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...Faculty of mathematics and natural sciences calculus variations its applications bachelor project november student m h mudde first supervisor dr a e sterk second prof j van der schaft abstract in this thesis the is studied we look at how opti mization problems are solved using euler lagrange equation functions that satisfy prescribed boundary conditions must also legendre s condition there be no conjugate points interval order to minimizer wegeneralize higher dimensions derivatives solve not only one dimensional but multi last investigate canonical form keywords optimization functional hamiltonian acknowledgements i want thank my rst for being best su pervisor could wish even though do live groningen he helped mein possible way send him drafts whenever wanted as many time every gave me adequate feedback immediately willing contents introduction functionals admissible variation transform degenerate cases necessary sucient determine nature an extremum curves shortest length minimal surfa...