Verified Certificate

Supported by the following organizations

This is to certify that James Long successfully completed and received a passing grade in 18.01.1x: Calculus 1A: Differentiation a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

David Jerison

David Jerison

Professor Department of Mathematics Massachusetts Institute of Technology

Gigliola Staffilani

Gigliola Staffilani

Abby Rockefeller Mauzé Professor Department of Mathematics Massachusetts Institute of Technology

Sanjay Sarma

Sanjay Sarma

Vice President for Open Learning Massachusetts Institute of Technology

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