Advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences are reported in the papers that form this volume. As design, analysis and manufacture become more integrated, the chances are that software users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily within the aforementioned integrated process. The maturity of BEM since 1978 has resulted in a substantial number of industrial applications of the method; this demonstrates its accuracy, robustness and ease of use. The range of applications still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. The included papers originate from the 45th conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM) and describe theoretical developments and new formulations, helping to expand the range of applications as well as the type of modelled materials in response to the requirements of contemporary industrial and professional environments.

The book is devoted to several topical questions in modern mathematical and theoretical physics, astrophysics, geophysics, and cosmology that remain unsolved within the framework of the standard approaches. To them, one can attribute unexplained properties of the magnetic fields of stars and planets, puzzles of the Earth's atmosphere, the phenomenon of ball lightning, the problem of a qualitative description for nuclear forces and their well-known property of saturation, enigmatic properties of spiral galaxies, the problem of the cosmological singularity, mysteries of the dark matter and dark energy, amongst others. To find theoretical ways for understanding such phenomena, new nonlinear generalizations of the classical field theories and advanced methods to solve nonlinear equations arising in them are studied and presented in this book.

Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences.

Maple is a comprehensive symbolic mathematics application which is well suited for demonstrating physical science topics and solving associated problems. Because Maple is such a rich application, it has a somewhat steep learning curve. Most existing texts concentrate on mathematics; the Maple help facility is too detailed and lacks physical science examples, many Maple-related websites are out of date giving readers information on older Maple versions. This book records the author's journey of discovery; he was familiar with SMath but not with Maple and set out to learn the more advanced application. It leads readers through the basic Maple features with physical science worked examples, giving them a firm base on which to build if more complex features interest them.

The world of single-board computing puts powerful coding tools in the palm of your hand. The portable Raspberry Pi computing platform with the power of Linux yields an exciting exploratory tool for beginning scientific computing. Science and Computing with Raspberry Pi takes the enterprising researcher, student, or hobbyist through explorations in a variety of computing exercises with the physical sciences. The book has tutorials and exercises for a wide range of scientific computing problems while guiding the user through: Configuring your Raspberry Pi and Linux operating system Understanding the software requirements while using the Pi for scientific computing Computing exercises in physics, astronomy, chaos theory, and machine learning

Combining insights from academic research and practical examples, this book aims to better understand the link between financial markets and innovation management. First, we are back to the very definition of innovation and what it means for financial and non-financial companies. Then, we analyze if efficient innovation management by companies is recognized and valued by financial markets. Finally, we focus on innovation within the financial sector: does it really create value outside the financial sector itself. Are Financial innovations value ... or risk creators?

Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory.

This book uses art photography as a point of departure for learning about physics, while also using physics as a point of departure for asking fundamental questions about the nature of photography as an art. Although not a how-to manual, the topics center around hands-on applications, sometimes illustrated by photographic processes that are inexpensive and easily accessible to students (including a versatile new process developed by the author, and first described in print in this series). A central theme is the connection between the physical interaction of light and matter on the one hand, and the artistry of the photographic processes and their results on the other. This is the third volume in this three-part series that uses art photography as a point of departure for learning about physics, while also using physics as a point of departure for asking fundamental questions about the nature of photography as an art. It focuses on the physics and chemistry of photographic light-sensitive materials, as well as the human retina. It also considers the fundamental nature of digital photography and its relationship to the analog photography that preceded it.

Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data.

This book is a revised and more comprehensive version of "Dynamics of Stochastic Systems." Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations. Part III deals with the analysis of specific physical problems associated with coherent phenomena.
A comprehensive update of "Dynamics of Stochastic Systems"Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and wavesIncludes problems for the reader to solve

This book demonstrates Microsoft EXCEL-based Fourier transform of selected physics examples. Spectral density of the auto-regression process is also described in relation to Fourier transform. Rather than offering rigorous mathematics, readers will "try and feel" Fourier transform for themselves through the examples. Readers can also acquire and analyze their own data following the step-by-step procedure explained in this book. A hands-on acoustic spectral analysis can be one of the ideal long-term student projects.

Holographic dualities are at the forefront of contemporary physics research, peering into the fundamental nature of our universe and providing best attempt answers to humankind's bold questions about basic physical phenomena. Yet, the concepts, ideas and mathematical rigors associated with these dualities have long been reserved for the specific field researchers and experts. This book shatters this long held paradigm by bringing several aspects of holography research into the class room, starting at the college physics level and moving up from there.

For courses in Business Mathematics. Focuses on current issues, real companies, and pragmatic business scenarios Business Mathematics by Clendenen and Salzman teaches students the mathematical skills they need for success in business, emphasizing mastery of business concepts and scenarios that require a mathematical solution. With a strong focus on current issues, real companies, and pragmatic business scenarios, the authors cover the full spectrum of basic business math, placing every concept in context with relevant examples. Along with an updated MyLab (TM) Math course, the 14th Edition has been significantly revised to modernize the text, improve discussions, and make the material more meaningful to students. This revision is packed with data, examples, graphs, photographs, and case studies that demonstrate the material's relevance as it teaches students to interpret data and information. A global perspective is emphasized through examples and exercises that highlight issues in other countries. Also available with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0135195969 / 9780135195963 Business Mathematics Plus MyLab Math with Pearson eText - Access Card Package Package consists of: 0134693329 / 9780134693323 Business Mathematics, 14e 0134836235 / 9780134836232 MyLab Math with Pearson eText - Access Card - for Business Mathematics, 14/e

Quartic anharmonic oscillator with potential V(x)= x(2) + g(2)x4 was the first non-exactly-solvable problem tackled by the newly-written Schroedinger equation in 1926. Since that time thousands of articles have been published on the subject, mostly about the domain of small g(2) (weak coupling regime), although physics corresponds to g(2) ~ 1, and they were mostly about energies.This book is focused on studying eigenfunctions as a primary object for any g(2). Perturbation theory in g(2) for the logarithm of the wavefunction is matched to the true semiclassical expansion in powers of : it leads to locally-highly-accurate, uniform approximation valid for any g(2) [0, ) for eigenfunctions and even more accurate results for eigenvalues. This method of matching can be easily extended to the general anharmonic oscillator as well as to the radial oscillators. Quartic, sextic and cubic (for radial case) oscillators are considered in detail as well as quartic double-well potential.

This book provides a concise introduction to both the special theory of relativity and the general theory of relativity. The format is chosen to provide the basis for a single semester course which can take the students all the way from the foundations of special relativity to the core results of general relativity: the Einstein equation and the equations of motion for particles and light in curved spacetime. To facilitate access to the topics of special and general relativity for science and engineering students without prior training in relativity or geometry, the relevant geometric notions are also introduced and developed from the ground up. Students in physics, mathematics or engineering with an interest to learn Einstein's theories of relativity should be able to use this book already in the second semester of their third year. The book could also be used as the basis of a graduate level introduction to relativity for students who did not learn relativity as part of their undergraduate training.

This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB (R) is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.

This book contains an extensive illustration of use of finite difference method in solving the boundary value problem numerically. A wide class of differential equations has been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, we have solved those of special functions like Hermite, Laguerre and Legendre. Those of Airy function, of stationary localised wavepacket, of the quantum mechanical problem of a particle in a 1D box, and the polar equation of motion under gravitational interaction have also been solved. Mathematica 6.0 has been used to solve the system of linear equations that we encountered and to plot the numerical data. Comparison with known analytic solutions showed nearly perfect agreement in every case. On reading this book, readers will become adept in using the method.

Uncertainties in GPS Positioning: A Mathematical Discourse describes the calculations performed by a GPS receiver and the problems associated with ensuring that the derived location is a close match to the actual location. Inaccuracies in calculating a location can have serious repercussions, so this book is a timely source for information on this rapidly evolving technology.