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Special Functions for Applied Scientists

This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.

Special Functions: Group Theoretical Aspects and Applications (Mathematics and Its Applications #18)

Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Special Functions in Fractional Calculus and Engineering (Mathematics and its Applications)

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations.This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.

Special Functions in Fractional Calculus and Engineering (Mathematics and its Applications)

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations.This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.

Special Functions in Physics with MATLAB

This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.

Special Functions of Mathematical (Applied and Numerical Harmonic Analysis)

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Special Functions of Mathematical Physics: A Unified Introduction with Applications

With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan­ tum mechanics. We have not attempted to provide the most extensive collec­ tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro­ vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (§3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (§§12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or­ thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications in physics.

Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor of Calixto P. Calderón (Springer Proceedings in Mathematics & Statistics #108)

This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.

Special Functions, Probability Semigroups, and Hamiltonian Flows (Lecture Notes in Mathematics #696)

Special Integrals of Gradshteyn and Ryzhik: the Proofs - Volume II

A Guide to the Evaluation of IntegralsSpecial Integrals of Gradshetyn and Ryzhik: the Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica to verify the formulas. You will discover the bea

Special Integrals of Gradshteyn and Ryzhik: the Proofs - Volume I

A Guide to the Evaluation of IntegralsSpecial Integrals of Gradshetyn and Ryzhik: The Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica to verify the formulas. Readers discover the beau

Special Metrics and Group Actions in Geometry (Springer INdAM Series #23)

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Special Needs and Drug Education (nasen spotlight)

Taking drugs is complex and there are concerns about the best ways of addressing drugs issues in schools - particularly for pupils with special educational needs. Many teachers are worried about discussing drugs with their pupils. They fear that they know too little and that some of their pupils may know too much. They also worry that talking about drugs to naive children may raise their interest. Yet the government expects all pupils to receive drug education and requires all schools to have a drug policy. It has ambitious targets in reducing the use of drugs by young people. This book aims to help teachers of pupils with special educational needs to assess what their contribution should be and identify what the particular issues associated with their pupils are. It will help schools to: create or revise a drugs policy plan a program of study deliver drug education appropriate to their pupils deal with drug related incident.

Special Needs and Drug Education (nasen spotlight)

Taking drugs is complex and there are concerns about the best ways of addressing drugs issues in schools - particularly for pupils with special educational needs. Many teachers are worried about discussing drugs with their pupils. They fear that they know too little and that some of their pupils may know too much. They also worry that talking about drugs to naive children may raise their interest. Yet the government expects all pupils to receive drug education and requires all schools to have a drug policy. It has ambitious targets in reducing the use of drugs by young people. This book aims to help teachers of pupils with special educational needs to assess what their contribution should be and identify what the particular issues associated with their pupils are. It will help schools to: create or revise a drugs policy plan a program of study deliver drug education appropriate to their pupils deal with drug related incident.

Special quadrilaterals (large print)

These pages show labelled geometric shapes on each page. It is a multi-page image set on two pages. There is a locator dot shown on each page, which will be at the top left when the image is the correct way up. Page 1 This page has three shapes on it. There is a square at the top, a rectangle in the middle and a parallelogram at the bottom of the page. The square: all sides are equal and all angles are equal. The diagonals bisect each other and cross at right angles. The rectangle: opposite sides are equal and all angles are equal. The diagonals bisect each other. The parallelogram: opposite sides are equal and parallel, and opposite angles are equal. The diagonals bisect each other. Page 2 This page has three shapes on it. There is a rhombus at the top, a kite in the middle and a trapezium at the bottom of the page. The rhombus: all sides are equal, opposite sides are parallel and opposite angles are equal. The diagonals bisect each other and cross at right angles. The kite: two pairs of sides are equal, one pair of opposite angles are equal. The diagonals bisect each other and cross at right angles. The trapezium: two unequal sides are parallel and interior angles add up to 360º

Special quadrilaterals (UEB contracted)

These pages show labelled geometric shapes on each page. It is a multi-page image set on two pages. There is a locator dot shown on each page, which will be at the top left when the image is the correct way up. Page 1 This page has three shapes on it. There is a square at the top, a rectangle in the middle and a parallelogram at the bottom of the page. The square: all sides are equal and all angles are equal. The diagonals bisect each other and cross at right angles. The rectangle: opposite sides are equal and all angles are equal. The diagonals bisect each other. The parallelogram: opposite sides are equal and parallel, and opposite angles are equal. The diagonals bisect each other. Page 2 This page has three shapes on it. There is a rhombus at the top, a kite in the middle and a trapezium at the bottom of the page. The rhombus: all sides are equal, opposite sides are parallel and opposite angles are equal. The diagonals bisect each other and cross at right angles. The kite: two pairs of sides are equal, one pair of opposite angles are equal. The diagonals bisect each other and cross at right angles. The trapezium: two unequal sides are parallel and interior angles add up to 360º

Special quadrilaterals (UEB uncontracted)

These pages show labelled geometric shapes on each page. It is a multi-page image set on two pages. There is a locator dot shown on each page, which will be at the top left when the image is the correct way up. Page 1 This page has three shapes on it. There is a square at the top, a rectangle in the middle and a parallelogram at the bottom of the page. The square: all sides are equal and all angles are equal. The diagonals bisect each other and cross at right angles. The rectangle: opposite sides are equal and all angles are equal. The diagonals bisect each other. The parallelogram: opposite sides are equal and parallel, and opposite angles are equal. The diagonals bisect each other. Page 2 This page has three shapes on it. There is a rhombus at the top, a kite in the middle and a trapezium at the bottom of the page. The rhombus: all sides are equal, opposite sides are parallel and opposite angles are equal. The diagonals bisect each other and cross at right angles. The kite: two pairs of sides are equal, one pair of opposite angles are equal. The diagonals bisect each other and cross at right angles. The trapezium: two unequal sides are parallel and interior angles add up to 360º

Special Relativity: For Inquiring Minds (Undergraduate Lecture Notes in Physics)

This textbook introduces the special theory of relativity at a level which is accessible to undergraduate students and even high school students with a strong foundation in algebra. The presentation emphasizes clean algebraic and geometrical methods, visualized with plenty of illustrations, resulting in a textbook that is modern and serious yet accessible. Replete with many solved exercises and copious spacetime diagrams, this book will help students develop relativistic intuition when encountering the subject for the first time. The emphasis on geometric methods, combined with the pedagogically appealing k-calculus approach, makes this book ideal for a self-contained course on special relativity or as supplementary reading for modern physics courses. It will also appeal to high schoolers with a strong math background who want to get ahead.

Special Relativity: Will it Survive the Next 101 Years? (Lecture Notes in Physics #702)

After about a century of success, physicists feel the need to probe the limits of validity of special-relativity base theories. This book is the outcome of a special seminar held on this topic. The authors gather in a single volume an extensive collection of introductions and reviews of the various facets involved, and also includes detailed discussion of philosophical and historical aspects.

Special Relativity (Undergraduate Lecture Notes in Physics)

This book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski space-time. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its co-variant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates.Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.

Special Relativity: An Introduction with 200 Problems and Solutions

Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using “heavier” mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a ´ la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones! As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity.

Special Relativity: An Introduction with 200 Problems and Solutions (Undergraduate Lecture Notes in Physics)

This textbook develops Special Relativity in a systematic way and offers the unique feature of having more than 200 problems with detailed solutions to empower students to gain a real understanding of this core subject in physics. This new edition has been thoroughly updated and has new sections on relativistic fluids, relativistic kinematics and on four-acceleration. The problems and solution section has been significantly expanded and short history sections have been included throughout the book.The approach is structural in the sense that it develops Special Relativity in Minkowski space following the parallel steps as the development of Newtonian Physics in Euclidian space. A second characteristic of the book is that it discusses the mathematics of the theory independently of the physical principles, so that the reader will appreciate their role in the development of the physical theory.The book is intended to be used both as a textbook for an advanced undergraduate teaching course in Special Relativity but also as a reference book for the future. In that respect it is linked to an online repository with more than 200 problems, carefully classified according to subject area and solved in detail, providing an independent problem book on Special Relativity.

Special Relativity (Lecture Notes in Physics Monographs #6)

Special Relativity (Springer Undergraduate Mathematics Series #6)

This book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.

Special Relativity and Quantum Theory: A Collection of Papers on the Poincaré Group (Fundamental Theories of Physics #33)

Special relativity and quantum mechanics are likely to remain the two most important languages in physics for many years to come. The underlying language for both disciplines is group theory. Eugene P. Wigner's 1939 paper on the Unitary Representations of the Inhomogeneous Lorentz Group laid the foundation for unifying the concepts and algorithms of quantum mechanics and special relativity. In view of the strong current interest in the space-time symmetries of elementary particles, it is safe to say that Wigner's 1939 paper was fifty years ahead of its time. This edited volume consists of Wigner's 1939 paper and the major papers on the Lorentz group published since 1939. . This volume is intended for graduate and advanced undergraduate students in physics and mathematics, as well as mature physicists wishing to understand the more fundamental aspects of physics than are available from the fashion-oriented theoretical models which come and go. The original papers contained in this volume are useful as supplementary reading material for students in courses on group theory, relativistic quantum mechanics and quantum field theory, relativistic electrodynamics, general relativity, and elementary particle physics. This reprint collection is an extension of the textbook by the present editors entitled "Theory and Applications of the Poincare Group." Since this book is largely based on the articles contained herein, the present volume should be viewed as a reading for the previous work. continuation of and supplementary We would like to thank Professors J. Bjorken, R. Feynman, R. Hofstadter, J.