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

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

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.

This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry. Containing over 171 diagrams, the approach allows for a straightforward treatment of its subject area. It is particularly attractive for its wealth of applications and variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry.
Examines topology of recent compact surfaces through the development of simple ideas in plane geometryContains a wealth of applications and a variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry

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

These volumes cover all the major aspects of numerical analysis. This particular volume discusses the solution of equations in Rn, Gaussian elimination, techniques of scientific computer, the analysis of multigrid methods, wavelet methods, and finite volume methods.

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.

Intended a both a textbook and a reference, Fourier Acoustics develops the theory of sound radiation uniquely from the viewpoint of Fourier Analysis. This powerful perspective of sound radiation provides the reader with a comprehensive and practical understanding which will enable him or her to diagnose and solve sound and vibration problems in the 21st Century. As a result of this perspective, Fourier Acoustics is able to present thoroughly and simply, for the first time in book form, the theory of nearfield acoustical holography, an important technique which has revolutionised the measurement of sound. Relying little on material outside the book, Fourier Acoustics will be invaluable as a graduate level text as well as a reference for researchers in academia and industry.
Key Features
* The physics of wave propogation and sound vibration in homogeneous media
*Acoustics, such as radiation of sound, and radiation from vibrating surfaces
*Inverse problems, such as the theory of nearfield acoustical holography
*Mathematics of specialized functions, such as spherical harmonics

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.
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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.

This text presents the 17th and concluding volume of the "Statistics Handbook". It covers order statistics, dealing primarily with applications. The book is divided into six parts as follows: results for specific distributions; linear estimation; inferential methods; prediction; goodness-of-fit tests; and applications. Theoretical advances have been made in this area of research, and order statistics has also found important applications in many diverse areas, these include life-testing and reliability, robustness studies, statistical quality control, filtering theory, signal processing, image processing, and radar target detection. A variety of theoretical researchers, statisticians and engineers have been brought together to produce this handbook, and the subject of order statistics has been split across volumes 16 and 17. Volume 17 focuses on applications and an extensive author and subject index aims to offer easy access to all the material included in both volumes.

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 series of volumes aims to cover the major aspects of Numerical Analysis, serving as the basic reference work on the subject. Each volume concentrates on one, two, or three, particular topics. Each article, is an in-depth survey, reflecting the most recent trends in the field, and is essentially self-contained. The handbook covers the basic methods of numerical analysis, under the following general headings: solution of equations in R n; finite difference methods; finite element methods; techniques of scientific computing; and optimization theory and systems science. It also covers the numerical solution of actual problems of contemporary interest in Applied Mathematics.

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

Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

This series of volumes aims to cover all the major aspects of numerical analysis, serving as the basic reference work on the subject. Each volume will concentrate on one, two or three particular topics. Each article, written by an expert, is an in-depth survey, reflecting the most recent trends in the field, and is essentially self-contained. The Handbook will cover the basic methods of numerical analysis, under the following general headings: solution of equations in Rn; finite difference methods; finite element methods; techniques of scientific computing; and optimization theory and systems science. It will also cover the numerical solution of actual problems of contemporary interest in applied mathematics, under the following headings: numerical methods of fluids; numerical methods for solids; and specific applications - including meteorology, seismology, petroleum mechanics and celestial mechanics.

* 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.

The papers in this volume consider a general area of study known as network routing. The underlying problems are conceptually simple, yet mathematically complex and challenging. How can we best route material or people from one place to another? Or, how can we best design a system (for instance locate facilities) to provide services and goods as efficiently and equitably as possible? The problems encountered in answering these questions often have an underlying combinatorial structure, for example, either we dispatch a vehicle or we do not, or we use one particular route or another. The problems also typically have an underlying network structure (a communication or transportation network). In addition, models for these problems are often very large with hundreds or thousands of constraints and variables. A companion volume in the "Handbook" series, entitled "Network Models", treats basic network models such as minimum cost flows, matching and the travelling salesman problem, as well as, several complex network topics, not directly related to routing, such as network design and network reliability.

Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is emphasised throughout.
Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to more advanced theories.
* Adopts a geometric approach
* Develops gradually, building from basics to the concept of isometry and vector calculus
* Assumes virtually no prior knowledge
* Numerous worked examples, exercises and challenge questions

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.

This book gives a rigorous yet physics focused introduction to mathematical logic that is geared towards natural science majors. We present the science major with a robust introduction to logic, focusing on the specific knowledge and skills that will unavoidably be needed in calculus topics and natural science topics in general rather than taking a philosophical-math-fundamental oriented approach that is commonly found in mathematical logic textbooks.

In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.

The central theme of this book is the study of self-dual connections on four-manifolds. The author's aim is to present a lucid introduction to moduli space techniques (for vector bundles with SO (3) as structure group) and to apply them to four-manifolds. The authors have adopted a topologists' perspective. For example, they have included some explicit calculations using the Atiyah-Singer index theorem as well as methods from equivariant topology in the study of the topology of the moduli space. Results covered include Donaldson's Theorem that the only positive definite form which occurs as an intersection form of a smooth four-manifold is the standard positive definite form, as well as those of Fintushel and Stern which show that the integral homology cobordism group of integral homology three-spheres has elements of infinite order. Little previous knowledge of differential geometry is assumed and so postgraduate students and research workers will find this both an accessible and complete introduction to currently one of the most active areas of mathematical research.