## Applications of functional analysis in engineering |

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### Contents

Physical Space Abstract Spaces | 1 |

Basic Vector Algebra | 13 |

Linear Independence Vector Components Space Dimension | 25 |

Copyright | |

18 other sections not shown

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### Common terms and phrases

approximate solution arbitrary assume Axiom Bessel Bessel's inequality bilinear boundary conditions boundary value problem Cauchy-Schwarz inequality Chapter coefficients Compare components concept consider convergence coordinate coordinate vectors corresponding defined denote derivative differential dimension displacement distance dx dy eigenvalue elastic elements equality equilibrium Euclidean space exact solution example fact Figure finite function F(x function space function vectors geometric given Hilbert space hyperplane hypersphere illustration implies inasmuch infinite number infinite-dimensional inner product inner product space intersection interval latter linear combination linear manifold linearly independent linearly independent vectors lower bound metric norm notation operator orthogonal projection orthonormal basis orthonormal vectors perpendicular plane position vector preceding equation Rayleigh-Ritz real numbers represented respectively satisfies scalar sequence spanned strain energy stress subspaces 9 symmetry theorem tions torsion translated subspaces triangle triangle inequality upper bound vector space zero vector