Massachusetts Institute of Technology This is to certify that Pio Verne has successfully completed Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows Issued: Feb. 7, 2026
Gareth McKinley

Engineering Professor

Massachusetts Institute of Technology

Dimitris Bertsimas

Vice Provost for Open Learning

Associate Dean, Online Education and Artificial Intelligence

Boeing Professor of Operations Research

Massachusetts Institute of Technology

Valid Certificate ID: b1f8c52f-1d59-4575-a956-593f64668550

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