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The lecture is 40-50 minutes long delivered by Professor David Jerison and covers the concept of partial differentiation and some simple applications. It is aimed at undergraduate students.

These lectures will give you some idea of how this subject is treated at university level.

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Video from MIT
Free lecture notes, exams, and videos are available from Massachusetts Institute of Technology at MIT. No registration required.

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
Methods (UK)M10Multivariable calculusXTRA-
OCR-MEI A-Level (UK - Pre-2017)FP3Multivariable calculusXTRA-
Universal (all site questions)MMultivariable calculusXTRA-