: The methodology of teaching used will be the traditional lesson.
Textbooks (and optional supplementary readings)
  • Salsa, Sandro, Partial differential equations in actionfrom modelling to theorySandro Salsa. Cham [etc.]: Springer, 2015. Cerca nel catalogo
  • L.C. Evans, Partial Differential Equations, 2nd edition. Providence, Rhode Island: American Mathematical Society, 2010. Cerca nel catalogo
  • W. A. Strauss, Partial Differential Equations. An Introduction. New York: Wiley, 1992. Cerca nel catalogo