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SUMMARY:Smooth Infinitesimal Analysis II - Filip Bár (University of Cambr
 idge)
DTSTART:20120215T160000Z
DTEND:20120215T170000Z
UID:TALK36439@talks.cam.ac.uk
CONTACT:Filip Bár
DESCRIPTION:We continue where we left off last time and proof the second d
 erivative factoring through the R-module of symmetric bilinear maps. We fi
 nish the section on derivatives in arbitrary dimensions with a Taylor theo
 rem and with exhibiting that homogeneity of a map implies its linearity in
  K-L R-modules.\n\nOur final chapter on SIA concerns the integration axiom
  and its implications. The elementary integral calculus will be obtained a
 s easily as the elementary differential calculus. Higherdimensional integr
 als will be constructed via Fubini's theorem as iterated integrals. As app
 lications we will discuss the Fermat-Reyes axiom and a proof of the reflex
 ivity of R^n.\n\nThe corresponding sections in Lavendhomme's book are the 
 second half of 1.2.3\, 1.3 and p. 84/85 of section 3.3.2\n\n
LOCATION:Centre for Mathematical Sciences\, MR4
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