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Focus on Partial Differential Equations and Analysis

Partial Differential Equations (PDEs) play a central role in physics, chemistry, biology, industry, mathematical finance, and image processing. Their analysis often requires deep mathematical techniques, which makes PDEs to at the heart of both historical and recent developments in analysis, geometry, and probability. Because of this and their applications, PDEs is a very active area of mathematics, the one with the largest number of publications.

pattern

Pattern formation with reaction-diffusion systems of PDEs

boundaries

Free boundaries and PDEs: the Stefan problem for melting ice

levy

Lévy flights and PDEs in finance, biological invasions...

Students interested in focusing on PDEs and Analysis are invited to select 45 ECTS from this list and the suggestions below:

Advanced course in PDEs 7.5 ECTS English MAMME
Mathematical Modeling with PDEs 7.5 ECTS English MAMME
Numerical Methods for PDEs 7.5 ECTS English MAMME
Stochastic Calculus 7.5 ECTS English Master in Advanced Mathematics, UB
Complex Analysis 9 ECTS English Master in Advanced Mathematics, UB

A minimum of 3 MAMME courses (22.5 ECTS) is mandatory.

Other appropriate courses (depending on the student interests) with connections to PDEs are:
Quantitative and Qualitative Methods in Dynamical Systems (Q1 MAMME), Hamiltonian Systems (Q2 MAMME), and courses within the Barcelona universities masters offer in Mathematical Finance, Mathematical Biology, Image Processing, Functional Analysis, or Differential Geometry.