General Quantum Numerical Analysis
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General Quantum Numerical Analysis
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Author : Svetlin G. Georgiev
language : en
Publisher: CRC Press
Release Date : 2024-05-03
General Quantum Numerical Analysis written by Svetlin G. Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-03 with Mathematics categories.
This book is focused on the qualitative theory of general quantum calculus, the modern name for the investigation of calculus without limits. It centers on designing, analysing and applying computational techniques for general quantum differential equations. The quantum calculus or q-calculus began with F.H. Jackson in the early twentieth century, but this kind of calculus had already been worked out by Euler and Jacobi. Recently, it has aroused interest due to high demand of mathematics that models quantum computing and the connection between mathematics and physics. Quantum calculus has many applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hyper-geometric functions and other sciences such as quantum theory, mechanics and the theory of relativity. The authors summarize the most recent contributions in this area. General Quantum Numerical Analysis is intended for senior undergraduate students and beginning graduate students of engineering and science courses. The twelve chapters in this book are pedagogically organized, each concluding with a section of practical problems.
Computational Quantum Mechanics
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Author : Joshua Izaac
language : en
Publisher: Springer
Release Date : 2019-02-15
Computational Quantum Mechanics written by Joshua Izaac and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-15 with Science categories.
Quantum mechanics undergraduate courses mostly focus on systems with known analytical solutions; the finite well, simple Harmonic, and spherical potentials. However, most problems in quantum mechanics cannot be solved analytically. This textbook introduces the numerical techniques required to tackle problems in quantum mechanics, providing numerous examples en route. No programming knowledge is required – an introduction to both Fortran and Python is included, with code examples throughout. With a hands-on approach, numerical techniques covered in this book include differentiation and integration, ordinary and differential equations, linear algebra, and the Fourier transform. By completion of this book, the reader will be armed to solve the Schrödinger equation for arbitrarily complex potentials, and for single and multi-electron systems.
Handbook Of Exact Solutions To Mathematical Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2024-08-26
Handbook Of Exact Solutions To Mathematical Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-26 with Mathematics categories.
This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.
Decision Analysis Through Modeling And Game Theory
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Author : William P. Fox
language : en
Publisher: CRC Press
Release Date : 2024-11-08
Decision Analysis Through Modeling And Game Theory written by William P. Fox and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-08 with Mathematics categories.
This unique book presents decision analysis in the context of mathematical modeling and game theory. The author emphasizes and focuses on the model formulation and modeling-building skills required for decision analysis, as well as the technology to support the analysis. The primary objective of Decision Analysis through Modeling and Game Theory is illustrative in nature. It sets the tone through the introduction to mathematical modeling. The text provides a process for formally thinking about the problem and illustrates many scenarios and illustrative examples. These techniques and this approach center on the fact (a) decision makers at all levels must be exposed to the tools and techniques available to help them in the decision process, (b) decision makers as well as analysts need to have and use technology to assist in the entire analysis process, (c) the interpretation and explanation of the results are crucial to understanding the strengths and limitations of modeling, and (d) the interpretation and use of sensitivity analysis is essential. The book begins with a look at decision-making methods, including probability and statistics methods under risk of uncertainty. It moves to linear programming and multi-attribute decision-making methods with a discussion of weighting methods. Game theory is introduced through conflict games and zero-sum or constant-sum games. Nash equilibriums are next, followed by utility theory. Evolutionary stable strategies lead to Nash arbitration and cooperation methods and N-person methods presented for both total and partial conflict games. Several real-life examples and case studies using game theory are used throughout. This book would be best used for a senior-level course in mathematics, operations research, or graduate-level courses or decision modeling courses offered in business schools. The book will be of interest to departments offering mathematical modeling courses with any emphasis on modeling for decision making.
Numerical Algorithms
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Author : Justin Solomon
language : en
Publisher: CRC Press
Release Date : 2015-06-24
Numerical Algorithms written by Justin Solomon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Computers categories.
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Exact Methods For Nonlinear Pdes
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2025-08-13
Exact Methods For Nonlinear Pdes written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-13 with Mathematics categories.
Exact Methods for Nonlinear PDEs describes effective analytical methods for finding exact solutions to nonlinear differential equations of mathematical physics and other partial differential equations and also demonstrates the practical applications of these methods. It covers the methods of generalized separation of variables, methods of functional separation of variables, the classical method of symmetry reductions, the direct method of symmetry reductions, the method of weak symmetry reductions, and the method of differential constraints. The book presents several simple methods for finding exact solutions to nonlinear partial differential equations (PDEs). These methods do not require specialized knowledge and aim to minimize intermediate calculations. For the first time, it discusses the application of nonrigorous, intuitive reasoning in deriving exact solutions to nonlinear PDEs. Each section provides numerous examples, problems, and exercises to help readers develop practical skills in applying the methods. The material is illustrated with equations of mass and heat transfer, hydrodynamics, wave theory, nonlinear optics, and other nonlinear equations of mathematical physics. The key points that distinguish this book from others in the field include: • it presents many methods in a simpler and more visual format; • it describes a number of simple methods for constructing exact solutions to nonlinear PDEs and delay PDEs; • it emphasizes and details the practical use of non-rigorous reasoning to derive exact solutions for nonlinear PDEs. The book is intended for a diverse audience, including researchers, university professors, engineers, postgraduates, and students specializing in applied mathematics, theoretical physics, and engineering sciences.
Mathematical Analysis And Numerical Methods For Science And Technology
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Author : Robert Dautray
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Analysis And Numerical Methods For Science And Technology written by Robert Dautray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
These 6 volumes -- the result of a 10 year collaboration between the authors, both distinguished international figures -- compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. The advent of high-speed computers has made it possible to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way.
Advanced Engineering Mathematics With Matlab
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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 2025-08-19
Advanced Engineering Mathematics With Matlab written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-19 with Mathematics categories.
In the five previous editions of Advanced Engineering Mathematics with MATLAB®, the author presented a text firmly grounded in mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines teaching and practical experience that is rare among authors of advanced engineering mathematics books. This edition continues to refine a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more practical option to align with the expectations of today’s students. The new edition of the author’s classic textbook continues on a path to creating the best possible learning resource for instructors and students alike. Through extensive class testing over five previous editions, including the author’s current course at the US Naval Academy, the book has been steadily improved. The primary mission of this edition is to dramatically increase the quality and quantity of examples and problems, especially in the chapters on differential equations and Laplace transforms. The chapters on differential equations, linear algebra, Fourier series, and Laplace transforms have seen the greatest changes. Of course, this edition continues to offer a wealth of examples and applications from scientific and engineering literature, a highlight of previous editions. MATLAB® remains central to the presentation and is employed to reinforce the concepts that are taught. Worked solutions are given in the back of the book. An Instructor’s Solutions Manual is also available.
Introducing Game Theory And Its Applications
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Author : Elliott Mendelson
language : en
Publisher: CRC Press
Release Date : 2024-08-02
Introducing Game Theory And Its Applications written by Elliott Mendelson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-02 with Mathematics categories.
This classic text, originally from the noted logician Elliot Mendelson, is intended to be an easy-to-read introduction to the basic ideas and techniques of game theory. It can be used as a class textbook or for self-study. Introducing Game Theory and its Applications, Second Edition presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the authors begin with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solutions. Here the authors present the simplex method based on linear programming for solving these games and develop within this presentation the required background. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory. The book is suitable for a first undergraduate course in game theory, or a graduate course for students with limited previous exposure. It is useful for students who need to learn some game theory for a related subject (e.g., microeconomics) and have a limited mathematical background. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences. The authors hope this book breeds curiosity about the subject as its design is meant to to satisfy the readers. The book will prepare readers for deeper study of game theory applications in many fields of study.
Mathematical Models And Methods For Ab Initio Quantum Chemistry
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Author : M. Defranceschi
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-11-16
Mathematical Models And Methods For Ab Initio Quantum Chemistry written by M. Defranceschi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-16 with Science categories.
On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.