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Glossary
Semester (Sem)
1First Semester
2Second Semester
AAnnual course
(1)First Half-semester
(2)Second Half-semester
Educational activities
ABasic activities
Language
Course completely offered in italian
Course completely offered in english
--Not available
Innovative teaching
The credits shown next to this symbol indicate the part of the course CFUs provided with Innovative teaching.
These CFUs include:
  • Subject taught jointly with companies or organizations
  • Blended Learning & Flipped Classroom
  • Massive Open Online Courses (MOOC)
  • Soft Skills
Course Details
Context
Academic Year 2018/2019
School School of Industrial and Information Engineering
Name (Bachelor of Science degree)(ord. 270) - MI (365) Mathematical Engineering
Track MFO - Formativo
Programme Year 3

Course Details
ID Code 078047
Course Title P.D.E. ANALITICAL AND NUMERICAL METHODS
Course Type Integrated Course
Credits (CFU / ECTS) 10.0
Semester Second Semester
Course Description Diffusion. Heat equation, well posed problems. Maximum principles. Fundamental solution. Random walk, symmetric and with drift. Brownian motion. Laplace equation. Well posed problems. Discrete harmonic functions. Fundamental solution, Newtonian potential. Green's function. Double and single layer potentials. Conservation laws. Traffic models. Characteristics.Shock and rarefaction waves. Rankine-Hugoniot condition. Riemann's problem. Vibrating string. D' 'Alembert formula. Duhamel's method. Kirchhoff and Poisson formula. Huygens principle. Distributions. Calculus. Hilbert. spaces. Projection, Riesz., Lax-Milgram Theorems. Sobolev spaces, traces. Variational formulation of boundary value problems for elliptic equations. Galerkin's method. Numerical methods for Partial Differential Equations in one space dimension. Finite Difference method. Galerkin methods: the Finite Element Method: basic features, convergence analysis for 1D problems. Error control: a-priori and a-posteriori analysis. Advection-diffusion problems. Stabilization techniques, Galerkin Generalized schemes for boundary layer problems. Parabolic problems. Space-time approximations with finite elements and finite differences. Hyperbolic (convection) problems. conservative finite difference schemes for scalar problems. Continuous and discontinuous finite elements. Finite Volumes.
Scientific-Disciplinary Sector (SSD)
Educational activities SSD Code SSD Description CFU
A
MAT/08
NUMERICAL ANALYSIS
5.0
A
MAT/05
MATHEMATICAL ANALYSIS
5.0

Schedule, add and removeAlphabetical groupCodeModule DescriptionProfessorCFUSem.LanguageCourse details
From (included)To (excluded)
--AZZZZ078046ANALITICAL AND NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS [2]Verani Marco5.02 (2)
078045ANALITICAL AND NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS [1]Salsa Sandro5.02 (1)
manifesti v. 3.4.13 / 3.4.13
Area Servizi ICT
24/07/2021