Transcription of DIFFERENTIAL FORMS AND INTEGRATION - UCLA Mathematics
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DIFFERENTIAL FORMS AND INTEGRATIONTERENCE TAOThe concept of INTEGRATION is of course fundamental in single-variable , there arethreeconcepts of INTEGRATION which appear in the subject: theindefinite integral f(also known as theanti-derivative), theunsigned definiteintegral [a,b]f(x)dx(which one would use to find area under a curve, or the massof a one-dimensional object of varying density), and thesigned definite integral baf(x)dx(which one would use for instance to compute the work required to movea particle fromatob).
integral generalises to the notion of a solution to a differential equation, or of an integral of a connection, vector field, or bundle. The unsigned definite integral ... higher dimensions and on general manifolds. 1. 2 TERENCE TAO To motivate the concept, let us informally revisit the one of the basic applications
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