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 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

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

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.

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

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.

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.

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

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.

The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time.
Key Features
* Treats differential geometry, differential topology, and quantum field theory
* Includes elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory
* Tackles problems of quantum field theory using differential topology as a tool

This book focuses on broadly defined areas of chemical information science- with special emphasis on chemical informatics- and computer-aided molecular design. The computational and cheminformatics methods discussed, and their application to drug discovery, are essential for sustaining a viable drug development pipeline. It is increasingly challenging to identify new chemical entities and the amount of money and time invested in research to develop a new drug has greatly increased over the past 50 years. The average time to take a drug from clinical testing to approval is currently 7.2 years. Therefore, the need to develop predictive computational techniques to drive research more efficiently to identify compounds and molecules, which have the greatest likelihood of being developed into successful drugs for a target, is of great significance. New methods such as high throughput screening (HTS) and techniques for the computational analysis of hits have contributed to improvements in drug discovery efficiency. The SARMs developed by Jurgen and colleagues have enabled display of SAR data in a more transparent scaffold/functional SAR table. There are many tools and databases available for use in applied drug discovery techniques based on polypharmacology. The cheminformatics approaches and methodologies presented in this volume and at the Skolnik Award Symposium will pave the way for improved efficiency in drug discovery. The lectures and the chapters also reflect the various aspects of scientific enquiry and research interests of the 2015 Herman Skolnik award recipient.

The subject of geomathematics focuses on the interpretation and classification of data from geoscientific and satellite sources, reducing information to a comprehensible form and allowing the testing of concepts. Sphere oriented mathematics plays an important part in this study and this book provides the necessary foundation for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area. This book bridges the existing gap between monographs on special functions of mathematical physics and constructive approximation in Euclidean spaces. The primary objective is to provide readers with an understanding of aspects of approximation by spherical harmonics, such as spherical splines and wavelets, as well as indicating future directions of research. Scalar, vectorial, and tensorial methods are each considered in turn. The concentration on spherical splines and wavelets allows a double simplification; not only is the number of independent variables reduced resulting in a lower dimensional problem, but also radial basis function techniques become applicable. When applied to geomathematics this leads to new structures and methods by which sophisticated measurements and observations can be handled more efficiently, thus reducing time and costs.

These worksheets provide extra practice exercises for every section of the text with ample space for students to show their work on the practice exercises and Math Coach problems. Additionally, the workbook is correlated to the new Guided Learning Videos and the Math Coach Videos so that students can follow along, take notes, and practice as they go.

This brand new series puts learners in charge with an exploratory inquiry-led approach to MYP Mathematics. Each full-colour book and accompanying eBook contains detailed worked examples, reflections, differentiated exercises, and check your knowledge questions to put learning into practice. Clear links to key concepts, related concepts and global contexts in addition to statements of inquiry and inquiry questions for each chapter. ATLs identified throughout. Investigations encourage learners to seek knowledge and develop ATL skills. Written by an international team of highly experienced authors and teachers, and led by Series Editor, Ibrahim Wazir, this new series matches the 2020 Subject Guide.

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in logic, mathematics, philosophy, and computer science.

The chapters in this monograph are contributions from the Advances in Quantum Monte Carlo symposium held at Pacifichem 2010, International Chemical Congress of Pacific Basin Societies. The symposium was dedicated to celebrate the career of James B. Anderson, a notable researcher in the field. Quantum Monte Carlo provides an ab initio solution to the Schroedinger equation by performing a random walk through configuration space in imaginary time. Benchmark calculations suggest that its most commonly-used variant, "fixed-node" diffusion Monte Carlo, estimates energies with an accuracy comparable to that of high-level coupled-cluster calculations. These two methods, each having advantages and disadvantages, are complementary "gold-standards" of quantum chemistry. There are challenges facing researchers in the field, several of which are addressed in the chapters in this monograph. These include improving the accuracy and precision of quantum Monte Carlo calculations; understanding the exchange nodes and utilizing the simulated electron distribution; extending the method to large and/or experimentally-challenging systems; and developing hybrid molecular mechanics/dynamics and Monte Carlo algorithms.