02560oam 2200493 450 991029947800332120190911112726.03-319-04295-510.1007/978-3-319-04295-4(OCoLC)871713309(MiFhGG)GVRL6XFD(EXLCZ)99371000000008367620131211d2014 uy 0engurun|---uuuuatxtccrHaar wavelets with applications /Ulo Lepik, Helle Hein1st ed. 2014.Cham [Switzerland] :Springer,2014.1 online resource (x, 207 pages) illustrationsMathematical Engineering,2192-4732"ISSN: 2192-4732."3-319-04294-7 Includes bibliographical references and index.Preliminaries -- Haar wavelets -- Solution of ordinary differential equations (ODEs) -- Stiff equations -- Integral equations -- Evolution equations -- Solving PDEs with the aid of two-dimensional Haar wavelets -- Fractional calculus -- Applying Haar wavelets in the optimal control theory -- Buckling of elastic beams -- Vibrations of cracked Euler-Bernoulli beams -- Free vibrations on non-uniform and axially functionally graded Euler-Bernoulli beams -- Vibrations of functionally graded Timoshenko beams -- Applying Haar wavelets in damage detection using machine learning methods.This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.Mathematical engineering.Haar system (Mathematics)System identificationMathematical modelsWavelets (Mathematics)Haar system (Mathematics)System identificationMathematical models.Wavelets (Mathematics)515.2433Lepik Üloauthttp://id.loc.gov/vocabulary/relators/aut989116Hein HelleMiFhGGMiFhGGBOOK9910299478003321Haar Wavelets2262112UNINA