Verified Certificate

Supported by the following organizations

This is to certify that Mark Paulenz successfully completed and received a passing grade in 3.032.1x: Mechanical Behavior of Materials: Linear Elastic Behavior a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Lorna J. Gibson

Lorna J. Gibson

Matoula S. Salapatas Professor of Materials Science and Engineering Massachusetts Institute of Technology

Krishna Rajagopal

Krishna Rajagopal

Dean for Digital Learning Massachusetts Institute of Technology

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About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.