Calculus o f Variations : What Doe s "Variation s Mean? Frank Jone s The purpos e o f thi s brie f introductio n t o ou r conferenc e i s t o explain som e o f th e philosoph y behin d wha t i s calle d "th e calculu s of variations" . I a m no t goin g t o giv e an y proofs , an d I a m goin g to b e ver y loos e i n m y hypotheses . Furthermore , I a m jus t goin g to giv e a ver y smal l tast e o f wha t sor t o f problem s ar e o f interes t within thi s subject . I fee l tha t thi s i s justified here , a s th e audienc e is sophisticated undergraduat e students , an d i t i s rare indee d fo r thi s subject t o b e taugh t i n an y undergraduat e cours e i n mathematics . The idea here is that th e calculus of variations i s more of a vague area o f mathematica l analysi s tha n i t i s a well-defined subjec t area . In all of the following I restrict attentio n to a real-valued function, and the sort o f domain where the function i s defined determine s wha t we call our analysis. Th e initial idea is that w e want t o figure out ho w to locate points in the domain wher e the function attain s a maximu m or a minimum value . ©2004 b y th e autho r 1 http://dx.doi.org/10.1090/stml/026/01

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