Marco Verani
Associate Professor of Numerical Analysis
MOX, Department of Mathematics
Politecnico di Milano

Mailing Address :
via Bonardi, 9
Politecnico di Milano
20133 Milano, Italy

Office : Edifcio "La Nave", Sixth Floor
Phone : +39 02 2399 4610
Fax : +39 02 2399 4606
E-mail : marco(dot)verani(at)polimi(dot)it
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 Scientific Interests   Publications   Teaching   Grants   Curriculum Vitae (pdf)                                                                         ResearcherID   Scopus   GoogleScholar


Scientific Interests

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Publications

To request any of these papers please e-mail me

Submitted
  1. M. Bruggi, N. Parolini, F. Regazzoni and M. Verani, Finite Element approximation of an evolutionary Topology Optimization problem, MOX-Preprint 14/2017. [preprint]

  2. I. Fumagalli, N. Parolini and M. Verani, On a free-surface problem with moving contact line: from variational principles to stable numerical approximations, MOX-Preprint 03/2017. [preprint]

  3. P. F. Antonietti, M. Bruggi, S. Scacchi and M. Verani, On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study, MOX-Preprint 58/2016. [arXiv]

  4. P. F. Antonietti, C. Facciola', A. Russo and M. Verani, Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids, MOX-Preprint 55/2016. [preprint]

  5. P. F. Antonietti, G. Manzini and M. Verani, The Fully Nonconforming Virtual Element Method for Biharmonic problems, MOX-Preprint 53/2016. [preprint] [arXiv]

  6. C. Andra', D. Brunetto, N. Parolini and M. Verani, Student interactions during class activities: a mathematical model, MOX-Preprint 39/2016. [preprint]

  7. E. Repossi, R. Rosso and M. Verani, A phase-field model for liquid-gas mixtures: mathematical modelling and Discontinuous Galerkin discretization, MOX-Preprint 27/2016. [preprint]

  8. A. Agosti, P. F. Antonietti, P. Ciarletta, M. Grasselli and M. Verani, A Cahn-Hilliard type equation with degenerate mobility and single-well potential. Part I: convergence analysis of a continuous Galerkin finite element discretization, MOX-Preprint 16/2016. [preprint]

Refereed Journal Papers
  1. P. F. Antonietti, P. Houston, X. Hu, M. Sarti and M. Verani, Multigrid algorithms for hp-version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes, accepted on Calcolo [arXiv]

  2. C. Canuto, R.H. Nochetto, R. Stevenson and M. Verani, On p-Robust Saturation for hp-AFEM, accepted on CAMWA. [preprint] [arXiv]

  3. P. F. Antonietti, B. Merlet, M. Pierre and M. Verani, Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation, AIMS Mathematics, 1 (2016) no.3, 178--194. [journal]

  4. C. Canuto, R.H. Nochetto, R. Stevenson and M. Verani, Adaptive Spectral Galerkin Methods with Dynamic Marking, SIAM J. Numer. Anal. 54 (2016) no.6, 3193--321 [journal]

  5. P. F. Antonietti, M. Sarti, M. Verani and Zikatanov, L. T. A uniform additive Schwarz preconditioner for the hp-version of Discontinuous Galerkin approximations of elliptic problems, J Sci Comput, 70(2016) no. 2: 608--630. [journal]

  6. C. Canuto, R.H. Nochetto, R. Stevenson and M. Verani, Convergence and Optimality of hp-AFEM, Numerische Mathematik, doi: 10.1007/s00211-016-0826-x [arXiv] [journal]

  7. G. Berlusconi, F. Calderoni, N. Parolini, M. Verani and C. Piccardi, Link Prediction in Criminal Networks: A Tool for Criminal Intelligence Analysis. PLoS ONE 11 (2016), no.4: e0154244. doi: 10.1371/journal.pone.0154244 [journal]

  8. I. Fumagalli, A. Manzoni, N. Parolini and M. Verani, Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems, ESAIM: Mathematical Modelling and Numerical Analysis, 50 (2016) no. 6: 1857--1885. [journal]

  9. P.F. Antonietti, L. Formaggia, A. Scotti, M. Verani and N. Verzotti, Mimetic finite difference approximation of flows in fractured porous media. ESAIM: Mathematical Modelling and Numerical Analysis 50 (2016), no.3, 809--832. [journal]

  10. P. F. Antonietti, L. Beirao da Veiga, S. Scacchi and M. Verani, A $C^1$ virtual element method for the Cahn-Hilliard equation with polygonal meshes, SIAM J. Numer. Anal. 54 (2016) no.1, 34--56. [journal]

  11. C. Giverso, M. Verani and P. Ciarletta, Emerging morphologies in round bacterial colonies: comparing volumetric versus chemotactic expansion, Biomechanics and Modeling in Mechanobiology 15 (2016) no. 3, 643--661. [journal]

  12. P. F. Antonietti, M. Grasselli, S. Stangalino and M. Verani, Discontinuous Galerkin approximation of linear parabolic problems with dynamic boundary conditions, J. Sci. Comput. 66 (2016), no.3, 1260--1280 [journal]

  13. P. F. Antonietti, M. Verani and L. Zikatanov, A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems, Computers and Mathematics with Applications, 70 (2015), no.11, 2674--2687 [journal]

  14. C. Andra', N. Parolini and M. Verani. Using gambling simulators to foster awareness about gambling risks, Digital Experience in Mathematics Education 1 (2015), no. 1, 59--78 [journal]

  15. C. Giverso, M. Verani and P. Ciarletta, Mechanically driven branching of bacterial colonies, ASME. J Biomech Eng. 137 (2015), no.7, 071003-071003-10. doi:10.1115/1.4030176. [journal]

  16. P. F. Antonietti, A. Dedner, P. Madhavan, S. Stangalino, B. Stinner and M. Verani, High order discontinuous Galerkin methods on surfaces, SIAM J. Numer. Anal. 53 (2015), no.2, 1145--1171 [journal]

  17. C. Giverso, M. Verani and P. Ciarletta, Branching instability in expanding bacterial colonies, Journal of the Royal Society Interface, 12 (2015) no. 104, doi:10.1098/rsif.2014.1290 [journal]

  18. P. F. Antonietti, M. Sarti and M. Verani, Multigrid algorithms for hp-discontinuous Galerkin discretizations of elliptic problems, SIAM J. Numer. Anal. 53 (2015), no.1, 598--618 [journal]

  19. I. Fumagalli, N. Parolini and M. Verani, Shape optimization for Stokes flow: a reference domain approach, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 49 (2015), no.4, 921--951 [journal]

  20. C. Canuto, V. Simoncini and M. Verani, Contraction and optimality properties of an adaptive Legendre-Galerkin method: the multi-dimensional case, J. Sci. Comput. 63 (2015), no.3, 769--798. [journal]

  21. C. Canuto, V. Simoncini and M. Verani, On the decay of the inverse of matrices that are sum of Kronecker products, Linear Algebra and Its Applications, 452 (2014), 21--39. [journal]

  22. P. F. Antonietti, L. Beirao da Veiga, N. Bigoni and M. Verani, Mimetic finite differences for nonlinear and control problems, M3AS 24 (2014), no.8, 1457--1493 . [journal]

  23. P. F. Antonietti, N. Bigoni and M. Verani, Mimetic finite difference approximation of quasilinear elliptic problems, Calcolo, 52 (2015), no.1, 45--67. [journal]

  24. P. F. Antonietti, L. Beirao da Veiga, D. Mora and M. Verani, A stream virtual element formulation of the Stokes problem on polygonal meshes, SIAM J. Numer. Anal. 52 (2014) no.1, 386--404. [journal]

  25. C. Canuto, R.H. Nochetto and M. Verani, Contraction and optimality properties of adaptive Legendre-Galerkin methods: the 1-dimensional case, Computers and Mathematics with Applications 67 (2014), no.4, 752--770. [journal]

  26. P.F. Antonietti, A. Borzi and M. Verani, Multigrid shape optimization governed by elliptic PDEs, SIAM J. Control Optim. 51 (2013), no. 2, 1417-1440 [journal]

  27. C. Canuto, R.H. Nochetto and M. Verani, Adaptive Fourier-Galerkin Methods, Math. Comp. 83 (2014), 1645--1687 . [journal]

  28. P.F. Antonietti, L. Beirao da Veiga, C. Lovadina and M. Verani, Hierarchical a posteriori error estimators for the mimetic discretization of elliptic problems, SIAM J. Numer. Anal. 51 (2013), no. 1, 654--675 [journal]

  29. P. F. Antonietti, N. Bigoni and M. Verani, A Mimetic Discretization of Elliptic Control Problems, J. Sci. Comput. 56 (2013), no. 1, 14--27 [journal]

  30. P. F. Antonietti, L. Beirao da Veiga and M. Verani, A Mimetic Discretization for Elliptic Obstacle Problems, Math. Comp. 82 (2013), 1379-1400 [journal]

  31. P. Morin, R. H. Nochetto, M. S. Pauletti and M. Verani, Adaptive finite element method for shape optimization. ESAIM: Control, Optimisation and Calculus of Variations, 18 (2012), no. 4, 1122--1149. [journal]

  32. M. Bruggi and M. Verani, A fully adaptive topology optimization algorithm with goal-oriented error control, Computers & Structures, 89 (2011), no. 15-16, 1481--1493. [journal]

  33. R. Ghelichi, S. Bagherifard, M. Guagliano and M. Verani, A numerical approach to assess the critical velocity in cold spray coating process, Surface and Coating Technology, 205 (2011), no. 23-24, 5294--5301. [journal]

  34. P. F. Antonietti, N. A. Fadel and M. Verani. Modelling and numerical simulation of the polymeric extrusion process in textile products, Communications in Applied and Industrial Mathematics, 1 (2010), no. 2, 1--13. [journal]

  35. P. F. Antonietti, P. Biscari, A. Tavakoli, M. Verani and M. Vianello, Theoretical study and numerical simulation of textiles, Appl. Math. Model. 35 (2011), no. 6, 2669--2681. [journal]

  36. L. Beirao da Veiga and M. Verani, A Posteriori boundary control for FEM approximation of elliptic eigenvalue problems, Numerical Methods for Partial Differential Equations, 28 (2012), no. 2, 369--388. [journal]

  37. S. Berrone and M. Verani, A New Marking Strategy for the Adaptive Finite Element Approximation of Optimal Control Constrained Problems, Optimization Methods and Software, 26 (2011), no. 4-5, 747--775. [journal]

  38. R.H. Nochetto, A. Veeser and M. Verani, A Safeguarded Dual Weighted Residual Method, IMA J. Numer. Anal. 29 (2009), no. 1, 126--140. [journal]

  39. R. Rosso and M. Verani, Stabilizing role of a curvature correction to line tension, SIAM J. Appl. Math. 69 (2008), no. 2, 524--551. [journal]

  40. S. Micheletti, S. Perotto and M. Verani, Goal oriented analysis via an adaptive Uzawa algorithm, IMA J. Numer. Anal. 28 (2008), no. 3, 619--646. [journal]

  41. G. Dogan, P. Morin, R.H. Nochetto and M. Verani, Discrete gradient flows for shape optimization and applications, Comput. Methods Appl. Mech. Engrg. no. 196 (2007), 3898--3914. [journal]

  42. R. Rosso, E.G. Virga and M. Verani, Second variation of the energy functional for adhering vesicles in two space dimensions, J.Phys.A 36 (2003), no. 50, 12475--12493. [journal]

  43. M. Verani, A Wavelet adaptive Newton method for the solution of nonlinear equations, Appl. Math. Lett. 16 (2003), no. 8, 1301--1306. [journal]

  44. S. Bertoluzza, S. Mazet and M. Verani, A nonlinear Richardson algorithm for the solution of elliptic PDE's, Math. Models Methods Appl. Sci. 13 (2003), no.2, 143--158. [journal]

  45. S. Bertoluzza and M. Verani, Convergence of a nonlinear wavelet algorithm for the solution of PDE's, Appl. Math. Lett. 16 (2003), no. 1, 113--118. [journal]

Book Chapters
  1. S. Berrone, A. Bonito and M. Verani, An Adaptive Fictitious Domain Method for Elliptic Problems, Advances in Discretization Methods: Discontinuities, Virtual Elements, Fictitious Domain Methods, SEMA SIMAI Springer Series 12, Springer International Publishing, G. Ventura and E. Benvenuti (ed.), 2016, doi: 10.1007/978-3-319-41246-7_11. [download]

  2. M. Falcone and M. Verani, Recent Results in Shape Optimization and Optimal Control for PDEs, Optimization with PDE Constraints, Lecture Notes in Computational Science and Engineering 101, Springer International Publishing Switzerland, R. Hoppe (ed.), 2014, doi: 10.1007/978-3-319-08025-3__3. [download]

  3. C. Canuto and M. Verani, On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems, Analysis and Numerics of Partial Differential Equations. In memory of Enrico Magenes, Springer INdAM Series, Vol. 4 (ISBN 978-88-470-2591-2), F. Brezzi, P.C. Franzone, U. Gianazza and G. Gilardi (Eds.), 2013. [download]

Books
  1. C. Andra', N. Parolini and M. Verani, BetOnMath: Azzardo e matematica a scuola, Springer, 2016 [website]

Refereed Conference Proceedings
  1. M. Bruggi, N. Parolini, F. Regazzoni and M. Verani. Finite element approximation of a time-dependent topology optimization problem. ECCOMAS Congress 2016 VII European Congress on Computational Methods in Applied Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (eds.) Crete Island, Greece, 5-10 June 2016 [download]

  2. P. A. Antonietti, M. Bruggi, S. Scacchi and M. Verani. VEM and Topology optimization on polygonal meshes. ECCOMAS Congress 2016 VII European Congress on Computational Methods in Applied Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (eds.) Crete Island, Greece, 5-10 June 2016 [download]

  3. C. Canuto, R. H. Nochetto, R. Stevenson, and M. Verani. High-order adaptive Galerkin methods. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Lecture Notes in Computational Science and Engineering 106, Springer International Publishing Switzerland, R. M. Kirby, M. Berzins, J. S. Hesthaven (eds.), 2015, pp. 51--72, doi:10.1007/978-3-319-19800-2, Hardcover ISBN 978-3-319-19799-9. [article]

  4. P.F. Antonietti, M. Sarti, M. Verani, Multigrid algorithms for high order discontinuous Galerkin methods. Domain decomposition methods in Science and Engineering XXII, Lecture Notes Comput. Sci. Eng. 104, Springer International Publishing Switzerland, T. Dickopf, M. J. Gander, L. Halpern, R. Krause, L. F. Pavarino (eds.), 2015, doi: 10.1007/978-3-319-18827-0, Hardcover ISBN 978-3-319-18826-3. [download]

  5. P. F. Antonietti, P. Panfili, A. Scotti, L. Turconi, M. Verani, A. Cominelli and L. Formaggia, Optimal techniques to simulate flow in fractured reservoirs, 14th European Conference on the Mathematics of Oil Recovery, ECMOR 2014. [download]

  6. P.F. Antonietti, N. Bigoni and M. Verani, Mimetic finite difference method for shape optimization problems. Numerical Mathematics and Advanced Applications-ENUMATH2013, Proceedings of the 10th European Conference on Numerical Mathematics and Advanced Applications, Springer Verlag Italia (2014). [download]

  7. P.F. Antonietti, L. Beirao da Veiga and M. Verani, An adaptive MFD method for the obstacle problem. Numerical Mathematics and Advanced Applications-ENUMATH2011, Proceedings of the 9th European Conference on Numerical Mathematics and Advanced Applications, Springer Verlag Italia (2012). [download]

  8. E. Gariboldi, M. Verani, C. Riva, Modelling of phase evolution during aluminizing processes, Advanced Material Research, vol.278 (2011), 228-233. [download]

  9. P. Morin, R. H. Nochetto, M.S. Pauletti and M. Verani, Adaptive SQP Method for Shape Optimization. Numerical Mathematics and Advanced Applications-ENUMATH2009, Proceedings of the 8th European Conference on Numerical Mathematics and Advanced Applications, Springer Verlag Italia (2010). [download]

  10. M. Verani, A wavelet based adaptive scheme for the solution of nonlinear equations, Numerical Mathematics and Advanced Applications-ENUMATH2001, Proceedings of the 4th European Conference on Numerical Mathematics and Advanced Applications, F. Brezzi, A. Buffa, S. Corsaro, A. Murli, Eds., Springer Verlag Italia (2003).

Preprints
  1. A. Tavakoli, P. F. Antonietti and M. Verani, Automatic computation of the impermeability of woven fabrics through image processing, MOX-Preprint 34/2013. [preprint]


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Current Teaching
2016-2017

Analytical and Numerical Methods for Mechanical Engineering (66h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

Numerical Calculus and Elements of Analysis (66h), Aerospace Engineering, Politecnico di Milano - Campus Bovisa



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Grants

10/2013-10/2015: 5 per mille Polisocial Award Project BetOnMath: Mathematics for problem gambling prevention, supported by Politecnico di Milano and Fondazione Politecnico.
Scientific Team: C. Andra', D. Brunetto, N. Parolini (co-PI), M. Verani (PI) [link]

01/2012-12/2012: Industrial Consulting Project Mathematical modeling of the single screw extrusion process for wire coating, Aristoncavi S.p.a.
Scientific Team: P.F. Antonietti (co-PI), D. Brunetto, P. Ferrandi, M. Verani (PI) [link]

2011-2013: Regional Project Dote Ricerca Applicata supported by Regione Lombardia and Carvico S.p.a.
(Research Topic: Mathematical and Numerical Modelling of fluidodynamics properties of textiles).
Scientific Team: P.F. Antonietti (co-PI), P. Colombo , M. Legramandi, A. Tavakoli, M. Verani (PI).

2008-2011: HOT-FDI Project Hollow and Transparent Fibers Design for Industries
Industrial Partners: Carvico S.p.A. e RadiciFil S.p.A.
Scientific Team: P. F. Antonietti, P. Biscari, N. A. Fadel, M. Vianello, A. Tavakoli, M. Verani (PI)

2008-2011: FIRB Materiali e tecnologie innovativi per il tessile italiano (MTIT)
Scientific Team: P.F. Antonietti, P. Biscari, N. A. Fadel, M. Vianello, A. Tavakoli, M. Verani (PI)


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Curriculum Vitae Extended version (pdf)

Education
Ph.D in Computational Mathematics and Operations Research, Università di Milano, Italy, 2003
Thesis: `` Nonlinear wavelet methods for the solution of PDEs '' [download]
advisor: S. Bertoluzza

Laurea in Matematica, Università di Pavia, Italy, 1998
Thesis: ``Aprossimazione Wavelet non lineare applicata a equazioni differenziali'' [download]
advisors: G.A. Pozzi and S. Bertoluzza

Current Position
Associate Professor of Numerical Analysis, MOX-Dipartimento di Matematica, Politecnico di Milano (since Apr. 2015)

Research Associate at the IMATI-CNR (formerly IAN-CNR), Pavia (since 2007)

Past Positions
Dec. 2002-April 2015:  Assistant Professor, MOX-Department of Mathematics, Politecnico di Milano, Italy

June. 2004-March. 2005:  Visiting Researcher, Department of Mathematics, University of Maryland, College Park, USA

2000-2002:  Ph.D. Student in Computational Mathematics and Operations Research , Università di Milano, Italy

Teaching
2015-2016

Control and Shape optimization problems & Polygonal Methods for PDEs (with P.F. Antonietti), PhD in Mathematical Models and Methods for Engineering, Politecnico di Milano

Mathematical Methods for Engineering (36h), Physical Engineering, Politecnico di Milano - Campus Leonardo

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

2014-2015

Mathematical Methods for Engineering (36h), Physical Engineering, Politecnico di Milano - Campus Leonardo

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

2013-2014

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

Numerical Methods for Optimization (36h), Master in Energy Engineering for an Environmentally Sustainable World, Politecnico di Milano - Campus Piacenza

2012-2013

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

Advanced Mathematical Methods for Energy Engineering (72h), Master in Energy Engineering for an Environmentally Sustainable World, Politecnico di Milano - Campus Piacenza

2011-2012

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

Advanced Numerical Methods for Energy Engineering (36h), Master in Energy Engineering for an Environmentally Sustainable World, Politecnico di Milano - Campus Piacenza

2010-2011

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

Advanced Numerical Methods for Energy Engineering (36h), Master in Energy Engineering for an Environmentally Sustainable World, Politecnico di Milano - Campus Piacenza

2009-2010

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Bovisa

Analytical and Numerical Methods for Mechanical Engineering (72h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

2008-2009

Numerical Methods for non-linear problems (with P. Antonietti e F.Nobile), PhD in Mathematical Models and Methods for Engineering, Politecnico di Milano

Numerical Methods for Shape Optimization and Fluid-Structure Interaction with application to Aerospace Engineering (with P.F. Antonietti and C. Vergara), Laboratory for Laurea Degree, Aerospace Engineering, Politecnico di Milano.

Numerical Methods for Aerospace Engineering (36h), Aerospace Engineering, Politecnico di Milano - Campus Bovisa

Numerical Methods for Mechanical Engineering (36h), Mechanical Engineering, Politecnico di Milano - Campus Bovisa

Numerical Methods for Mechanical Engineering (36h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

2007-2008

Numerical Methods for Aerospace Engineering (36h), Aerospace Engineering, Politecnico di Milano - Campus Bovisa

Numerical Methods for Mechanical Engineering (36h), Mechanical Engineering, Politecnico di Milano - Campus Bovisa

Numerical Methods for Mechanical Engineering (36h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

2006-2007

Linear Algebra and Numerical Calculus (36h), Mechanical Engineering, Politecnico di Milano - Campus Bovisa

Numerical Methods for Mechanical Engineering (36h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

2005-2006

Linear Algebra and Numerical Calculus (36h), Mechanical Engineering, Politecnico di Milano - Campus Bovisa

Linear Algebra and Numerical Calculus (36h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza (Teaching Assistant, Teacher: M. Frontini).

Numerical Methods for Mechanical Engineering (36h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza

2004-2005
Numerical Calculus (36h), Mechanical Engineering, Politecnico di Milano - Campus Bovisa

Numerical Calculus, Mechanical Engineering, Politecnico di Milano - Campus Lecco (Teaching Assistant, Teacher: S. Perotto).

2003-2004

Numerical Calculus (36h), Mechanical Engineering, Politecnico di Milano - Campus Bovisa

Numerical Methods for Mechanical Engineering, Mechanical Engineering, Politecnico di Milano (Teaching Assistant, Teacher: F. Saleri)

Numerical Methods for Mechanical Engineering (36h), Mechanical Engineering, Politecnico di Milano - Campus Piacenza (Teaching Assistant, Teacher: S. Micheletti)

Introduction to Matlab (10h), Informatic Engineering, Politecnico di Milano.

2002-2003

Numerical Analysis (72h), Electronic Engineering, Università di Pavia - Campus Mantova

Numerical Calculus, Mechanical Engineering, Politecnico di Milano (Teaching Assistant, Teacher: A. Veneziani)

Numerical Calculus, Mechanical Engineering, Politecnico di Milano (Teaching Assistant, Teacher: R. Sacco)

Numerical Calculus, Aerospace Engineering, Politecnico di Milano (Teaching Assistant, Teacher: F. Saleri).

2001-2002

Numerical Analysis (72h), Electronic Engineering, Università di Pavia - Campus Mantova

Linear Algebra, Electronic Engineering, Università di Pavia (Teaching Assistant, Teacher: M. Grieco)

2001-2002

Linear Algebra, Electronic Engineering, Università di Pavia (Teaching Assistant, Teacher: M. Grieco)

Approximation Methods I, Mathematics, Università di Milano (Teaching Assistant, Teacher: L. Pavarino)

1999-2000

Numerical Calculus, Chemical Sciences, Universtà di Pavia (Teaching Assistant, Teacher: L. Della Croce)

Analysis II, Geological Sciences, Università di Pavia (Teaching Assistant, Teacher: G. Toscani)



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