Calculus of VariationsThis concise text offers an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, its subjects include practical direct methods for solution of variational problems. Each chapter features numerous illustrative problems, with solutions. 1961 edition. |
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absolute value admissible curves applies arbitrary arbitrary constants argument assume boundary conditions boundary point calculate called central field centre Chapter choose chosen circle close Consequently consider consists constant constrained coordinate functions corresponding depend derivative determined difference differential equation domain end points Euler equation exact Examine the extrema EXAMPLE exists fact field fixed follows func fundamental necessary condition given gives an extremum hence holds homogeneous homogeneous function increment independent instance integral integrand interval involved isoperimetric limit linear lying maximum mean mean value theorem method minima move multipliers obtain occur ordinary parameter particular pass pencil positive problem of extrema reduces relations respect satisfy sense solution solving straight lines strong minimum sufficiently suppose surface taken takes the form tangent term tion tional turns vanishes variable variational problem varying