Applications of functional analysis in engineering

摘要: 1. Physical Space. Abstract Spaces.- Comment 1.1.- 2. Basic Vector Algebra.- Axioms 2.1-2.3 and Definitions 2.1-2.3.- 2.4-2.8.- Theorem 2.1 (Parallelogram Law).- Problems.- 3. Inner Product of Vectors. Norm.- 3.1 3.2.- Pythagorean Theorem.- Minkowski Inequality.- Cauchy-Schwarz 4. Linear Independence. Components. Space Dimension.- Span. Basis. Components.- 5. Euclidean Spaces Many Dimensions.- 5.1-5.6.- 5.7-5.9.- Orthogonal Projections.- Inequalities.- Gram-Schmidt Orthogonalization Process.- lp-Space.- 6. Infinite-Dimensional Section 6.1. Convergence a Sequence Vectors in ??.- Cauchy Sequence.- 6.2. Span, Basis.- 6.3. Manifold.- Subspace.- Distance.- Remark 6.1.- 7. Spaces. Hilbert Space.- Axioms.- Product.- Pre-Hilbert Dimension. Completeness. Separability.- Metric Ca?t?b l1.- Normed Banach Fourier Coefficients.- Bessel's Inequality. Parseval's Equality.- 7.1. Contraction Mapping.- 8. Function Hilbert, Dirichlet, Products.- Positive Semi-Definite Metric.- Semi-Norm.- Clapeyron Rayleigh-Betti Differential Operators. Functionals.- Variational Principles.- Bending Isotropic Plates.- Torsion Bars.- 8.1. Theory Quantum Mechanics.- 9. Some Geometry Translated Subspaces.- Intrinsic Extrinsic Vectors.- Hyperplanes.- Convexity.- Perpendicularity. Complement. Direct Sum.- n-Spheres Hyperspheres.- Balls.- 10. Closeness Functions. Approximation the Mean. Expansions.- Uniform Convergence. Mean Square.- Energy ?2.- Generalized Series.- Eigenvalue 11. Bounds Lower Upper Bounds.- Neumann Problem. Dirichlet Integral.- Problem.- Hypercircle.- Geometrical Illustrations.- Mean.- Example 11.1. an Anisotropic Bar (Numerical Example).- 11.2. for Deflection Plates Solution at Point.- 11.1.1. The L*L Method Kato-Fujita.- Poisson's 11.1.2. Diaz-Greenberg Method.- 11.3. Circular Plate 11.1.3. Washizu Procedure.- 11.4. 12. Elastic State Vector.- Uniqueness Vertices.- Hypersphere. Hyperplane. 12.1. on State.- Fundamental Auxiliary States.- Cylinder Gravity Field Galerkin 12.2. Green's Function.- 12.3. Hypercircle 12.4. A Comment.- 13. Illustrations. Projection 13.1. Arithmetic Progression 13.2. Heated Approximations. Chebyshev 13.3. 14. Rayleigh-Ritz Trefftz Methods.- 14.1. Coordinate Admissibility.- Sequences Lagrange Castigliano Torsional Rigidity.- 14.2. Biharmonic More General 14.3. Remark.- 14.4. Improvement 15. 15.1. Inverse Symmetry Nondegeneracy Forms.- 15.2. Minimum 15.3. Laws' Approach.- Reciprocal Theorems.- 15.4. Plane Tripod.- Lines Self-Equilibrated Stress Equilibrium Principle.- Maximum 16. Distributions. Sobolev 16.1. Distributions.- Delta Test Functions.- Distribution.- Differentiation An Example.- 16.2. Answers to References.