This contributed volume collects papers presented at a special session of the conference Computational and Mathematical Methods in Science and Engineering (CMMSE) held in Cadiz, Spain from June 30 - July 6, 2019. Covering the applications of integral methods to scientific developments in a variety of fields, ranging from pure analysis to petroleum engineering, the chapters in this volume present new results in both pure and applied mathematics. Written by well-known researchers in their respective disciplines, each chapter shares a common methodology based on a combination of analytic and computational tools. This approach makes the collection a valuable, multidisciplinary reference on how mathematics can be applied to various real-world processes and phenomena. Computational and Analytic Methods in Science and Engineering will be ideal for applied mathematicians, physicists, and research engineers.

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.

This contributed volume collects papers presented at a special session of the conference Computational and Mathematical Methods in Science and Engineering (CMMSE) held in Cadiz, Spain from June 30 - July 6, 2019. Covering the applications of integral methods to scientific developments in a variety of fields, ranging from pure analysis to petroleum engineering, the chapters in this volume present new results in both pure and applied mathematics. Written by well-known researchers in their respective disciplines, each chapter shares a common methodology based on a combination of analytic and computational tools. This approach makes the collection a valuable, multidisciplinary reference on how mathematics can be applied to various real-world processes and phenomena. Computational and Analytic Methods in Science and Engineering will be ideal for applied mathematicians, physicists, and research engineers.

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.

This book focuses on the topics which provide the foundation for practicing engineering mathematics: ordinary differential equations, vector calculus, linear algebra and partial differential equations. Destined to become the definitive work in the field, the book uses a practical engineering approach based upon solving equations and incorporates computational techniques throughout.

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.

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Numerical methods constitute an analytical tool scientific and technological valuable today. The development of computers has allowed its development to solve complex problems, from the simulation of a phenomenon or device, to the study of complex systems such as simulation of evolution of a galaxy or stress analysis and stability of an aircraft.This proposal is applicable to any introductory course on the subject. The use of software and the use of visualizations support the learning process combined with the basic learning programming through mathematical problems are directly applicable to science and engineering, as well as the proposal for consideration and programming methods more specific, and the use of problem-based learning. This will allow the reader to understand the relationship of discipline with applications in engineering.We have considered a number of applications including integrated through the horizontality of the methods for solving complex application problems. Modern software is included directly in each method, where each should be programmed as a mark of professional practice due. Currently, even if one could ignore the learning of numerical methods by using specialized software programming it allows the reader to understand the complexity and the need to solve certain problems by simulating and programming, even assisted by this. The dimensioning of the firmness is the definition of its geometric and constitutive aspects. Consideration of it as a structure and application of the principles of mechanics, the concept of mechanics Firmes arises. This discipline mainly adopts two types of methods for determining the characteristics of the firmness: empirical methods, based on knowledge through experience, and analytical methods based on mathematical modeling of the structure.Analytical Methods were developed in the second half of the twentieth century, in parallel with the evolution of computing. Models of the firmness based on the theory of Burmister (for flexible pavements) and Westergaard (for firmness concrete) were being computerized in increasingly complex programs that behavior patterns were added to estimate the service life of the structure. Thus, analytical methods resulted in software, due to the advantages of calculation that entails.In 1906, the Russian botanist M. Tswett conducted an experiment that led to the discovery of what is now known as chromatography. Placed an extract pigment plant on top of a glass column filled with calcium carbonate (CaCO3). By adding ether, noted that mixing original separated into different colored bands that descended through the column at different speeds. A characteristic feature of chromatography is the presence of two phases; arranged so that while one remains stationary within the system (stationary phase), the other moves along it (mobile phase). The key to the separation in chromatography is that the speed with which it moves each substance depends on its relative affinity for both phases (equilibrium distribution). In the experiment Tswett, separation of pigments plant was achieved thanks to each one of them had an affinity for different phases. In general, the components more akin to the stationary phase are moving slowly (more retained) while more akin to the mobile phase (less retained) move faster. Consequently, the chromatographic medium (column, plate or paper) works as a driver of the speed of each substance constituting the mixture, thus achieving separation and using a detector, chemical characterization. Although the basic principles are the same, it is customary to classify chromatographic methods depending on the physical state of the mobile phase: - Liquid chromatography. The mobile phase is a solvent or solvent mixture and stationary phase solid that interacts with the substances to be separated (liquid chromatograph-solid) or liquid immiscible with the mobile phase, deposited on the surface of a solid ( liquid-liquid chromatography). This form of chromatography can be performed with different experimental arrangements: column, in a thin layer on the paper. - Gas chromatography. In this case the mobile phase is an inert gas (helium or nitrogen) and stationary phase is a solid (gas-solid chromatography) or a liquid "sustained" by an inert solid (GLC). This type of chromatography column is provided as it is the only way that the mobile phase flowing gas remains confined within the system. Application areas are diverse and encompass virtually every activity involved in chemistry, for example, is used in: - The analysis of drugs and drugs in biological fluids such as saliva, blood, urine; - Follow the transformation of the substances responsible for the neurological transmission; - Determining the presence of contaminants in the environment;- Deciphering the composition of fossil fuels; - Perform quality control of products manufactured chemicals and pharmaceuticals; in short, the list of examples is endless. In this book we have taken several analytical methods that have been accessed through a bibliographic research and information technology, in order to analyze the characteristics of each of them and update their status of validity. The aim of this study is to make a comparison between different methods and determine the degree of acceptance and use thereof. This is intended to bring together the available knowledge of analytical methods to recognize its advantages and limitations, which can serve as a basis for the development of new methods or improving existing ones.