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Model Reduction for Circuit Simulation (Lecture Notes in Electrical Engineering)
Model Reduction for Circuit Simulation (Lecture Notes in Electrical Engineering)

Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems...

Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics)
Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics)
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important...
Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics (Theoretical and Mathematical Physics)
Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics (Theoretical and Mathematical Physics)
Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also...
An Introduction to Fronts in Random Media (Surveys and Tutorials in the Applied Mathematical Sciences)
An Introduction to Fronts in Random Media (Surveys and Tutorials in the Applied Mathematical Sciences)
The aim of this book is to give a user friendly tutorial of an interdisciplinary research topic (fronts in random media) to senior undergraduates and beginning graduate students with basic knowledge of partial differential equations (PDE) and probability. The approach taken is semi-formal, using elementary methods to introduce ideas and motivate...
Principles of Partial Differential Equations (Problem Books in Mathematics)
Principles of Partial Differential Equations (Problem Books in Mathematics)

This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to master solution techniques. The...

Numerical Solution of Partial Differential Equations on Parallel Computers
Numerical Solution of Partial Differential Equations on Parallel Computers

Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need...

Pedestrian Dynamics: Feedback Control of Crowd Evacuation (Understanding Complex Systems)
Pedestrian Dynamics: Feedback Control of Crowd Evacuation (Understanding Complex Systems)
The importance of controlling pedestrian flow especially during emergencies is being understood by researchers to be a very important research area. Currently, the use of static emergency routes is not efficient, since during emergencies, the preferred routes might be congested, or worse yet might not even exist. Hence, it is...
The Finite Element Method: Theory, Implementation, and Applications (Texts in Computational Science and Engineering)
The Finite Element Method: Theory, Implementation, and Applications (Texts in Computational Science and Engineering)

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational...

Spectral Methods in MATLAB (Software, Environments, Tools)
Spectral Methods in MATLAB (Software, Environments, Tools)
This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high...
Implementing Models of Financial Derivatives, with CD-ROM: Object Oriented Applications with VBA
Implementing Models of Financial Derivatives, with CD-ROM: Object Oriented Applications with VBA

Implementing Models of Financial Derivatives is a comprehensivetreatment of advanced implementation techniques in VBA for modelsof financial derivatives. Aimed at readers who are already familiarwith the basics of VBA it emphasizes a fully object orientedapproach to valuation applications, chiefly in the context of MonteCarlo simulation but...

Hypernumbers and Extrafunctions: Extending the Classical Calculus (SpringerBriefs in Mathematics)
Hypernumbers and Extrafunctions: Extending the Classical Calculus (SpringerBriefs in Mathematics)

“Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by...

Problems on Partial Differential Equations (Problem Books in Mathematics)
Problems on Partial Differential Equations (Problem Books in Mathematics)

This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs. Though the text reflects the classical theory, the main emphasis is on introducing readers to the latest developments based on the notions of weak solutions and Sobolev spaces.

In numerous problems, the student is asked to...

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