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Efficient Transient Noise Analysis in Circuit Simulation
The current technological progress in microelectronics is driven by the desire to decrease feature sizes, increase frequencies and the need for low supply voltages. Amongst other effects the signal-to-noise ratio decreases and the transient noise analysis becomes necessary in the simulation of electronic circuits. Taking the inner electronic noise into account by means of Gaussian white noise currents, mathematical modelling leads to stochastic differential algebraic equations (SDAEs) with a large number of small noise sources. The simulation of such systems requires an efficient numerical time integration by mean-square convergent numerical methods. In this thesis, adaptive linear multi-step Maruyama schemes to solve stochastic differential equations (SDEs) and SDAEs are developed. A reliable local error estimate for systems with small noise is provided and a strategy for controlling the step-size and the number of solution paths simultaneously in one approximation is presented. Numerical experiments on industrial relevant real-life applications illustrate the theoretical findings.
Scientific Computing in Electrical Engineering SCEE 2008
This book is a collection of 65 selected papers presented at the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in Espoo, Finland, in 2008. The aim of the SCEE 2008 conference was to bring together scientists from academia and industry, e.g. mathematicians, electrical engineers, computer scientists, and physicists, with the goal of intensive discussions on industrially relevant mathematical problems, with an emphasis on modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems.This extensive reference work is divided into five parts: 1. Computational electromagnetics, 2. Circuit simulation, 3. Coupled problems, 4. Mathematical and computational methods, and 5. Model-order reduction. Each part starts with an general introduction followed by the actual papers.
Scientific Computing in Electrical Engineering
This book is a collection of selected papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sinaia, Romania, in 2006. The series of SCEE conferences aims at addressing mathematical problems which have a relevance to industry, with an emphasis on modeling and numerical simulation of electronic circuits, electromagnetic fields but also coupled problems and general mathematical and computational methods.
Real-World Problems for Secondary School Mathematics Students
This is a book full of ideas for introducing real world problems into mathematics classrooms and assisting teachers and students to benefit from the experience. Taken as a whole these contributions provide a rich resource for mathematics teachers and their students that is readily available in a single volume. Nowadays there is a universal emphasis on teaching for understanding, motivating students to learn mathematics and using real world problems to improve the mathematics experience of school students. However, using real world problems in mathematics classrooms places extra demands on teachers in terms of extra-mathematical knowledge e.g. knowledge of the area of applications, and pedago...
High Performance CMOS Range Imaging
This work is dedicated to CMOS based imaging with the emphasis on the noise modeling, characterization and optimization in order to contribute to the design of high performance imagers in general and range imagers in particular. CMOS is known to be superior to CCD due to its flexibility in terms of integration capabilities, but typically has to be
Mathematics – Key Technology for the Future
This book is about the results of a number of projects funded by the BMBF in the initiative "Mathematics for Innovations in Industry and Services". It shows that a broad spectrum of analytical and numerical mathematical methods and programming techniques are used to solve a lot of different specific industrial or services problems. The main focus is on the fact that the mathematics used is not usually standard mathematics or black box mathematics but is specifically developed for specific industrial or services problems. Mathematics is more than a tool box or an ancilarry science for other scientific disciplines or users. Through this book the reader will gain insight into the details of mathematical modeling and numerical simulation for a lot of industrial applications.
The Learning and Teaching of Mathematical Modelling
This book takes stock of the state of affairs of the teaching and learning of mathematical modelling with regard to research, development and practice. It provides a conceptual framework for mathematical modelling in mathematics education at all education levels, as well as the background and resources for teachers to acquire the knowledge and competencies that will allow them to successfully include modelling in their teaching, with an emphasis on the secondary school level. Mathematics teachers, mathematics education researchers and developers will benefit from this book. Expertly written and researched, this book includes a comprehensive overview of research results in the field, an expos...
Progress in Industrial Mathematics at ECMI 2010
ECMI, the European Consortium for Mathematics in Industry, is the European brand associated with applied mathematics for industry and organizes highly successful biannual conferences. In this series, the ECMI 2010, the 16th European Conference on Mathematics for Industry, was held in the historic city hall of Wuppertal in Germany. It covered the mathematics of a wide range of applications and methods, from circuit and electromagnetic device simulation to model order reduction for chip design, uncertainties and stochastics, production, fluids, life and environmental sciences, and dedicated and versatile methods. These proceedings of ECMI 2010 emphasize mathematics as an innovation enabler for industry and business, and as an absolutely essential pre-requiste for Europe on its way to becoming the leading knowledge-based economy in the world.
Monte Carlo-Algorithmen
Der Text gibt eine Einführung in die Mathematik und die Anwendungsmöglichkeiten der Monte Carlo-Methoden und verwendet dazu durchgängig die Sprache der Stochastik. Der Leser lernt die Grundprinzipien und wesentlichen Eigenschaften dieser Verfahren kennen und wird dadurch in den Stand versetzt, dieses wichtige algorithmische Werkzeug kompetent einsetzen und die Ergebnisse interpretieren zu können. Anhand ausgewählter Fragestellungen wird er außerdem an aktuelle Forschungsfragen und -ergebnisse in diesem Bereich herangeführt. Behandelt werden die direkte Simulation, Methoden zur Simulation von Verteilungen und stochastischen Prozessen, Varianzreduktion, sowie Markov Chain Monte Carlo-Methoden und die hochdimensionale Integration. Es werden Anwendungsbeispiele aus der Teilchenphysik und der Finanz- und Versicherungsmathematik präsentiert, und anhand des Integrationsproblems wird gezeigt, wie sich die Frage nach optimalen Algorithmen formulieren und beantworten lässt.
Neue Materialien für einen realitätsbezogenen Mathematikunterricht 4
Der vorliegende Band ist der vierte Band mit "Neuen Materialien für einen realitätsbezogenen Mathematikunterricht". Er enthält eine Sammlung von aktualisierten und überarbeiteten Beiträgen zur Istron-Schriftenreihe aus den letzten 25 Jahren, die uns als besonders fruchtbar und anregend erschienen, als „Best of“ dieser Schriftenreihe. Seit 1991 gibt es eine deutschsprachige ISTRON-Gruppe, die das Ziel verfolgt, Modellierungen und Realitätsbezüge in den (all-)täglichen Mathematikunterricht zu integrieren. Die ISTRON-Gruppe gibt seit dieser Zeit eine Schriftenreihe mit Materialien für einen realitätsbezogenen Mathematikunterricht heraus. Diese Reihe richtet sich an Mathematiklehrende an Schulen und Hochschulen, aber auch an Studierende und Dozierende in der Weiterbildung. Die Beiträge zeigen, wie man mathematische Anwendungen und Modellierungen im alltäglichen Mathematikunterricht implementieren kann. Es werden interessante, relevante und aktuelle Themen aufgegriffen, für denUnterricht aufbereitet und lernerorientiert dargestellt.
