Verified Certificate

Supported by the following organizations

This is to certify that Volodymyr Vreshch successfully completed and received a passing grade in 18.02.1x: Multivariable Calculus 1: Vectors and Derivatives a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Larry Guth

Larry Guth

Claude Shannon Professor of Mathematics MacVicar Faculty Fellow Massachusetts Institute of Technology

Sanjay Sarma

Sanjay Sarma

Vice President for Open Learning Massachusetts Institute of Technology

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