Intended for upper-level undergraduate and graduate courses in chemistry, physics, mathematics and engineering, this text is also suitable as a reference for advanced students in the physical sciences. Detailed problems and worked examples are included.
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Classroom-tested, Advanced Mathematical Methods in Science and Engineering, Second Edition presents methods of applied mathematics that are particularly suited to address physical problems in science and engineering. Numerous examples illustrate the various methods of solution and answers to the end-of-chapter problems are included at the back of the book. After introducing integration and solution methods of ordinary differential equations (ODEs), the book presents Bessel and Legendre functions as well as the derivation and methods of solution of linear boundary value problems for physical systems in one spatial dimension governed by ODEs. It also covers complex variables, calculus, and integrals; linear partial differential equations (PDEs) in classical physics and engineering; the derivation of integral transforms; Green’s functions for ODEs and PDEs; asymptotic methods for evaluating integrals; and the asymptotic solution of ODEs. New to this edition, the final chapter offers an extensive treatment of numerical methods for solving non-linear equations, finite difference differentiation and integration, initial value and boundary value ODEs, and PDEs in mathematical physics. Chapters that cover boundary value problems and PDEs contain derivations of the governing differential equations in many fields of applied physics and engineering, such as wave mechanics, acoustics, heat flow in solids, diffusion of liquids and gases, and fluid flow. An update of a bestseller, this second edition continues to give students the strong foundation needed to apply mathematical techniques to the physical phenomena encountered in scientific and engineering applications.
Appropriate for advanced undergraduate and graduate students in a variety of scientific and engineering fields, this text introduces linear and nonlinear problems and their associated models. The first part covers linear systems, emphasizing perturbation or approximation techniques and asymptotic methods. The second part comprises nonlinear problems, including weakly nonlinear oscillatory systems and nonlinear difference equations. The two parts, both of which include exercises, merge smoothly, and many of the nonlinear techniques arise from the study of the linear systems. 1990 edition. 70 figures. 4 tables. Appendix. Index.
A comprehensive introduction to the multidisciplinary applications of mathematical methods, revised and updated The second edition of Essentials of Mathematical Methods in Science and Engineering offers an introduction to the key mathematical concepts of advanced calculus, differential equations, complex analysis, and introductory mathematical physics for students in engineering and physics research. The book’s approachable style is designed in a modular format with each chapter covering a subject thoroughly and thus can be read independently. This updated second edition includes two new and extensive chapters that cover practical linear algebra and applications of linear algebra as well as a computer file that includes Matlab codes. To enhance understanding of the material presented, the text contains a collection of exercises at the end of each chapter. The author offers a coherent treatment of the topics with a style that makes the essential mathematical skills easily accessible to a multidisciplinary audience. This important text: • Includes derivations with sufficient detail so that the reader can follow them without searching for results in other parts of the book • Puts the emphasis on the analytic techniques • Contains two new chapters that explore linear algebra and its applications • Includes Matlab codes that the readers can use to practice with the methods introduced in the book Written for students in science and engineering, this new edition of Essentials of Mathematical Methods in Science and Engineering maintains all the successful features of the first edition and includes new information.
A Practical, Interdisciplinary Guide to Advanced Mathematical Methods for Scientists and Engineers Mathematical Methods in Science and Engineering, Second Edition, provides students and scientists with a detailed mathematical reference for advanced analysis and computational methodologies. Making complex tools accessible, this invaluable resource is designed for both the classroom and the practitioners; the modular format allows flexibility of coverage, while the text itself is formatted to provide essential information without detailed study. Highly practical discussion focuses on the “how-to” aspect of each topic presented, yet provides enough theory to reinforce central processes and mechanisms. Recent growing interest in interdisciplinary studies has brought scientists together from physics, chemistry, biology, economy, and finance to expand advanced mathematical methods beyond theoretical physics. This book is written with this multi-disciplinary group in mind, emphasizing practical solutions for diverse applications and the development of a new interdisciplinary science. Revised and expanded for increased utility, this new Second Edition: Includes over 60 new sections and subsections more useful to a multidisciplinary audience Contains new examples, new figures, new problems, and more fluid arguments Presents a detailed discussion on the most frequently encountered special functions in science and engineering Provides a systematic treatment of special functions in terms of the Sturm-Liouville theory Approaches second-order differential equations of physics and engineering from the factorization perspective Includes extensive discussion of coordinate transformations and tensors, complex analysis, fractional calculus, integral transforms, Green's functions, path integrals, and more Extensively reworked to provide increased utility to a broader audience, this book provides a self-contained three-semester course for curriculum, self-study, or reference. As more scientific disciplines begin to lean more heavily on advanced mathematical analysis, this resource will prove to be an invaluable addition to any bookshelf.
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
For 1st and 2nd year undergraduate maths students and students studying Engineering. Used as a set of working notes rather than a textbook in the usual sencse of the word, these notes provide students with practice in the fundamental techniques of mathematical methods. Authors from the Royal Melbourne Institute of Technology.
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous examples, completely worked out, together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable in using advanced mathematical tools in junior, senior, and beginning graduate courses.
A solid foundation for a number of topics of interest to science and engineering students is provided in this self- contained text that assumes only a basic understanding of related mathematics.
A solutions manual that provides the answers to every third problem in Donald McQuarrie's original text Mathematical Methods for Scientists and Engineers.
A complete introduction to the multidisciplinary applications of mathematical methods In order to work with varying levels of engineering and physics research, it is important to have a firm understanding of key mathematical concepts such as advanced calculus, differential equations, complex analysis, and introductory mathematical physics. Essentials of Mathematical Methods in Science and Engineering provides a comprehensive introduction to these methods under one cover, outlining basic mathematical skills while also encouraging students and practitioners to develop new, interdisciplinary approaches to their research. The book begins with core topics from various branches of mathematics such as limits, integrals, and inverse functions. Subsequent chapters delve into the analytical tools that are commonly used in scientific and engineering studies, including vector analysis, generalized coordinates, determinants and matrices, linear algebra, complex numbers, complex analysis, and Fourier series. The author provides an extensive chapter on probability theory with applications to statistical mechanics and thermodynamics that complements the following chapter on information theory, which contains coverage of Shannon's theory, decision theory, game theory, and quantum information theory. A comprehensive list of references facilitates further exploration of these topics. Throughout the book, numerous examples and exercises reinforce the presented concepts and techniques. In addition, the book is in a modular format, so each chapter covers its subject thoroughly and can be read independently. This structure affords flexibility for individualizing courses and teaching. Providing a solid foundation and overview of the various mathematical methods and applications in multidisciplinary research, Essentials of Mathematical Methods in Science and Engineering is an excellent text for courses in physics, science, mathematics, and engineering at the upper-undergraduate and graduate levels. It also serves as a useful reference for scientists and engineers who would like a practical review of mathematical methods.
In recent years, mathematical techniques applied to novel disciplines within the science and engineering have experienced extraordinary growth. Advanced Mathematical Techniques in Science and Engineering focusses on a detailed range of mathematics applied within various fields of science and engineering for different tasks. Topics of focus include: Analysis of Consensus-Building Time in Social GroupsModeling of intersystem accidents in critical infrastructure systemsStochastic approaches to analysis and modeling of multi-sources and big dataPerformance evaluation of computational DoS attack on access point in Wireless LANsRanking methods for decision-making under uncertaintyUnderstanding time delay based Modeling & Diffusion of technological productsRole of soft computing in science and engineeringComplex system reliability analysis and optimizationTree growth models in forest ecosystems modelling This research book can be used as a reference for students in a final year undergraduate engineering course, such as mechanical, mechatronics, industrial, computer science, information technology, etc. Furthermore, the book can serve as a valuable reference for academics, engineers and researchers in these and related subject areas.
The material in this book attempts to address mathematical calculations common to both the environmental science and engineering professionals. The book provides the reader with nearly 100 solved illustrative examples. The interrelationship between both theory and applications is emphasized in nearly all of the 35 chapters. One key feature of this book is that the solutions to the problems are presented in a stand-alone manner. Throughout the book, the illustrative examples are laid out in such a way as to develop the reader’s technical understanding of the subject in question, with more difficult examples located at or near the end of each set. In presenting the text material, the authors have stressed the pragmatic approach in the application of mathematical tools to assist the reader in grasping the role of mathematical skills in environmental problem-solving situations. The book is divided up into five (V) parts: Introduction Analytical Analysis Numerical Analysis Statistical Analysis Optimization
Mathematical Methods in Science and Engineering: Applications in Optics and Photonics helps students build a conceptual appreciation for critical mathematical methods, as well as the physical feel and intuition for select mathematical ideas. Throughout the text, examples are provided from the field of optics and photonics to clarify key concepts. The book features 13 targeted chapters that begin with a brief introduction to the topical area and then dive directly into the subject matter. Students learn about properties of numbers, methods of mathematical reasoning, Euclidean geometry, the fundamentals of complex number theory, and techniques to deal with finite as well as infinite sums and products. Dedicated chapters speak to key concepts of multivariate calculus, the properties of analytic functions of a complex variable, Fourier transformation, methods of solving partial differential equations, the Sturm-Liouville theory, and special functions, including Euler's gamma function, Riemann's zeta function, and the Airy and Bessel functions. Elementary matrix algebra, vector calculus, and probability, random variables, and stochastic processes are addressed. Mathematical Methods in Science and Engineering is well suited for graduate-level courses in optical sciences, physics, and engineering. Masud Mansuripur holds a doctorate in electrical engineering and master's degrees in mathematics and electrical engineering from Stanford University. He is a professor of optical sciences and chair of Optical Data Storage at the University of Arizona. Dr. Mansuripur is also the founder and president of MM Research, Inc., a company that develops and markets simulation software for the optics industry. His professional research interests include classical electrodynamics, problems associated with radiation pressure and photon momentum, interaction of light and matter, optical, magnetic, and macromolecular data storage, thin-film and multilayer optics, magneto-optical materials, and information theory and digital signal processing.
The topics of this set of student-oriented books are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.