Economic theories can be expressed in words, numbers, graphs and symbols. The existing traditional economics textbooks cover all four methods, but the general focus is often more on writing about the theory and methods, with few practical examples. With an increasing number of universities having introduced mathematical economics at undergraduate level, Basic mathematics for economics students aims to fill this gap in the field. Basic mathematics for economics students begins with a comprehensive chapter on basic mathematical concepts and methods (suitable for self-study, revision or tutorial purposes) to ensure that students have the necessary foundation. The book is written in an accessible style and is extremely practical. Numerous mathematical economics examples and exercises are provided as well as fully worked solutions using numbers, graphs and symbols. Basic mathematics for economics students is aimed at all economics students. It focuses on quantitative aspects and especially complements the three highly popular theoretical economics textbooks, Understanding microeconomics, Understanding macroeconomics and Economics for South African students, all written by Philip Mohr and published by Van Schaik Publishers.

Microfluidics: Modeling, Mechanics and Mathematics, Second Edition provides a practical, lab-based approach to nano- and microfluidics, including a wealth of practical techniques, protocols and experiments ready to be put into practice in both research and industrial settings. This practical approach is ideally suited to researchers and R&D staff in industry. Additionally, the interdisciplinary approach to the science of nano- and microfluidics enables readers from a range of different academic disciplines to broaden their understanding. Alongside traditional fluid/transport topics, the book contains a wealth of coverage of materials and manufacturing techniques, chemical modification/surface functionalization, biochemical analysis, and the biosensors involved. This fully updated new edition also includes new sections on viscous flows and centrifugal microfluidics, expanding the types of platforms covered to include centrifugal, capillary and electro kinetic platforms.

Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools necessary to characterize Gaussian processes. The book focuses on the particular case of the linear combination of independent fractional and sub-fractional Brownian motions with different Hurst indices. Stochastic integration with respect to these processes is considered, as is the study of the existence and uniqueness of solutions of related SDE's. Applications in finance and statistics are also explored, with each chapter supplying a number of exercises to illustrate key concepts.

Dark Silicon and the Future of On-chip Systems, Volume 110, the latest release in the Advances in Computers series published since 1960, presents detailed coverage of innovations in computer hardware, software, theory, design and applications, with this release focusing on an Introduction to dark silicon and future processors, a Revisiting of processor allocation and application mapping in future CMPs in the dark silicon era, Multi-objectivism in the dark silicon age, Dark silicon aware resource management for many-core systems, Dynamic power management for dark silicon multi-core processors, Topology specialization for networks-on-chip in the dark silicon era, and Emerging SRAM-based FPGA architectures.

Quantifying and Managing Soil Functions in Earth's Critical Zone: Combining Experimentation and Mathematical Modelling, Volume 142, the latest in the Advances in Agronomy series continues its reputation as a leading reference and first-rate source for the latest research in agronomy. Each volume contains an eclectic group of reviews by leading scientists throughout the world. Five volumes are published yearly, ensuring that the authors' contributions are disseminated to the readership in a timely manner. As always, the subjects covered are varied and exemplary of the myriad of subject matter dealt with by this long-running serial.

Engineering is mathematics in action. But engineering students do not always see the link between what they learn in mathematics and how this applies to engineering problems.

From relatively simple questions, like determining the maximum weight a beam can support to complex projects like mapping out the most efficient electrical flow for a city’s traffic lights, mathematics is essential.

In July 2009, many experts in the mathematical modeling of biological sciences gathered in Les Houches for a 4-week summer school on the mechanics and physics of biological systems. The goal of the school was to present to students and researchers an integrated view of new trends and challenges in physical and mathematical aspects of biomechanics. While the scope for such a topic is very wide, they focused on problems where solid and fluid mechanics play a central role. The school covered both the general mathematical theory of mechanical biology in the context of continuum mechanics but also the specific modeling of particular systems in the biology of the cell, plants, microbes, and in physiology.
These lecture notes are organized (as was the school) around five different main topics all connected by the common theme of continuum modeling for biological systems: Bio-fluidics, Bio-gels, Bio-mechanics, Bio-membranes, and Morphogenesis. These notes are not meant as a journal review of the topic but rather as a gentle tutorial introduction to the readers who want to understand the basic problematic in modeling biological systems from a mechanics perspective.

Modelling and Control in Biomedical Systems (including Biological Systems) was held in Reims, France, 20-22 August 2006. This Symposium was organised by the University of Reims Champagne Ardenne and the Societe de l Electricite, de l Electronique et des TIC (SEE).
The Symposium attracted practitioners in engineering, information technology, mathematics, medicine and biology, and other related disciplines, with authors from 24 countries. Besides the abstracts of the four plenary lectures, this volume contains the 92 papers that were presented by their authors at the Symposium
The papers included two invited keynote presentations given by internationally prominent and well-recognised research leaders: Claudio Cobelli, whose talk is titled "Dynamic modelling in diabetes: from whole body to genes"; and Irving J. Bigio, whose talk is titled "Elastic scattering spectroscopy for non-invasive detection of cancer." Two prestigious industrial speakers were also invited to give keynote presentations: Terry O'Brien from LIDCO, whose talk is titled "LIDCO: From the laboratory to protocolized goal directed therapy"; and Lorenzo Quinzio of Philips, whose talk is titled "Clinical decision support in monitoring and information systems."
* A valuable source of information on the state-of- the-art in Modelling and Control in Biomedical Systems
* Including abstracts of four plenary lectures, and 92 papers presented by their authors"

A series of seminal technological revolutions has led to a new generation of electronic devices miniaturized to such tiny scales where the strange laws of quantum physics come into play. There is no doubt that, unlike scientists and engineers of the past, technology leaders of the future will have to rely on quantum mechanics in their everyday work. This makes teaching and learning the subject of paramount importance for further progress. Mastering quantum physics is a very non-trivial task and its deep understanding can only be achieved through working out real-life problems and examples. It is notoriously difficult to come up with new quantum-mechanical problems that would be solvable with a pencil and paper, and within a finite amount of time. This book remarkably presents some 700+ original problems in quantum mechanics together with detailed solutions covering nearly 1000 pages on all aspects of quantum science. The material is largely new to the English-speaking audience. The problems have been collected over about 60 years, first by the lead author, the late Prof. Victor Galitski, Sr. Over the years, new problems were added and the material polished by Prof. Boris Karnakov. Finally, Prof. Victor Galitski, Jr., has extended the material with new problems particularly relevant to modern science.

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic.
Infinite Words explores "all" aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Buchi, McNaughton and Schutzenberger.
Serves as both an introduction to the field and as a reference book.
Contains numerous exercises desgined to aid students and readers.
Self-contained chapters provide helpful guidance for lectures.

A 'stochastic' process is a 'random' or 'conjectural' process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance.
This book deals with the tools and techniques used in the stochastic process - estimation, optimisation and recursive logarithms - in a form accessible to engineers and which can also be applied to Matlab.
Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximisation. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.
*An engineering approach to applied probabilities and statistics
*Presents examples related to practical engineering applications, such as reliability, randomness and use of resources
*Readers with varying interests and mathematical backgrounds will find this book accessible

This book is carefully designed to be used on a wide range of introductory courses at first degree and HND level in the U.K., with content matched to a variety of first year degree modules from IEng and other BSc Engineering and Technology courses. Lecturers will find the breadth of material covered gears the book towards a flexible style of use, which can be tailored to their syllabus, and used along side the other IIE Core Textbooks to bring first year students up to speed on the mathematics they require for their engineering degree.
*Features real-world examples, case studies, assignments and knowledge-check questions throughout
*Introduces key mathematical methods in practical engineering contexts
*Bridges the gap between theory and practice

This book may be used as a companion for introductory laboratory courses, as well as possible STEM projects. It covers essential Microsoft EXCEL(R) computational skills while analyzing introductory physics projects. Topics of numerical analysis include: multiple graphs on the same sheet, calculation of descriptive statistical parameters, a 3-point interpolation, the Euler and the Runge-Kutter methods to solve equations of motion, the Fourier transform to calculate the normal modes of a double pendulum, matrix calculations to solve coupled linear equations of a DC circuit, animation of waves and Lissajous figures, electric and magnetic field calculations from the Poisson equation and its 3D surface graphs, variational calculus such as Fermat's least traveling time principle, and the least action principle. Nelson's stochastic quantum dynamics is also introduced to draw quantum particle trajectories.

For a physicist noise is not just about sounds. It refers to any random physical process that blurs measurements and, in so doing, stands in the way of scientific knowledge. This short book deals with the most common types of noise, their properties, and some of their unexpected virtues. The text assumes that the reader knows the basics of probability theory and explains the most useful mathematical concepts related to noise. Finally, it aims at making this subject more widely known, and stimulating interest in its study in young physicists.

Working through this student-centred text readers will be brought up to speed with the modelling of control systems using Laplace, and given a solid grounding of the pivotal role of control systems across the spectrum of modern engineering. A clear, readable text is supported by numerous worked example and problems.
* Key concepts and techniques introduced through applications
* Introduces mathematical techniques without assuming prior knowledge
* Written for the latest vocational and undergraduate courses

Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.
Multigrid methods are invaluable to researchers in scientific disciplines including physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines. They are also becoming increasingly important in economics and financial mathematics.
Readers are presented with an invaluable summary covering 25 years of practical experience acquired by the multigrid research group at the Germany National Research Center for Information Technology. The book presents both practical and theoretical points of view.
* Covers the whole field of multigrid methods from its elements up to the most advanced applications
* Style is essentially elementary but mathematically rigorous
* No other book is so comprehensive and written for both practitioners and students

This book provides a rigorous, physics-focused introduction to set theory that is geared towards natural science majors. The science major is presented with a robust introduction to set theory, which concentrates on the specific knowledge and skills that will be needed in calculus topics and natural science topics in general.

The objective of this publication is to comprehensively discuss the possibilities of producing steels with pre-determined attributes, demanded by the customer to fit exacting specifications. The information presented in the book has been designed to indicate the reasons for the expenses and to aid in the process of overcoming the difficulties and reducing the costs.

In nine detailed chapters, the authors cover topics including: steel as a major contributor to the economic wealth of a country in terms of its capabilities and production current concerns of major steel producers phenomena contributing to the quality of the product information concerning the boundary conditions of the rolling process and initial conditions, put to use by mathematical models the solid state incremental approach and flow formulation parameters and variables - most of which make use of the exponential nature of phenomena that are activated by thermal energy the application of three dimensional analysis to shape rolling the evaluation of parameters by a form of inverse analysis to the flat rolling process knowledge based modeling, using artificial intelligence, expert systems and neural networks

They conclude that when either mathematical or physical modeling of the rolling process is considered and the aim is to satisfy the demands for customers, it is possible to produce what the customer wants, exactly.
"

In recent years, there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter.

Since the earliest days of human existence, the clash of thunder and trembling of the hills has struck fear into the hearts of seasoned warriors and tribal villagers alike. Great gods, demi-gods, and heroes were created to explain the awesome, mysterious, and incomprehensibly powerful forces of Nature in a feeble attempt to make sense of the world around them. To our advanced scientific minds today, these explanations seem childish and ridiculous; however, the power to flatten thousands of square miles of ancient forest, create massive holes in the Earth itself, and cause mountains to tremble to their very roots are more than enough reason to believe. Indeed, perhaps our scientific advancement has caused us to not fully or completely appreciate the awesome scale and power that Nature can wield against us. The study of shock wave formation and dynamics begins with a study of waves themselves. Simple harmonic motion is used to analyze the physical mechanisms of wave generation and propagation, and the principle of superposition is used to mathematically generate constructive and destructive interference. Further development leads to the shock singularity where a single wave of immense magnitude propagates and decays through various media. Correlations with the fields of thermodynamics, meteorology, crater formation, and acoustics are made, as well as a few special applications. Direct correlation is made to events in Arizona, Siberia, and others. The mathematical requirement for this text includes trigonometry, differential equations, and large series summations, which should be accessible to most beginning and advanced university students. This text should serve well as supplementary material in a course covering discrete wave dynamics, applied thermodynamics, or extreme acoustics.

This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardt systems with singular nonlinearity in anisotropic media. These nonlinear problems appear as mathematical models in various branches of Physics, Mechanics, Genetics, Economics, Engineering, and they are also relevant in Quantum Physics and Differential Geometry.
One of the main purposes of this volume is to deduce decay rates for general classes of solutions in terms of estimates of particular problems. Much of the material included in this volume is devoted to the asymptotic analysis of solutions and to the qualitative study of related bifurcation problems. Numerical approximations illustrate many abstract results of this volume. A systematic description of the most relevant singular phenomena described in these lecture notes includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity.
The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear singularphenomena

Mathematical modelling modules feature in most university undergraduate mathematics courses. As one of the fastest growing areas of the curriculum it represents the current trend in teaching the more complex areas of mathematics. This book introduces mathematical modelling to the new style of undergraduate - those with less prior knowledge, who require more emphasis on application of techniques in the following sections: What is mathematical modelling?; Seeing modelling at work through population growth; Seeing modelling at work through published papers; Modelling in mechanics.
Written in the lively interactive style of the Modular Mathematics Series, this text will encourage the reader to take part in the modelling process.

* Assumes no prior knowledge
* Adopts a modelling approach
* Numerous tutorial problems, worked examples and exercises included
* Elementary topics augmented by planetary motion and rotating frames
This text provides an invaluable introduction to mechanicsm confining attention to the motion of a particle. It begins with a full discussion of the foundations of the subject within the context of mathematical modelling before covering more advanced topics including the theory of planetary orbits and the use of rotating frames of reference. Truly introductory, the style adoped is perfect for those unfamiliar with the subject and, as emphasis is placed on understanding, readers who have already studied maechanics will also find a new insight into a fundamental topic.