• Technology, Engineering & Agriculture
      April 2018

      Mathematik für angewandte Wissenschaften

      Ein Lehrbuch für Ingenieure und Naturwissenschaftler

      by Joachim Erven, Dietrich Schwägerl

      Grundlagen: Mengen, reelle Zahlen, elementare Funktionen, Grenzwerte; Lineare Algebra (wesentlich ergänzt): Vektorräume, lineare Gleichungssysteme, Matrizen, Eigenwerte, analytische Geometrie, Skalarprodukt, Norm; komplexe Zahlen: GAUSSsche Zahlenebene, komplexe Funktionen, Anwendungen in der Technik; Differentialrechnung: Differenzierbarkeit, Ableitungsregeln, Anwendung auf Näherungen und Grenzwerte, NEWTON-Iteration; Integralrechnung: Unbestimmtes, bestimmtes, uneigentliches Integral, Hauptsatz der Differential- und Integralrechnung, Integrationsmethoden, praktische Anwendungen, numerische Integration; Ebene und räumliche Kurven: Parameterdarstellung von Kurven, Kurvengleichung in Polarkoordinaten; Reihen: Konvergenzkriterien, Potenzreihen, FOURIER-Reihen; Funktionen mehrerer Variablen: Partielle und vollständige Differenzierbarkeit, Doppelintegrale, Kurvenintegrale, Flächen im Raum, Umrisse; Differentialgleichungen: Elementare Verfahren für Dgln 1. und 2. Ordnung, lineare Dgln, Dgl-Systeme. Neu enthalten: Lineare Ausgleichsrechnung, Nabla-Kalkül, LAPLACE-Transformation, RUNGE-KUTTA-Verfahren In diesem Lehrbuch werden alle notwendigen Mathematikgrundlagen für Ingenieure und Naturwissenschaftler in einem Band dargestellt. Viele anschauliche Beispiele führen in die Thematik ein und vertiefen das Gelernte anhand von über 300 Grafiken. Mit mehr als 300 Übungsaufgaben mit Lösungen eignet sich das Buch hervorragend zum Selbststudium. Die Erstauflage dieses Buches, 1999 unter dem Titel »Mathematik für Ingenieure« erschienen, entstand aus Vorlesungen, die die beiden Autoren in verschiedenen Fachbereichen der Hochschule München gehalten haben. In der Folge wurden mehrfach Überarbeitungen und Ergänzungen vorgenommen.

    • Science & Mathematics
      August 2000

      Nonlinear Wave Equations Perturbed by Viscous Terms

      by Petr P. Mosolov, Viktor P. Maslov, Maria A. Shishkova

      The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, BrasilWalter D. Neumann, Columbia University, New York, USAMarkus J. Pflaum, University of Colorado, Boulder, USADierk Schleicher, Jacobs University, Bremen, GermanyKatrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2018)Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

    • Technology, Engineering & Agriculture
      February 2008

      Mathematik für Ingenieure

      by Joachim Erven, Dietrich Schwägerl

      Mathematik - muss das sein? Ja, und mit den Beispielen in diesem Buch macht's sogar Spaß. Denn hier wird Mathematik anhand alltäglicher Probleme erklärt. So lassen sich mathematische Grundlagen darstellen und Methoden und Werkzeuge entwickeln. Die ganze fürs Studium notwendige Mathematik wird anwendbar präsentiert. Zahlreiche Bilder und ausführlich durchgerechnete Beispiele veranschaulichen den Stoff; viele Übungsaufgaben mit Lösungen machen fit für die Prüfung.

    • Science & Mathematics
      November 2000

      Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data

      by V. P. Golubyatnikov

      The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

    • Business, Economics & Law
      March 2009

      Quantitative Methoden der Wirtschaftswissenschaften

      Ein Mathematik-Lehrbuch mit 35 Abbildungen und 131 Aufgaben nebst ausführlich ausgearbeiteten Lösungen

      by Claus-Michael Langenbahn

      Wirtschaftwissenschaften und Mathematik sind eng miteinander verflochtene Fachgebiete. Aus diesem Grund ist es für Wirtschaftswissenschaftler unerlässlich, sich schon im Grundstudium fundierte Kenntnisse etwa in Finanzmathematik oder Extremwertberechnung anzueignen. Um dieses Wissen verständlich zu vermitteln, erklärt der Autor einerseits die Vorgehensweisen anhand von Praxisbeispielen und zahlreichen Anwendungen. Zum anderen werden die gängigen Methoden ausführlich beleuchtet, damit der Lernende in die Lage versetzt wird, die vorgestellten Modelle zu analysieren, weiterzuentwickeln und an die eigenen Erfordernisse anzupassen. Die Verständnisfragen und Aufgaben mit Lösungen zu jedem Kapitel, erleichtern es dem Studierenden, die eigenen Fortschritte zu überprüfen und Wissenslücken aufzuspüren. Die acht Klausuraufgaben mit angegebener Gewichtung helfen, die Prüfungssituation zu simulieren. Abgerundet wird das Lehrbuch durch ein Repetitorium Schulmathematik, durch das die wichtigsten Grundlagen aufgefrischt werden können.

    • Science & Mathematics
      June 2017

      Nonlinear Dynamics

      Mathematical Models for Rigid Bodies with a Liquid

      by Ivan A. Lukovsky

      This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the “fluid-structure” interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid.

    • Science & Mathematics
      November 2018

      Numerical Tensor Methods

      Tensor Trains in Mathematics and Computer Science

      by Ivan Oseledets

      Covering both theoretical foundations and applications in mathematics and engineering, this graduate textbook introduces numerical, tensor-based methods for tackling high-dimensional problems. Concepts known as tensor trains, matrix product states or hierarchical tensor networks have a range of applications in differential equations, multidimensional integration, machine learning, condensed matter physics, and theoretical chemistry.

    • Science & Mathematics
      September 2017

      The Robust Multigrid Technique

      For Black-Box Software

      by Sergey I. Martynenko

      This book presents a detailed description of a robust pseudomultigrid algorithm for solving (initial-)boundary value problems on structured grids in a black-box manner. To overcome the problem of robustness, the presented Robust Multigrid Technique (RMT) is based on the application of the essential multigrid principle in a single grid algorithm. It results in an extremely simple, very robust and highly parallel solver with close-to-optimal algorithmic complexity and the least number of problem-dependent components. Topics covered include an introduction to the mathematical principles of multigrid methods, a detailed description of RMT, results of convergence analysis and complexity, possible expansion on unstructured grids, numerical experiments and a brief description of multigrid software, parallel RMT and estimations of speed-up and efficiency of the parallel multigrid algorithms, and finally applications of RMT for the numerical solution of the incompressible Navier Stokes equations. Potential readers are graduate students and researchers working in applied and numerical mathematics as well as multigrid practitioners and software programmers. ContentsIntroduction to multigridRobust multigrid techniqueParallel multigrid methodsApplications of multigrid methods in computational fluid dynamics

    • Science & Mathematics
      December 2018

      Rigid Body Dynamics

      by Alexey V. Borisov, Ivan S. Mamaev, Higher Education Press Ltd. Comp.

      This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics.

    • Science & Mathematics
      November 2018

      Direct and Large-Eddy Simulation

      by Bernard J. Geurts

      This authoritative book presents an overview of the mathematics behind the simulation of turbulent flows and discusses in detail the phenomenology of turbulence in fluid dynamics, direct and large-eddy simulations, subgrid modeling, and also covers validation and reliability issues.

    • Science & Mathematics
      September 2017

      Optimal Structural Design

      Contact Problems and High-Speed Penetration

      by Nikolay V. Banichuk, Svetlana Yu. Ivanova

      This monograph studies optimization problems for rigid punches in elastic media and for high-speed penetration of rigid strikers into deformed elastoplastic, concrete, and composite media using variational calculations, tools from functional analysis, and stochastic and min-max (guaranteed) optimization approaches with incomplete data. The book presents analytical and numerical results developed by the authors during the last ten years. ContentsPart I: Quasi-statics of contact interactionOptimal contact pressure and optimal punch shapeInfluence of forces applied outside contact regionShape optimization of punch moving with frictionOptimization in contact problems under incomplete dataApplication of probabilistic dataMinimization of material wearMultiobjective optimization of contact pressure, wear of material, and energy dissipation Part II: High-speed penetration into deformable mediumOptimization of impactor shapeStrikers of nonaxisymmetric optimal shapeMultiobjective optimization of rigid shellOptimization of truncated rotating strikersPenetration into solid medium under strength constraintsSome problems of global multipurpose structural optimizationAnalytical and numerical estimations of optimal parameters of layered slabStriker shape optimization using condition of minimal ballistic limit velocity for layered slabs Part III: AppendicesNonadditive functionals and extremum conditionsMultivariant estimation of functionals and their sensitivityBasic ideas of multicriteria optimizationEvolutionary algorithm of global optimization

    • Science & Mathematics
      July 2018

      Attractors and Inertial Manifolds

      by Boling Guo, Liming Ling, Yansheng Ma, Hui Yang

      This book presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics.

    • Science & Mathematics
      February 2018

      Regularization Algorithms for Ill-Posed Problems

      by Anatoly B. Bakushinsky, Mikhail M. Kokurin, Mikhail Yu. Kokurin

      This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. ContentsIntroductionRegularization Methods For Linear EquationsFinite Difference MethodsIterative Regularization MethodsFinite-Dimensional Iterative ProcessesVariational Inequalities and Optimization Problems

    • Science & Mathematics
      March 2018

      Optimal Methods for Ill-Posed Problems

      With Applications to Heat Conduction

      by Vitalii P. Tanana, Anna I. Sidikova

      The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. ContentsModulus of continuity of the inverse operator and methods for solving ill-posed problemsLavrent’ev methods for constructing approximate solutions of linear operator equations of the first kindTikhonov regularization methodProjection-regularization methodInverse heat exchange problems

    • Science & Mathematics
      August 2018

      Hamilton-Jacobi-Bellman Equations

      Numerical Methods and Applications in Optimal Control

      by Dante Kalise, Karl Kunisch, Zhiping Rao, Marianne Akian, Jan Blechschmidt, Nikolai D. Botkin, Max Jensen, Axel Kröner, Athena Picarelli, Iain Smears, Karsten Urban, Mickaël D. Chekroun, Roland Herzog, Ilja Kalmykov, Johannes Diepolder, Eric Fodjo, Honghu Liu, Christoph Reisinger, Julen Rotaetxe Arto, Sebastian Steck, Varvara L. Turova

      Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, dynamic programming requires the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerics of such problems using finite elements, semi-Lagrangian schemes, sparse grid and high-dimensional approximation, and model reduction techniques.

    • Science & Mathematics
      July 2018

      Maxwell’s Equations

      Analysis and Numerics

      by Ulrich Langer, Dirk Pauly, Sergey I. Repin

      The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansjörg Albrecher, University of Lausanne, SwitzerlandHeinz W. Engl, Johannes Kepler University Linz, Austria; University of Vienna, AustriaRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria

    • Science & Mathematics
      November 2018

      Space-Time Methods

      Applications to Partial Differential Equations

      by Ulrich Langer, Olaf Steinbach

      The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansjörg Albrecher, University of Lausanne, SwitzerlandHeinz W. Engl, Johannes Kepler University Linz, Austria; University of Vienna, AustriaRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria

    • Science & Mathematics
      July 2018

      Attractors and Methods

      by Boling Guo, Liming Ling, Yansheng Ma, Hui Yang

      This book presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics.

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