Perturbation Methods for Engineers and Scientists examines the main techniques of perturbation expansions applied to both differential equations and integral expressions. It describes several fluid dynamics applications, including aerofoils, boundary layers in momentum heat, and mass transfer. In addition, it applies the multiple scale technique to the description of surface roughness effects in lubrication. The book's intuitive, rather than formal, approach enables these advanced techniques to be used by scientists and engineers as well as by students.

This book is designed to be a vital companion to math textbooks covering the topics of precalculus, calculus, linear algebra, differential equations, and probability and statistics. While these existing textbooks focus mainly on solving mathematic problems using the old paper-and-pencil method, this book teaches how to solve these problems using Maxima open-source software. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, and matrices. One of the benefits of using Maxima to solve mathematics problems is the immediacy with which it produces answers. Investing in learning Maxima now will pay off in the future, particularly for students and beginning professionals in mathematics, science, and engineering. The volume will help readers to apply nearly all of the Maxima skills discussed here to future courses and research.

The aim of this book is to make the subject easier to understand. This book provides clear concepts, tools, and techniques to master the subject -tensor, and can be used in many fields of research. Special applications are discussed in the book, to remove any confusion, and for absolute understanding of the subject. In most books, they emphasize only the theoretical development, but not the methods of presentation, to develop concepts. Without knowing how to change the dummy indices, or the real indices, the concept cannot be understood. This book takes it down a notch and simplifies the topic for easy comprehension. Features Provides a clear indication and understanding of the subject on how to change indices Describes the original evolution of symbols necessary for tensors Offers a pictorial representation of referential systems required for different kinds of tensors for physical problems Presents the correlation between critical concepts Covers general operations and concepts

A Computational Approach to Statistical Learning gives a novel introduction to predictive modeling by focusing on the algorithmic and numeric motivations behind popular statistical methods. The text contains annotated code to over 80 original reference functions. These functions provide minimal working implementations of common statistical learning algorithms. Every chapter concludes with a fully worked out application that illustrates predictive modeling tasks using a real-world dataset. The text begins with a detailed analysis of linear models and ordinary least squares. Subsequent chapters explore extensions such as ridge regression, generalized linear models, and additive models. The second half focuses on the use of general-purpose algorithms for convex optimization and their application to tasks in statistical learning. Models covered include the elastic net, dense neural networks, convolutional neural networks (CNNs), and spectral clustering. A unifying theme throughout the text is the use of optimization theory in the description of predictive models, with a particular focus on the singular value decomposition (SVD). Through this theme, the computational approach motivates and clarifies the relationships between various predictive models. Taylor Arnold is an assistant professor of statistics at the University of Richmond. His work at the intersection of computer vision, natural language processing, and digital humanities has been supported by multiple grants from the National Endowment for the Humanities (NEH) and the American Council of Learned Societies (ACLS). His first book, Humanities Data in R, was published in 2015. Michael Kane is an assistant professor of biostatistics at Yale University. He is the recipient of grants from the National Institutes of Health (NIH), DARPA, and the Bill and Melinda Gates Foundation. His R package bigmemory won the Chamber's prize for statistical software in 2010. Bryan Lewis is an applied mathematician and author of many popular R packages, including irlba, doRedis, and threejs.

Das Standardwerk HUETTE erscheint in der 35., aktualisierten Auflage in der Reihe Springer Reference Technik. Diese Reihe bietet allen Ingenieurinnen und Ingenieuren - ob im Studium oder in allen Formen des Berufslebens - zielfuhrendes Fachwissen in aktueller, kompakter und verstandlicher Form. Die HUETTE enthalt in drei Banden die Grundlagen des Ingenieurwissens sowie oekonomisch-gesellschaftliche Kapitel, die das Ingenieurwissen erganzen. Band 3 umfasst Elektro- und informationstechnische Grundlagen: Elektrotechnik Messtechnik Regelungs- und Steuerungstechnik Informatik Informationsmanagement Band 1 Mathematisch-naturwissenschaftliche und allgemeine Grundlagen Band 2 Grundlagen des Maschinenbaus und erganzende Facher

This detailed yet accessible text provides an essential introduction to the advanced mathematical methods at the core of theoretical physics. The book steadily develops the key concepts required for an understanding of symmetry principles and topological structures, such as group theory, differentiable manifolds, Riemannian geometry, and Lie algebras. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering. The material has been subject to more than twenty years of feedback from students, ensuring that explanations and examples are lucid and considered, and numerous worked examples and exercises reinforce key concepts and further strengthen readers' understanding. This text unites a wide variety of important topics that are often scattered across different books, and provides a solid platform for more specialized study or research.

To succeed in the lab, it is crucial to be comfortable with the math calculations that are part of everyday work. This accessible introduction to common laboratory techniques focuses on the basics, helping even readers with good math skills to practice the most frequently encountered types of problems. Basic Laboratory Calculations for Biotechnology, Second Edition discusses very common laboratory problems, all applied to real situations. It explores multiple strategies for solving problems for a better understanding of the underlying math. Primarily organized around laboratory applications, the book begins with more general topics and moves into more specific biotechnology laboratory techniques at the end. This book features hundreds of practice problems, all with solutions and many with boxed, complete explanations; plus hundreds of "story problems" relating to real situations in the lab. Additional features include: Discusses common laboratory problems with all material applied to real situations Presents multiple strategies for solving problems help students to better understand the underlying math Provides hundreds of practice problems and their solutions Enables students to complete the material in a self-paced course structure with little teacher assistance Includes hundreds of "story problems"that relate to real situations encountered in the laboratory

This book provides the first systematic critique of the concept of climate change adaptation within the field of international development. Drawing on a reworked political ecology framework, it argues that climate is not something 'out there' that we adapt to. Instead, it is part of the social and biophysical forces through which our lived environments are actively yet unevenly produced. From this original foundation, the book challenges us to rethink the concepts of climate change, vulnerability, resilience and adaptive capacity in transformed ways. With case studies drawn from Pakistan, India and Mongolia, it demonstrates concretely how climatic change emerges as a dynamic force in the ongoing transformation of contested rural landscapes. In crafting this synthesis, the book recalibrates the frameworks we use to envisage climatic change in the context of contemporary debates over development, livelihoods and poverty. With its unique theoretical contribution and case study material, this book will appeal to researchers and students in environmental studies, sociology, geography, politics and development studies.

This second edition of The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance has been fully updated and revised to reflect recent developments in the theory and practical applications of wavelet transform methods. The book is designed specifically for the applied reader in science, engineering, medicine and finance. Newcomers to the subject will find an accessible and clear account of the theory of continuous and discrete wavelet transforms, while readers already acquainted with wavelets can use the book to broaden their perspective. One of the many strengths of the book is its use of several hundred illustrations, some in colour, to convey key concepts and their varied practical uses. Chapters exploring these practical applications highlight both the similarities and differences in wavelet transform methods across different disciplines and also provide a comprehensive list of over 1000 references that will serve as a valuable resource for further study. Paul Addison is a Technical Fellow with Medtronic, a global medical technology company. Previously, he was co-founder and CEO of start-up company, CardioDigital Ltd (and later co-founded its US subsidiary, CardioDigital Inc) - a company concerned with the development of novel wavelet-based methods for biosignal analysis. He has a master's degree in engineering and a PhD in fluid mechanics, both from the University of Glasgow, Scotland (founded 1451). His former academic life as a tenured professor of fluids engineering included the output of a large number of technical papers, covering many aspects of engineering and bioengineering, and two textbooks: Fractals and Chaos: An Illustrated Course and the first edition of The Illustrated Wavelet Transform Handbook. At the time of publication, the author has over 100 issued US patents concerning a wide range of medical device technologies, many of these concerning the wavelet transform analysis of biosignals. He is both a Chartered Engineer and Chartered Physicist.

In recent years, mathematics has experienced amazing growth in the engineering sciences. Mathematics forms the common foundation of all engineering disciplines. This book provides a comprehensive range of mathematics applied in various fields of engineering for different tasks such as civil engineering, structural engineering, computer science, and electrical engineering, among others. It offers chapters that develop the applications of mathematics in engineering sciences, conveys the innovative research ideas, offers real-world utility of mathematics, and has a significance in the life of academics, practitioners, researchers, and industry leaders. Features Focuses on the latest research in the field of engineering applications Includes recent findings from various institutions Identifies the gaps in the knowledge in the field and provides the latest approaches Presents international studies and findings in modeling and simulation Offers various mathematical tools, techniques, strategies, and methods across different engineering fields

This book surveys the broad landscape of differential equations, including elements of partial differential equations (PDEs), and concisely presents the topics of most use to engineers. It introduces each topic with a motivating application drawn from electrical, mechanical, and aerospace engineering. The text has reviews of foundations, step-by-step explanations, and sets of solved problems. It fosters students' abilities in the art of approximation and self-checking. The book addresses PDEs with and without boundary conditions, which demonstrates strong similarities with ordinary differential equations and clear illustrations of the nature of solutions. Furthermore, each chapter includes word problems and challenge problems. Several extended computing projects run throughout the text.

Is anything truly random? Does infinity actually exist? Could we ever see into other dimensions?

In this delightful journey of discovery, David Darling and extraordinary child prodigy Agnijo Banerjee draw connections between the cutting edge of modern maths and life as we understand it, delving into the strange would we like alien music? and venturing out on quests to consider the existence of free will and the fantastical future of quantum computers. Packed with puzzles and paradoxes, mind-bending concepts and surprising solutions, this is for anyone who wants life s questions answered even those you never thought to ask.

Percolation theory deals with clustering, criticality, diffusion, fractals, phase transitions and disordered systems. It provides a quantitative model for understanding these phenomena, and therefore provides a theoretical, statistical background to many physical and natural science disciplines. The scope of this book covers the basic theory for the graduate while it also reaches into the specialized fields of disordered systems and renormalization groups. Readers are expected to be able to handle some fundamental mathematical procedures such as integration and differentiation of single variable functions, probability and statistics. They will also find it useful if they have some computer programming experience for example in Fortran. While percolation is treated as being a fundamentally physical concept, its relevance to various natural and living systems is addressed. Much of the book deals with systems lying close to the critical point phase transition point, where the subject is at its most interesting and sensitive. This book should be of value to all those who deal with systems which exhibit critical points and phase transition behaviour.

eBook available with sample pages: 0203211596

Predicting Motion presents the core ideas of Newtonian mechanics, starting from Newton's laws and the idea that changes in motion are predictable given the forces that cause them. Richly illustrated with questions and answers for self-assessment, it carefully introduces concepts, such as kinetics and potential energy, linear momentum, torque (the rotational analogue of force), and angular momentum, and explains their role in predicting motion. Although no prior knowledge of this topic is required, the book focuses on the significance of differential equations in making such predictions. It also provides an up-to-date treatment of mechanics with accounts of relativistic collisions and the implications of chaos theory for the future of the solar system and for galaxies that contain black holes.

This book introduces linear transformation and its key results, which have applications in engineering, physics, and various branches of mathematics. Linear transformation is a difficult subject for students. This concise text provides an in-depth overview of linear trans-formation. It provides multiple-choice questions, covers enough examples for the reader to gain a clear understanding, and includes exact methods with specific shortcuts to reach solutions for particular problems. Research scholars and students working in the fields of engineering, physics, and different branches of mathematics need to learn the concepts of linear transformation to solve their problems. This book will serve their need instead of having to use the more complex texts that contain more concepts then needed. The chapters mainly discuss the definition of linear transformation, properties of linear transformation, linear operators, composition of two or more linear transformations, kernels and range of linear transformation, inverse transformation, one-to-one and onto transformation, isomorphism, matrix linear transformation, and similarity of two matrices.

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents a myriad of approaches to finding exact solutions for a diversity of nonlinear problems. These include group-theoretic methods, the direct method of Clarkson and Kruskal, traveling waves, hodograph methods, balancing arguments, embedding special solutions into a more general class, and the infinite series approach. The author's approach is entirely constructive. Numerical solutions either motivate the analysis or confirm it, therefore they are treated alongside the analysis whenever possible. Many examples drawn from real physical situations-primarily fluid mechanics and nonlinear diffusion-illustrate and emphasize the central points presented. Accessible to a broad base of readers, Self-Similarity and Beyond illuminates a variety of productive methods for meeting the challenges of nonlinearity. Researchers and graduate students in nonlinearity, partial differential equations, and fluid mechanics, along with mathematical physicists and numerical analysts, will re-discover the importance of exact solutions and find valuable additions to their mathematical toolkits.

This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many of these scientifically exotic activities, but could not see how they fit into their own scientific interests, or how they could be made compatible with the way they understand science. It is also for beginners who have not yet decided where their scientific talents could be most productively applied. The book provides insight into the long-term direction of science and show how to develop the skills necessary to successfully do research in the twenty-first century.

Focusing on the application of mathematics to chemical engineering, Applied Mathematical Methods for Chemical Engineers addresses the setup and verification of mathematical models using experimental or other independently derived data. The book provides an introduction to differential equations common to chemical engineering, followed by examples of first-order and linear second-order ordinary differential equations. Later chapters examine Sturm-Liouville problems, Fourier series, integrals, linear partial differential equations, regular perturbation, combination of variables, and numerical methods emphasizing the method of lines with MATLAB (R) programming examples. Fully revised and updated, this Third Edition: Includes additional examples related to process control, Bessel Functions, and contemporary areas such as drug delivery Introduces examples of variable coefficient Sturm-Liouville problems both in the regular and singular types Demonstrates the use of Euler and modified Euler methods alongside the Runge-Kutta order-four method Inserts more depth on specific applications such as nonhomogeneous cases of separation of variables Adds a section on special types of matrices such as upper- and lower-triangular matrices Presents a justification for Fourier-Bessel series in preference to a complicated proof Incorporates examples related to biomedical engineering applications Illustrates the use of the predictor-corrector method Expands the problem sets of numerous chapters Applied Mathematical Methods for Chemical Engineers, Third Edition uses worked examples to expose several mathematical methods that are essential to solving real-world process engineering problems.

Modern engineering processes and tasks are highly complex, multi- and interdisciplinary, requiring the cooperative effort of different specialists from engineering, mathematics, computer science and even social sciences. Optimization methodologies are fundamental instruments to tackle this complexity, giving the possibility to unite synergistically team members' inputs and thus decisively contribute to solving new engineering technological challenges. With this context in mind, the main goal of Engineering Optimization 2014 is to unite engineers, applied mathematicians, computer and other applied scientists working on research, development and practical application of optimization methods applied to all engineering disciplines, in a common scientific forum to present, analyze and discuss the latest developments in this area. Engineering Optimization 2014 contains the edited papers presented at the 4th International Conference on Engineering Optimization (ENGOPT2014, Lisbon, Portugal, 8-11 September 2014). ENGOPT2014 is the fourth edition of the biennial "International Conference on Engineering Optimization". The first conference took place in 2008 in Rio de Janeiro, the second in Lisbon in 2010 and the third in Rio de Janeiro in 2012. The contributing papers are organized around the following major themes: - Numerical Optimization Techniques - Design Optimization and Inverse Problems - Effi cient Analysis and Reanalysis Techniques - Sensitivity Analysis - Industrial Applications - Topology Optimization For Structural Static and Dynamic Failures - Optimization in Oil and Gas Industries - New Advances in Derivative-Free Optimization Methods for Engineering Optimization - Optimization Methods in Biomechanics and Biomedical Engineering - Optimization of Laminated Composite Materials - Inverse Problems in Engineering Engineering Optimization 2014 will be of great interest to engineers and academics in engineering, mathematics and computer science.

"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons.

While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields.

Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA."

If your students struggle with standard deviation or statistical tests, this is the book for them. This textbook companion will help improve their essential maths skills for psychology, whichever awarding body specification you're following. You can use it throughout the course, whenever you feel they need some extra help. - Develop understanding of both maths and psychology with all worked examples and questions within a psychology context - Improve confidence with a step-by-step approach to every maths skill - Measure progress with guided and non-guided questions - Understand misconceptions with full worked solutions to every question - Feel confident in expert guidance from experienced teacher and examiner Molly Marshall, reviewed by Dorothy Coombs, Editor of ATP Today, former Chair of the Association for the Teaching of Psychology and experienced biology, psychology and FSMQ Statistics teacher

This book introduces and explains the parametric accelerated life testing (ALT) methodology as a new reliability methodology based on statistics, to help avoid recalls of products in the marketplace. The book includes problems and case studies to help with reader comprehension. It provides an introduction to reliability design of the mechanical system as an alternative to Taguchi's experimental methodology and enables engineers to correct faulty designs and determine if the targeted product reliability is achieved. Additionally, it presents a robust design methodology of mechanical products to withstand a variety of loads. This book is intended for engineers of many fields, including industrial engineers, mechanical engineers, and systems engineers.

A Totally Different Outlook on Power Electronic System Analysis Power Electronic Systems: Walsh Analysis with MATLAB (R) builds a case for Walsh analysis as a powerful tool in the study of power electronic systems. It considers the application of Walsh functions in analyzing power electronic systems, and the advantages offered by Walsh domain analysis of power electronic systems. Solves Power Electronic Systems in an Unconventional Way This book successfully integrates power electronics as well as systems and control. Incorporating a complete orthonormal function set very much unlike the sine-cosine functions, it introduces a blending between piecewise constant orthogonal functions and power electronic systems. It explores the background and evolution of power electronics, and discusses Walsh and related orthogonal basis functions. It develops the mathematical foundation of Walsh analysis, and first- and second-order system analyses by Walsh technique. It also describes the Walsh domain operational method and how it is applied to linear system analysis. Introduces Theories Step by Step While presenting the underlying principles of Walsh analysis, the authors incorporate many illustrative examples, and include a basic introduction to linear algebra and MATLAB (R) programs. They also examine different orthogonal piecewise constant basis functions like Haar, Walsh, slant, block pulse functions, and other related orthogonal functions along with their time scale evolution. * Analyzes pulse-fed single input single output (SISO) first- and second-order systems * Considers stepwise and continuously pulse width modulated chopper systems * Describes a detailed analysis of controlled rectifier circuits * Addresses inverter circuits Power Electronic Systems: Walsh Analysis with MATLAB (R) is written for postgraduate students, researchers, and academicians in the area of power electronics as well as systems and control.

Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. For the first time, this book gives the systematic group analysis of main postulates of classical and relativistic mechanics. The consistent presentation of Lie group theory is illustrated by plentiful examples. Symmetries and conservation laws of differential equations are studied. Specific equations and problems of mechanics and physics are considered, and exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi and more. The author pays particular attention to the application of group analysis to developing asymptotic methods of applied mathematics in problems with small parameter. The methods are used to solve basic equations (Van Der Pol's equation, Duffing equation, etc.) encountered in the theory of nonlinear oscillations. This book is intended for a wide range of scientists, engineers and students in the fields of applied mathematics, mechanics and physics.

Now in its ninth edition, Bird's Engineering Mathematics has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, supported by practical engineering examples and applications to ensure that readers can relate theory to practice. Some 1,300 engineering situations/problems have been 'flagged-up' to help demonstrate that engineering cannot be fully understood without a good knowledge of mathematics. The extensive and thorough topic coverage makes this a great text for a range of level 2 and 3 engineering courses - such as for aeronautical, construction, electrical, electronic, mechanical, manufacturing engineering and vehicle technology - including for BTEC First, National and Diploma syllabuses, City & Guilds Technician Certificate and Diploma syllabuses, and even for GCSE and A-level revision. Its companion website at www.routledge.com/cw/bird provides resources for both students and lecturers, including full solutions for all 2,000 further questions, lists of essential formulae, multiple-choice tests, and illustrations, as well as full solutions to revision tests for course instructors.