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Solvable One-Dimensional Multi-State Models for Statistical and Quantum Mechanics
by Rajendran Saravanan Aniruddha ChakrabortyThis book highlights the need for studying multi-state models analytically for understanding the physics of molecular processes. An intuitive picture about recently solved models of statistical and quantum mechanics is drawn along with presenting the methods developed to solve them. The models are relevant in the context of molecular processes taking place in gaseous phases and condensed phases, emphasized in the introduction. Chapter 1 derives the arisal of multi-state models for molecular processes from the full Hamiltonian description. The model equations are introduced and the literature review presented in short. In Chapter 2, the time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-state descriptions are discussed. Their corresponding analytical results derive new equilibrium concepts in reversible reactions and studies the effect of system and molecular parameters in condensed-phase chemical dynamics. In Chapter 3, time-domain methods to solve quantum scattering problems are developed. Along side introducing a brand new solvable model in quantum scattering, it discusses transient features of quantum two-state models. In interest with electronic transitions, a new solvable two-state model with localized non-adiabatic coupling is also presented. The book concludes by proposing the future scope of the model, thereby inviting new research in this fundamentally important and rich applicable field.
Solved Exercises in Fractional Calculus (Studies in Systems, Decision and Control #240)
by Edmundo Capelas de OliveiraThis book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.
Solved Exercises in Fractional Calculus (Studies in Systems, Decision and Control #589)
by Edmundo Capelas de Oliveira Jayme VazThis textbook provides a comprehensive exploration of special functions and fractional calculus, offering a structured approach through solved and proposed exercises. Covering key mathematical concepts such as Mittag-Leffler functions, Kilbas-Saigo functions, and the Erdélyi-Kober fractional integral, it balances theoretical insights with practical applications. Appendices introduce Barnes G-functions and demonstrate the use of Mathematica for fractional calculus, expanding the book&’s accessibility. With an updated index and extensive references, this edition serves as a valuable resource for researchers, graduate students, and professionals in applied mathematics and related fields.
Solved Problems and Systematic Introduction to Special Relativity (Undergraduate Lecture Notes in Physics)
by Michael TsamparlisIn most undergraduate physics classes Special Relativity is taught from a simplistic point of view using Newtonian concepts rather than the relativistic way of thinking. This results in students often finding it difficult to understand properly the new approach/new ideas, and consequently to solve relativistic problems. Furthermore, a number of books treat the theory using advanced mathematics which is not necessary for the first approach to the theory. This book is intended to serve two roles: a. To treat a student in a systematic constructive way to the basic structure of the theory and b. To provide a large number of solved in-detail problems in the kinematics and dynamics of Special Relativity. Concerning the first aim the book introduces the basics of four-dimensional mathematics, i.e., Lorentz metric, relativistic tensors, and prepares, through working examples, the transition to General Relativity, which requires, besides the relativistic concepts, the use of Differential Geometry and tensor analysis. The presentation is concise and does not replace a book on Special Relativity. Concerning the second intention the large number of problems provides the necessary material which can be used in order to familiarize the student with the relativistic “world”. These problems can be used in the class by the teachers either as working examples or as problem sheets. It will be our pleasure if the book will be useful to both students and teachers.
Solved Problems in Analysis: As Applied to Gamma, Beta, Legendre and Bessel Functions (Dover Books on Mathematics)
by Orin J. Farrell Bertram RossNearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. The first two chapters examine gamma and beta functions, including applications to certain geometrical and physical problems such as heat-flow in a straight wire. The following two chapters treat Legendre polynomials, addressing applications to specific series expansions, steady-state heat-flow temperature distribution, gravitational potential of a circular lamina, and application of Gauss's mechanical quadrature formula with pertinent table. The final chapters explore Bessel functions, discussing differentiation formulas, generating functions, relations to Legendre polynomials, and other applications.This volume constitutes a useful tool for professional engineers and experimental physicists. Students of mathematics, physics, and engineering will particularly benefit from the book's expanded solutions.
Solved Problems in Geostatistics
by Clayton V. Deutsch K. Daniel Khan Oy LeuangthongThis unique book presents a learn-by-doing introduction to geostatistics.Geostatistics provides the essential numerical tools for addressing research problems that are encountered in fields of study such as geology, engineering, and the earth sciences. Illustrating key methods through both theoretical and practical exercises, Solved Problems in Geostatistics is a valuable and well-organized collection of worked-out problems that allow the reader to master the statistical techniques for modeling data in the geological sciences.The book's scope of coverage begins with the elements from statistics and probability that form the foundation of most geostatistical methodologies, such as declustering, debiasing methods, and Monte Carlo simulation. Next, the authors delve into three fundamental areas in conventional geostatistics: covariance and variogram functions; kriging; and Gaussian simulation. Finally, special topics are introduced through problems involving utility theory, loss functions, and multiple-point geostatistics.Each topic is treated in the same clearly organized format. First, an objective presents the main concepts that will be established in the section. Next, the background and assumptions are outlined, supplying the comprehensive foundation that is necessary to begin work on the problem. A solution plan demonstrates the steps and considerations that have to be taken when working with the exercise, and the solution allows the reader to check their work. Finally, a remarks section highlights the overarching principles and noteworthy aspects of the problem.Additional exercises are available via a related Web site, which also includes data related to the book problems and software programs that facilitate their resolution. Enforcing a truly hands-on approach to the topic, Solved Problems in Geostatistics is an indispensable supplement for courses on geostatistics and spatial statistics a the upper-undergraduate and graduate levels.It also serves as an applied reference for practicing professionals in the geosciences.
Solved Problems in Nonlinear Oscillations: A sourcebook for scientists and engineers
by Lin Wang Zeng He Wen JiangThis is an open access book. This textbook contains about 200 fully solved problems in analytical and numerical methods for nonlinear osccillations. These comprise all the end-of-chapter problems in Ali H. Nayfeh and Dean T. Mook’s famous textbook Nonliear Oscillations. Mathematical software are adopted to make those solutions more accessible from a graphical point of view. This book can be adopted as a supplement to course work study for graduates or senior undergraduates. Since many exercise problems are adapted from scientific research papers, this book also has a good reference value for scientists and engineers who work in nonlinear vibration.
Solved Problems in Quantum Mechanics (UNITEXT for Physics)
by Leonardo AngeliniThis book presents a large collection of problems in Quantum Mechanics that are solvable within a limited time and using simple mathematics. The problems test both the student’s understanding of each topic and their ability to apply this understanding concretely. Solutions to the problems are provided in detail, eliminating only the simplest steps. No problem has been included that requires knowledge of mathematical methods not covered in standard courses, such as Fuchsian differential equations. The book is in particular designed to assist all students who are preparing for written examinations in Quantum Mechanics, but will also be very useful for teachers who have to pose problems to their students in lessons and examinations.
Solved Problems in Thermodynamics and Statistical Physics
by Gregor Skačej Primož ZiherlThis book contains a modern selection of about 200 solved problems and examples arranged in a didactic way for hands-on experience with course work in a standard advanced undergraduate/first-year graduate class in thermodynamics and statistical physics. The principles of thermodynamics and equilibrium statistical physics are few and simple, but their application often proves more involved than it may seem at first sight. This book is a comprehensive complement to any textbook in the field, emphasizing the analogies between the different systems, and paves the way for an in-depth study of solid state physics, soft matter physics, and field theory.
Solved and Unsolved Problems of Structural Chemistry
by Milan Randic Marjana Novic Dejan PlavsicSolved and Unsolved Problems of Structural Chemistry introduces new methods and approaches for solving problems related to molecular structure. It includes numerous subjects such as aromaticity-one of the central themes of chemistry-and topics from bioinformatics such as graphical and numerical characterization of DNA, proteins, and proteomes. It a
Solved: How other countries cracked the world's biggest problems (and we can too)
by Andrew WearDenmark is set to achieve 100 per cent renewable energy by 2030. Iceland has topped the gender equality rankings for a decade and counting. South Korea&’s average life expectancy will soon reach ninety. How have these places achieved such remarkable outcomes? And how can we apply those lessons to our own communities? The future we want is already here - it's just not evenly distributed. By bringing together for the first time tried and tested solutions to society's most pressing problems, from violence to inequality, Andrew Wear shows that the world we want to live in is already within reach. Solved is a much-needed dose of optimism in an atmosphere of doom and gloom. Informative, accessible and revelatory, it is a celebration of the power of human ingenuity to make the future brighter for everyone.
Solvency: Models, Assessment and Regulation
by Arne SandstromUntil now there were no published analyses of the recent solvency work conducted in Europe, specifically the risk categories proposed by the International Actuarial Association (IAA). Answering the insurance industry's demand in the wake of the EU Solvency II project, Solvency: Models, Assessment and Regulation provides a concrete summary and revie
Solving Business Problems Using a Calculator (Sixth Edition)
by Mildred K. PoliskySolving Business Problems Using a Calculator follows current trends in office technology, teaches the touch method, explains common calculator features, and emphasizes business problem solving. In the sixth edition, the text's popular features have been maintained along with its concise explanations and emphasis on the use of the calculator as a problem-solving tool.
Solving Differential Equations in R
by Francesca Mazzia Jeff Cash Karline SoetaertMathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.
Solving Hyperbolic Equations with Finite Volume Methods
by M. Elena Vázquez-CendónFinite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author's experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software within the framework of Computational Fluid Dynamics (CFD).
Solving Numerical PDEs: Problems, Applications, Exercises
by Luca Formaggia Alessandro Veneziani Fausto SaleriThis book stems from the long standing teaching experience of the authors in the courses on Numerical Methods in Engineering and Numerical Methods for Partial Differential Equations given to undergraduate and graduate students of Politecnico di Milano (Italy), EPFL Lausanne (Switzerland), University of Bergamo (Italy) and Emory University (Atlanta, USA). It aims at introducing students to the numerical approximation of Partial Differential Equations (PDEs). One of the difficulties of this subject is to identify the right trade-off between theoretical concepts and their actual use in practice. With this collection of examples and exercises we try to address this issue by illustrating "academic" examples which focus on basic concepts of Numerical Analysis as well as problems derived from practical application which the student is encouraged to formalize in terms of PDEs, analyze and solve. The latter examples are derived from the experience of the authors in research project developed in collaboration with scientists of different fields (biology, medicine, etc.) and industry. We wanted this book to be useful both to readers more interested in the theoretical aspects and those more concerned with the numerical implementation.
Solving Optimization Problems with the Heuristic Kalman Algorithm: New Stochastic Methods (Springer Optimization and Its Applications #212)
by Rosario ToscanoThis text focuses on simple and easy-to-use design strategies for solving complex engineering problems that arise in several fields of engineering design, namely non-convex optimization problems. The main optimization tool used in this book to tackle the problem of nonconvexity is the Heuristic Kalman Algorithm (HKA). The main characteristic of HKA is the use of a stochastic search mechanism to solve a given optimization problem. From a computational point of view, the use of a stochastic search procedure appears essential for dealing with non-convex problems.The topics discussed in this monograph include basic definitions and concepts from the classical optimization theory, the notion of the acceptable solution, machine learning, the concept of preventive maintenance, and more. The Heuristic Kalman Algorithm discussed in this book applies to many fields such as robust structured control, electrical engineering, mechanical engineering, machine learning, reliability, and preference models. This large coverage of practical optimization problems makes this text very useful to those working on and researching systems design. The intended audience includes industrial engineers, postgraduates, and final-year undergraduates in various fields of systems design.
Solving Ordinary and Partial Boundary Value Problems in Science and Engineering (Applied and Computational Mechanics)
by Karel RektorysThis book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations.Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary.Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.
Solving Partial Differential Equation Applications with PDE2D
by Granville SewellSolve engineering and scientific partial differential equation applications using the PDE2D software developed by the author Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author that can be applied to a wide variety of science and engineering problems. The equations studied include many time-dependent, steady-state and eigenvalue applications such as diffusion, heat conduction and convection, image processing, math finance, fluid flow, and elasticity and quantum mechanics, in one, two, and three space dimensions. The author begins with some simple "0D" problems that give the reader an opportunity to become familiar with PDE2D before proceeding to more difficult problems. The book ends with the solution of a very difficult nonlinear problem, which requires a moving adaptive grid because the solution has sharp, moving peaks. This important book: Describes a finite-element program, PDE2D, developed by the author over the course of 40 years Derives the ordinary and partial differential equations, with appropriate initial and boundary conditions, for a wide variety of applications Offers free access to the Windows version of the PDE2D software through the author’s website at www.pde2d.com Offers free access to the Linux and MacOSX versions of the PDE2D software also, for instructors who adopt the book for their course and contact the author at www.pde2d.com Written for graduate applied mathematics or computational science classes, Solving Partial Differential Equation Applications with PDE2D offers students the opportunity to actually solve interesting engineering and scientific applications using the accessible PDE2D.
Solving Polynomial Equation Systems: Algebraic Solving
by Teo MoraThis third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. <P><P>The book begins with the 'standard' solutions (Gianni–Kalkbrener Theorem, Stetter Algorithm, Cardinal–Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Solving Polynomial Equation Systems: Buchberger Theory and Beyond
by Teo MoraIn this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Solving Problems in Mathematical Analysis, Part I: Sets, Functions, Limits, Derivatives, Integrals, Sequences and Series (Problem Books in Mathematics)
by Tomasz RadożyckiThis textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis.Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work.Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.
Solving Problems in Mathematical Analysis, Part II: Definite, Improper and Multidimensional Integrals, Functions of Several Variables and Differential Equations (Problem Books in Mathematics)
by Tomasz RadożyckiThis textbook offers an extensive list of completely solved problems in mathematical analysis. This second of three volumes covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis.Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work.Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.
Solving Problems in Mathematical Analysis, Part III: Curves and Surfaces, Conditional Extremes, Curvilinear Integrals, Complex Functions, Singularities and Fourier Series (Problem Books in Mathematics)
by Tomasz RadożyckiThis textbook offers an extensive list of completely solved problems in mathematical analysis. This third of three volumes covers curves and surfaces, conditional extremes, curvilinear integrals, complex functions, singularities and Fourier series. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis.Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work.Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.
Solving Problems in Thermal Engineering: A Toolbox for Engineers (Power Systems)
by Viktor Józsa Róbert KovácsThis book provides general guidelines for solving thermal problems in the fields of engineering and natural sciences.Written for a wide audience, from beginner to senior engineers and physicists, it provides a comprehensive framework covering theory and practice and including numerous fundamental and real-world examples. Based on the thermodynamics of various material laws, it focuses on the mathematical structure of the continuum models and their experimental validation. In addition to several examples in renewable energy, it also presents thermal processes in space, and summarizes size-dependent, non-Fourier, and non-Fickian problems, which have increasing practical relevance in, e.g., the semiconductor industry. Lastly, the book discusses the key aspects of numerical methods, particularly highlighting the role of boundary conditions in the modeling process.The book provides readers with a comprehensive toolbox, addressing a wide variety of topics in thermal modeling, from constructing material laws to designing advanced power plants and engineering systems.