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Computer-Algebra-Systeme (CAS) und computerorientierte numerische Verfahren (CNV) vereinfachen den praktischen Umgang mit der Mathematik ganz entscheidend und werden in immer weiteren Bereichen angewendet. Bei ingenieurmäßigen Anwendungen kommen CAS und CNV nicht nur für anspruchsvolle mathematische Aufgabenstellungen und Herleitungen in Betracht, sondern auch als Engineering Desktop Software für alle Berechnungen. Mathcad stellt eine Vielfalt an Werkzeugen zur Verfügung und verbindet mathematische Formeln, Berechnungen, Texte, Grafiken usw. in einem einzigen Arbeitsblatt. So lassen sich Berechnungen und ihre Resultate besonders einfach illustrieren, visualisieren und kommentieren. Dieses Lehr- und Arbeitsbuch, aus dem vierbändigen Werk "Angewandte Mathematik mit Mathcad", richtet sich vor allem an Schülerinnen und Schüler höherer Schulen, Studentinnen und Studenten, Naturwissenschaftlerinnen und Naturwissenschaftler und Anwender, speziell im technischen Bereich, die sich über eine computerorientierte Umsetzung mathematischer Probleme informieren wollen und dabei die Vorzüge von Mathcad möglichst effektiv nützen möchten. Angewandte Mathematik mit Mathcad Lehr- und Arbeitsbuch Band 1: Einführung in Mathcad Band 2: Komplexe Zahlen und Funktionen, Vektoralgebra und analytische Geometrie, Matrizenrechnung, Vektoranalysis Band 3: Differential- und Integralrechnung Band 4: Reihen, Transformationen, Differential- und Differenzengleichungen.

Engineering mathematics. --- Engineering --- Mathematical physics. --- Mathematical analysis. --- Algebra. --- Computational intelligence. --- Mathematical and Computational Engineering Applications. --- Mathematical Methods in Physics. --- Analysis. --- Algebra. --- Computational Intelligence. --- Theoretical, Mathematical and Computational Physics. --- Data processing.

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This monograph contains theoretical foundations of the spectral method for fatigue life determination where the authors discuss a rule of description of random loading states with the matrix of power spectral density functions of the stress/strain tensor components. Some chosen criteria of multiaxial fatigue failure being linear combinations of stress or strain components on the critical plane are analyzed. The formula proposed in this book enables to determine power spectral density of the equivalent history directly from the components of the power spectral density matrix of the multidimensional stochastic process. It presents the assumptions and the procedure of determination of basic relationships of the spectral method. The authors work out equations determining the fatigue life according to the spectral method using various linear hypotheses of fatigue damage accumulation. The algorithm of fatigue life contains five blocks: 1 – determination of loading, 2 – determination of the critical plane position for the assumed multiaxial fatigue failure criterion, 3 – determination of power spectral density of the equivalent stress or strain, 4 – determination of statistical parameters of the equivalent parameter responsible for fatigue damage, and 5 – fatigue life calculation according to a suitable hypothesis of damage accumulation. The book can be also recommended to postgraduate and PhD students with an interest in fatigue of engineering materials.

Materials --- Fatigue --- Mathematics. --- Materials -- Fatigue -- Mathematics. --- Materials -- Fatigue. --- Applied Mathematics --- Materials Science --- Chemical & Materials Engineering --- Engineering & Applied Sciences --- Dynamic testing. --- Engineering --- Engineering materials --- Industrial materials --- Dynamic loading (Materials) --- Loading, Dynamic (Materials) --- Loads, Dynamic (Materials) --- Engineering. --- Applied mathematics. --- Engineering mathematics. --- Continuum mechanics. --- Buildings --- Building. --- Construction. --- Engineering, Architectural. --- Materials science. --- Building Construction. --- Continuum Mechanics and Mechanics of Materials. --- Appl.Mathematics/Computational Methods of Engineering. --- Materials Science, general. --- Design and construction. --- Building --- Material science --- Physical sciences --- Architectural engineering --- Construction --- Construction science --- Engineering, Architectural --- Structural design --- Structural engineering --- Architecture --- Construction industry --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Engineering analysis --- Mathematical analysis --- Industrial arts --- Technology --- Design and construction --- Mathematics --- Engineering design --- Manufacturing processes --- Dynamic testing --- Testing --- Mechanics. --- Mechanics, Applied. --- Materials. --- Building Construction and Design. --- Solid Mechanics. --- Mathematical and Computational Engineering. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Buildings—Design and construction. --- Solids. --- Mathematical and Computational Engineering Applications. --- Materials Science. --- Data processing. --- Solid state physics --- Transparent solids

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The mechanics of Coupled Fields is a discipline at the edge of modern research connecting Continuum Mechanics with Solid State Physics. It integrates the Mechanics of Continuous Media, Heat Conductivity and the theory of Electromagnetism that are usually studied separately. For an accurate description of the influence of static and dynamic loadings, high temperatures and strong electromagneticfields in elastic media and constructive installations, a new approach is required; an approach that has the potential to establish a synergism between the above-mentioned fields. Throughout the book a vast number of problems are considered: two-dimensional problems of electro-magneto-elasticity as well as static and dynamical problems for piecewise homogeneous compound piezoelectric plates weakened by cracks and openings. The boundary conditions, the constructive equations and the mathematical methods for their solution are thoroughly presented, so that the reader can get a clear quantitative and qualitative understanding of the phenomena taking place. This book is for the specialists in Continuous Mechanics, Acoustics and Defectoscopy, and also for advanced undergraduate and graduate -level students in Applied Mathematics, Physics, Engineering Mechanics and Physical Sciences.

Continuum mechanics. --- Solid state physics. --- Thermal conductivity. --- Electromagnetic theory. --- Elasticity. --- Milieux continus, Mécanique des --- Physique de l'état solide --- Conductivité thermique --- Théorie électromagnétique --- Elasticité --- Continuum mechanics --- Solid state physics --- Thermal conductivity --- Electromagnetic theory --- Elasticity --- Engineering & Applied Sciences --- Chemical & Materials Engineering --- Applied Mathematics --- Materials Science --- Elastic properties --- Young's modulus --- Coefficient of conductivity --- Conductivity, Heat --- Conductivity, Thermal --- Heat conductivity --- Mechanics of continua --- Engineering. --- Magnetism. --- Magnetic materials. --- Applied mathematics. --- Engineering mathematics. --- Materials science. --- Appl.Mathematics/Computational Methods of Engineering. --- Continuum Mechanics and Mechanics of Materials. --- Magnetism, Magnetic Materials. --- Materials Science, general. --- Engineering, general. --- Mechanics, Analytic --- Field theory (Physics) --- Material science --- Physical sciences --- Engineering --- Engineering analysis --- Mathematical analysis --- Materials --- Mathematical physics --- Physics --- Electricity --- Magnetics --- Construction --- Industrial arts --- Technology --- Mathematics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Heat --- Transport theory --- Solids --- Properties --- Conduction --- Measurement --- Mechanics. --- Mechanics, Applied. --- Materials. --- Mathematical and Computational Engineering. --- Solid Mechanics. --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Solids. --- Mathematical and Computational Engineering Applications. --- Materials Science. --- Technology and Engineering. --- Data processing. --- Transparent solids