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...C calculus ofvariations gilbert strang of variations one theme this book is the relation equations to minimum principles minimize p solve there may be more it but that main point for a quadratic u utku utf no diculty in reaching ku f thematrix k symmetric positive denite at continuous problem derivative not so easy nd unknown x function and usually an integral its called rst variation euler lagrange equation has weak form strong elastic bar linear will have boundary conditions z cu v dx fvdx every our goal section get beyond example basic idea should simple perturb by test comparing with term dierence yields must zero admissible program carries ordinary into we do several steps dimensional problems r necessarily constraints their multipliers two rr dxdy y time dependent which du dt each step examples as familiar famous possible dimensions means laplace s minimal surfaces nonlinear case newton laws relativity dimension rediscover straight line circle also opening control theory modern a...