Verified Certificate

Supported by the following organizations

This is to certify that Kisaki Watanabe successfully completed and received a passing grade in MMFEC2x: Calculus II: Multivariable Functions a course of study offered by DelftX, an online learning initiative of Delft University of Technology.

Noted by

Professor Arno Smets

Professor Arno Smets

Director of Learning for Life Education on behalf of the Quality Assurance Board Delft University of Technology

About edX

edX offers interactive online classes and MOOCs from the world’s best universities, including MIT, Harvard, Berkeley, University of Texas, and many others. edX is a mission driven initiative created by founding partners Harvard and MIT.

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.