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  • Syllabus for Calculus of Variations - Uppsala University, Sweden?
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Applications of Calculus of Variations to Physics - MAT - Spring - Universitetet i Oslo

Hardcover, good condition, w. Shape of a hanging rope. Restrictions imposed through finite or differential equationsChapter 5. Geometrical Optics: Fermat's Principle 1.

Syllabus for Calculus of Variations

Law of refraction Snell's law 2. Fermat's principle and the calculus of variationsChapter 6. Dynamics of Particles 1. Potential and kinetic energies. Generalized coordinates 3.

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Hamilton's principle. Lagrange equations of motion 3. Generalized momenta. Hamilton equations of motion. Canonical transformations 5.


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  • Syllabus for Calculus of Variations - Uppsala University, Sweden.

The Hamilton-Jacobi differential equation 6. Principle of least action 7. The extended Hamilton's principleChapter 7. Extremization of a double integral 2. The vibrating string 3. Eigenvalue-eigenfunction problem for the vibrating string 4. Eigenfunction expansion of arbitrary functions. Minimum characterization of the eigenvalue-eigenfunction problem 5. General solution of the vibrating-string equation 6. Approximation of the vibrating-string eigenvalues and eigenfunctions Ritz method 7.

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Remarks on the distinction between imposed and free end-point conditionsChapter 8. Isoperimetric problem leading to a Sturm-Liouville system 2. Transformation of a Sturm-Liouville system 3. Two singular cases: Laguerre polynomials, Bessel functionsChapter 9. Extremization of a multiple integral 2. Change of independent variables. Transformation of the laplacian 3. The vibrating membrane 4.

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Eigenvalue-eigenfunction problem for the membrane 5. Membrane with boundary held elastically. The free membrane 6. Orthogonality of the eigenfunctions. Expansion of arbitrary functions 7. General solution of the membrane equation 8. The rectangular membrane of uniform density 9. The minimum characterization of the membrane eigenvalues Consequences of the minimum characterization of the membrane eigenvalues The maximum-minimum characterization of the membrane eigenvalues The asymptotic distribution of the membrane eigenvalues Approximation of the membrane eigenvaluesChapter Theory of Elasticity 1.

Stress and strain 2. General equations of motion and equilibrium 3. General aspects of the approach to certain dynamical problems 4. Bending of a cylindrical bar by couples 5. Transverse vibrations of a bar 6. The eigenvalue-eigenfunction problem for the vibrating bar 7. Pickup not available. About This Item We aim to show you accurate product information.

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Calculus of Variations - Minimizing Path Length

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