Computational Methods for Applied Inverse Problems

The advent of high-speed computers has encouraged a growing demand for newly graduated engineers to possess the basic skills of computational methods for heat and mass transfer and fluid dynamics. Com

The critical role of trace gases in global atmospheric change makes an improved understanding of these gases imperative. Measurements of the distributions of these gases in space and time provide important information, but the interpretation of this information often involves ill-conditioned model inversions. A variety of techniques have therefore been developed to analyze these problems. Inverse Problems in Atmospheric Constituent Transport is the first book to give comprehensive coverage of work on this topic. The trace gas inversion problem is presented in general terms and the various different approaches are unified by treating the inversion problem as one of statistical estimation. Later chapters demonstrate the application of these methods to studies of carbon dioxide, methane, halocarbons and other gases implicated in global climate change. This book is aimed at graduate students and researchers embarking upon studies of global atmospheric change, biogeochemical cycles and Eart

Here is a book for anyone who would like to become better acquainted with the modern tools of numerical analysis for several significant computational problems arising in finance. The authors review s

For freshman/sophomore-level courses in Linear Algebra. This book provides an applied introduction to the basic ideas, computational techniques, and applications of linear algebra. The most applied of

Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two, seemingly disparate, settings. This text focuses on global methods. This means that morphisms, typically arising from symmetry or direct product decomposition, are employed to transform new problems into more restricted and easily solvable settings whilst preserving essential structure. This book is based on Professor Harper's many years' experience in teaching this subject and is ideal for graduate students entering the field. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science. Applied systematically, the global point of view can lead to surprising insights and results, and established researchers will find this to be a valuable reference wo

Examining the physical and technical foundation for recent progress with this technique, Applied Scanning Probe Methods offers a timely and comprehensive overview of SPM applications, now that industr

This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, a package for computation of these maps.

The critical role of trace gases in global atmospheric change makes an improved understanding of these gases imperative. Measurements of the distributions of these gases in space and time provide important information, but the interpretation of this information often involves ill-conditioned model inversions. A variety of techniques have therefore been developed to analyze these problems. Inverse Problems in Atmospheric Constituent Transport is the first book to give comprehensive coverage of work on this topic. The trace gas inversion problem is presented in general terms and the various different approaches are unified by treating the inversion problem as one of statistical estimation. Later chapters demonstrate the application of these methods to studies of carbon dioxide, methane, halocarbons and other gases implicated in global climate change. This book is aimed at graduate students and researchers embarking upon studies of global atmospheric change, biogeochemical cycles and Eart

Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and ground and marine vehicles. This 2001 book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition has a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for thr

This text offers a clear and refreshing exposition of the dynamics of mechanical systems from an engineering perspective. Basic concepts are thoroughly covered, then applied in a systematic manner to solve problems in mechanical systems that have recognisable applications to engineering practice. All theoretical discussions are accompanied by numerous illustrative examples, and each chapter offers a wealth of homework problems. The treatment of the kinematics of particles and rigid bodies is extensive. In this new edition, the author has revised and reorganized sections to enhance understanding of physical principles, and he has modified and added examples, as well as homework problems. The new edition also contains a thorough development of computational methods for solving the differential equations of motion for constrained systems.

A text intended for advanced graduate students, computational scientists and engineers, and researchers in applied numerical analysis and mathematical software development. The authors survey a wide

Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astrono

This volume contains the results of the workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, held in Karlsruhe, Germany, and represents a balanced selection of

Perturbation methods are one of the fundamental tools used by all applied mathematicians and theoretical physicists. In this book, the author has managed to present the theory and techniques underlying such methods in a manner which will give the text wide appeal to students from a broad range of disciplines. Asymptotic expansions, strained coordinates and multiple scales are illustrated by copious use of examples drawn from all areas of applied mathematics and theoretical physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather to give a physical understanding of the subtle balances in a complex problem.

Computational thinking is increasingly gaining importance in modern biology, due to the unprecedented scale at which data is nowadays produced. Bridging the cultural gap between the biological and computational sciences, this book serves as an accessible introduction to computational concepts for students in the life sciences. It focuses on teaching algorithmic and logical thinking, rather than just the use of existing bioinformatics tools or programming. Topics are presented from a biological point of view, to demonstrate how computational approaches can be used to solve problems in biology such as biological image processing, regulatory networks, and sequence analysis. The book contains a range of pedagogical features to aid understanding, including real-world examples, in-text exercises, end-of-chapter problems, colour-coded Python code, and 'code explained' boxes. User-friendly throughout, Computational Thinking for Life Scientists promotes the thinking skills and self-efficacy req

Computational thinking is increasingly gaining importance in modern biology, due to the unprecedented scale at which data is nowadays produced. Bridging the cultural gap between the biological and computational sciences, this book serves as an accessible introduction to computational concepts for students in the life sciences. It focuses on teaching algorithmic and logical thinking, rather than just the use of existing bioinformatics tools or programming. Topics are presented from a biological point of view, to demonstrate how computational approaches can be used to solve problems in biology such as biological image processing, regulatory networks, and sequence analysis. The book contains a range of pedagogical features to aid understanding, including real-world examples, in-text exercises, end-of-chapter problems, colour-coded Python code, and 'code explained' boxes. User-friendly throughout, Computational Thinking for Life Scientists promotes the thinking skills and self-efficacy req

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus

Data-driven computational neuroscience facilitates the transformation of data into insights into the structure and functions of the brain. This introduction for researchers and graduate students is the first in-depth, comprehensive treatment of statistical and machine learning methods for neuroscience. The methods are demonstrated through case studies of real problems to empower readers to build their own solutions. The book covers a wide variety of methods, including supervised classification with non-probabilistic models (nearest-neighbors, classification trees, rule induction, artificial neural networks and support vector machines) and probabilistic models (discriminant analysis, logistic regression and Bayesian network classifiers), meta-classifiers, multi-dimensional classifiers and feature subset selection methods. Other parts of the book are devoted to association discovery with probabilistic graphical models (Bayesian networks and Markov networks) and spatial statistics with po

This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of eac

In recent years, applied mathematics has been used in all novel disciplines of scientific development. Advances in Applied Mathematical Problems summarizes interdisciplinary work within the field of a

The Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB®, this book supports readers in applying appropriate analytical or computational methods to solving real research questi

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for

This title covers recent progress in advanced analytical and associated numerical methods applied to problems arising in all areas of electromagnetics. It focuses on applying advanced or novel mathema

This book is a guide to numerical methods for solving fluid dynamics problems. The most widely used discretization and solution methods, which are also found in most commercial CFD-programs, are descr

Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean–variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean–variance optimization, multi-period models, and add

Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solu

This book presents computational and statistical methods used by intelligent systems within the concept of Industry 4.0. The methods include among others evolution-based and swarm intelligence-based m

The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods de

This book is a guide to the use of inverse theory for estimation and conditional simulation of flow and transport parameters in porous media. It describes the theory and practice of estimating properties of underground petroleum reservoirs from measurements of flow in wells, and it explains how to characterize the uncertainty in such estimates. Early chapters present the reader with the necessary background in inverse theory, probability and spatial statistics. The book demonstrates how to calculate sensitivity coefficients and the linearized relationship between models and production data. It also shows how to develop iterative methods for generating estimates and conditional realizations. The text is written for researchers and graduates in petroleum engineering and groundwater hydrology, and can be used as a textbook for advanced courses on inverse theory in petroleum engineering. It includes many worked examples to demonstrate the methodologies and a selection of exercises.

Everyday Applied Geophysics 1 covers the physical methods permitting the environmental exploration of the sub-surface in 1, 2, 3 or 4 dimensions (the last is for time-lapse in terms of physical enviro

This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics, CIBB 2016, held

Gain Confidence in Modeling Techniques Used for Complicated Bridge StructuresBridge structures vary considerably in form, size, complexity, and importance. The methods for their computational analysis

Papers presented at the 18th International Conference on Computational Methods and Experimental Measurements form this book, which includes research from scientists, researchers and specialists who pe

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It

This volume introduces a series of different data-driven computational methods for analyzing group processes through didactic and tutorial-based examples. A number of data-driven methods adapted to gr

For courses in Statistical Methods for the Social Sciences . Statistical methods applied to social sciences, made accessible to all through an emphasis on concepts Statistical Methods for t

Annual Reports in Computational Chemistry provides timely and critical reviews of important topics in computational chemistry as applied to all chemical disciplines. Topics covered include quantum che