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Published byThomas Phillips Modified 6년 전
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1주 : 서론 및 유의 사항 2주 : Calculus of variations I 3주 : Calculus of variation II 4주 : Ordinary differential equations 5주 : Sturm-Liouville theory-orthogonal functions 6주 : Gamma, beta function 7주 : Bessel function 8주 : 중간 시험 9주 : Spherical function 10주 : 복소 함수 I (Fundamental) 11주 : 복소 함수 II (Cauchy's integral) 12주 : 복소 함수 III (Calculus of residues) 13주 : Tensor I 14주 : Tensor II 15주 : 기말 시험
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Calculus of Variation
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The Euler Equation x y Y(x) y(x) (x2, y2) (x1, y1) x y Arbitrary h(x) x2 x1
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More general formulation
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Euler equation
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Example
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Cycloid (x1, y1) (x, y) (x2, y2) x y
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(4.2)
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From Eq. (4.2)
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x y O A P B C a q x y
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Lagrange Equation
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Example
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