Volker Mehrmann's Books

Linear Algebra

By: Jörg Liesen,Volker Mehrmann

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This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.

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Page Count

321

Publisher

Springer

Published Date

ISBN 10

3319243462

ISBN 13

9783319243467

Differential-algebraic Equations

Analysis and Numerical Solution

By: PETER KUNKEL; VOLKER MEHRMANN.,Peter Kunkel,Volker Ludwig Mehrmann

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Differential-algebraic Equations

Analysis and Numerical Solution

By: PETER KUNKEL; VOLKER MEHRMANN.,Peter Kunkel,Volker Ludwig Mehrmann

Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge--Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study.

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377

ISBN 10

3037195177

ISBN 13

9783037195178

MATHEON

Mathematics for Key Technologies

By: Peter Deuflhard

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MATHEON

Mathematics for Key Technologies

By: Peter Deuflhard

Mathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these! The last three of its facets have been the focus of the research and development in the Berlin-based DFG Research Center MATHEON in the last twelve years. Through these activities MATHEON has become an international trademark for carrying out creative, application-driven research in mathematics and for cooperating with industrial partners in the solution of complex problems in key technologies. Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as Optimization, Discrete Mathematics, Numerical Analysis, Scientific Computing, Applied Analysis and Stochastic Analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in the solution of the challenging problems in key technologies. This book presents in seven chapters the highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of "showcases" are presented that illustrate a few success stories.

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453

Published Date

ISBN 10

3037196378

ISBN 13

9783037196373

Dimension Reduction of Large-Scale Systems

Proceedings of a Workshop held in Oberwolfach, Germany, October 19-25, 2003

By: Peter Benner,Volker Mehrmann,Danny C. Sorensen

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Dimension Reduction of Large-Scale Systems

Proceedings of a Workshop held in Oberwolfach, Germany, October 19-25, 2003

By: Peter Benner,Volker Mehrmann,Danny C. Sorensen

In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

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Page Count

420

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540245456

ISBN 13

9783540245452

Book's by Volker Mehrmann

Linear Algebra

Linear Algebra

Differential-algebraic Equations

Differential-algebraic Equations

MATHEON

MATHEON

Dimension Reduction of Large-Scale Systems

Dimension Reduction of Large-Scale Systems

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