Mathematical Modeling for Business Analytics is written for decision makers at all levels. This book presents the latest tools and techniques available to help in the decision process. The interpretation and explanation of the results are crucial to understanding the strengths and limitations of modeling. This book emphasizes and focuses on the aspects of constructing a useful model formulation, as well as building the skills required for decision analysis. The book also focuses on sensitivity analysis. The author encourages readers to formally think about solving problems by using a thorough process. Many scenarios and illustrative examples are provided to help solve problems. Each chapter is also comprehensively arranged so that readers gain an in-depth understanding of the subject which includes introductions, background information and analysis. Both undergraduate and graduate students taking methods courses in methods and discrete mathematical modeling courses will greatly benefit from using this book. Boasts many illustrative examples to help solve problems Provides many solutions for each chapter Emphasizes model formulation and helps create model building skills for decision analysis Provides the tools to support analysis and interpretation

Wide-Ranging Coverage of Parametric Modeling in Linear and Nonlinear Mixed Effects ModelsMixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools presents a rigorous framework for describing, implementing, and using mixed effects models. With these models, readers can perform parameter estimation and modeling across a whole population of individuals at the same time. Easy-to-Use Techniques and Tools for Real-World Data ModelingThe book first shows how the framework allows model representation for different data types, including continuous, categorical, count, and time-to-event data. This leads to the use of generic methods, such as the stochastic approximation of the EM algorithm (SAEM), for modeling these diverse data types. The book also covers other essential methods, including Markov chain Monte Carlo (MCMC) and importance sampling techniques. The author uses publicly available software tools to illustrate modeling tasks. Methods are implemented in Monolix, and models are visually explored using Mlxplore and simulated using Simulx. Careful Balance of Mathematical Representation and Practical ImplementationThis book takes readers through the whole modeling process, from defining/creating a parametric model to performing tasks on the model using various mathematical methods. Statisticians and mathematicians will appreciate the rigorous representation of the models and theoretical properties of the methods while modelers will welcome the practical capabilities of the tools. The book is also useful for training and teaching in any field where population modeling occurs.

Problem Solving is essential to solve real-world problems. Advanced Problem Solving with Maple: A First Course applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. It is intended for a course introducing students to mathematical topics they will revisit within their further studies. The authors present mathematical modeling and problem-solving topics using Maple as the computer algebra system for mathematical explorations, as well as obtaining plots that help readers perform analyses. The book presents cogent applications that demonstrate an effective use of Maple, provide discussions of the results obtained using Maple, and stimulate thought and analysis of additional applications. Highlights: The book's real-world case studies prepare the student for modeling applications Bridges the study of topics and applications to various fields of mathematics, science, and engineering Features a flexible format and tiered approach offers courses for students at various levels The book can be used for students with only algebra or calculus behind them About the authors: Dr. William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his Ph.D. at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles. William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM). *Please note that the Maple package, "PSM", is now on the public area of the Maple Cloud. To access it: * From the web: 1. Go to the website https://maple.cloud 2. Click on "packages" in the left navigation pane 3. Click on "PSM" in the list of packages. 4. Click the "Download" button to capture the package. * From Maple: 1. Click on the Maple Cloud icon (far right in the Maple window toolbar). Or click on the Maple Cloud button on Maple's Start page to go to the website. 2. Click on the "packages" in the navigation pane 3. Click on "PSM" in the list of packages. The package then downloads into Maple directly.

Field Programmable Gate Arrays (FPGAs) are currently recognized as the most suitable platform for the implementation of complex digital systems targeting an increasing number of industrial electronics applications. They cover a huge variety of application areas, such as: aerospace, food industry, art, industrial automation, automotive, biomedicine, process control, military, logistics, power electronics, chemistry, sensor networks, robotics, ultrasound, security, and artificial vision. This book first presents the basic architectures of the devices to familiarize the reader with the fundamentals of FPGAs before identifying and discussing new resources that extend the ability of the devices to solve problems in new application domains. Design methodologies are discussed and application examples are included for some of these domains, e.g., mechatronics, robotics, and power systems.

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction. It equips readers with powerful domain-independent methods for reducing risk based on algebraic inequalities and demonstrates the significant benefits derived from the application for risk and uncertainty reduction. Algebraic inequalities: * Provide a powerful reliability improvement, risk and uncertainty reduction method that transcends engineering and can be applied in various domains of human activity * Present an effective tool for dealing with deep uncertainty related to key reliability-critical parameters of systems and processes * Permit meaningful interpretations which link abstract inequalities with the real world * Offer a tool for determining tight bounds for the variation of risk-critical parameters and complying the design with these bounds to avoid failure * Allow optimising designs and processes by minimising the deviation of critical output parameters from their specified values and maximising their performance This book is primarily for engineering professionals and academic researchers in virtually all existing engineering disciplines.

Discusses replacement, repair, and inspection Offers estimation and statistical tests Covers accelerated life testing Explores warranty analysis manufacturing Includes service reliability

This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture.

Introduction to Computational Models with Python explains how to implement computational models using the flexible and easy-to-use Python programming language. The book uses the Python programming language interpreter and several packages from the huge Python Library that improve the performance of numerical computing, such as the Numpy and Scipy modules. The Python source code and data files are available on the author's website. The book's five sections present: An overview of problem solving and simple Python programs, introducing the basic models and techniques for designing and implementing problem solutions, independent of software and hardware tools Programming principles with the Python programming language, covering basic programming concepts, data definitions, programming structures with flowcharts and pseudo-code, solving problems, and algorithms Python lists, arrays, basic data structures, object orientation, linked lists, recursion, and running programs under Linux Implementation of computational models with Python using Numpy, with examples and case studies The modeling of linear optimization problems, from problem formulation to implementation of computational models This book introduces the principles of computational modeling as well as the approaches of multi- and interdisciplinary computing to beginners in the field. It provides the foundation for more advanced studies in scientific computing, including parallel computing using MPI, grid computing, and other methods and techniques used in high-performance computing.

Despite significant advances in technology and equipment for rolled steel, the computerization of production processes and the steady increase in production of sheet steel, recent scientific and technological achievements have not been compiled in the special literature and revealed to a wide range of specialists. This book details new approaches, computational techniques, and reliable calculation methods of leaf-rolling modes, forecasting and optimization of the technologies, increasing productivity of the mill and a radical improvement in the quality of steel products.

Computer simulation is an effective and popular universal tool that can be applied to almost all disciplines. Requiring only basic knowledge of programming, mathematics, and probability theory, Computer Simulation: A Foundational Approach Using Python takes a hands-on approach to programming to introduce the fundamentals of computer simulation. The main target of the book is computer science and engineering students who are interested mainly in directly applying the techniques to their research problems. The book will be of great interest to senior undergraduate and starting graduate students in the fields of computer science and engineering and industrial engineering.

Modeling Tools for Environmental Engineers and Scientists enables environmental professionals, faculty, and students with minimal computer programming skills to develop computer-based mathematical models for natural and engineered environmental systems. The author illustrates how commercially available syntax-free authoring software can be adapted to create customized, high-level models of environmental phenomena in groundwater, soil, aquatic, and atmospheric systems, and in engineered reactors. This book includes a review of mathematical modeling and fundamental concepts such as material balance, reactor configurations, and fate and transport of environmental contaminants. It illustrates, using numerous examples, how mathematical and dynamic modeling software can be applied in analyzing and simulating natural and engineered environmental systems. The tools and examples included are applicable to a wide range of problems, both in the classroom and in the field.

Quantitative Methods in Transportation provides the most useful, simple, and advanced quantitative techniques for solving real-life transportation engineering problems. It aims to help transportation engineers and analysts to predict travel and freight demand, plan new transportation networks, and develop various traffic control strategies that are safer, more cost effective, and greener. Transportation networks can be exceptionally large, and this makes many transportation problems combinatorial, and the challenges are compounded by the stochastic and independent nature of trip-planners decision making. Methods outlined in this book range from linear programming, multi-attribute decision making, data envelopment analysis, probability theory, and simulation to computer techniques such as genetic algorithms, simulated annealing, tabu search, ant colony optimization, and bee colony optimization. The book is supported with problems and has a solutions manual to aid course instructors.

Solid geometry is defined as the study of the geometry of three-dimensional solid figures in Euclidean space. There are numerous techniques in solid geometry, mainly analytic geometry and methods using vectors, since they use linear equations and matrix algebra. Solid geometry is quite useful in everyday life, for example, to design different signs and symbols such as octagon shape stop signs, to indicate traffic rules, to design different 3D objects like cubicles in gaming zones, innovative lifts, creative 3D interiors, and to design 3D computer graphics. Studying solid geometry helps students to improve visualization and increase logical thinking and creativity since it is applicable everywhere in day-to-day life. It builds up a foundation for advanced levels of mathematical studies. Numerous competitive exams include solid geometry since its foundation is required to study other branches like civil engineering, mechanical engineering, computer science engineering, architecture, etc. This book is designed especially for students of all levels, and can serve as a fundamental resource for advanced level studies not only in mathematics but also in various fields like engineering, interior design, architecture, etc. It includes theoretical aspects as well as numerous solved examples. The book includes numerical problems and problems of construction as well as practical problems as an application of the respective topic. A special feature of this book is that it includes solved examples using the mathematical tool MATLAB.

Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Without sacrificing scientific strictness, this introduction to the field guides readers through mathematical modeling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behavior of the dynamics of physical flow.
The book is carefully divided into three main parts:
- The design of mathematical models of physical fluid flow;
- A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events;
- The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situations.
Both students and experts wanting to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from this combination of all relevant aspects in one handy volume.

Examines classic algorithms, geometric diagrams, and mechanical principles for enhancing visualization of statistical estimation procedures and mathematical concepts in physics, engineering, and computer programming.

Modelling large-scale wave fields and their interaction with coastal and offshore structures has become much more feasible over the last two decades with increases in computer speeds. Wave modelling can be viewed as an extension of wave theory, a mature and widely published field, applied to practical engineering through the use of computer tools. Information about the various wave models which have been developed is often widely scattered in the literature, and consequently this is one of the first books devoted to wave models and their applications. At the core of the book is an introduction to various types of wave models. For each model, the theoretical assumptions, the application range, and the advantages and limitations are elaborated. The combined use of different wave models from large-scale to local-scale is highlighted with a detailed discussion of the application and matching of boundary conditions. At the same time the book provides a grounding in hydrodynamics, wave theory, and numerical methods which underlie wave modelling. It presents the theoretical background and also shows how to use these models for achieving different engineering tasks, illustrated and reinforced with case study examples.

The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of derivative securities. It includes all the tools necessary for readers to understand how the stochastic integral is constructed with respect to a general continuous martingale. The author develops the stochastic calculus from first principles, but at a relaxed pace that includes proofs that are detailed, but streamlined to applications to finance. The treatment requires minimal prerequisites-a basic knowledge of measure theoretic probability and Hilbert space theory-and devotes an entire chapter to application in finances, including the Black Scholes market, pricing contingent claims, the general market model, pricing of random payoffs, and interest rate derivatives. Continuous Stochastic Calculus with Application to Finance is your first opportunity to explore stochastic integration at a reasonable and practical mathematical level. It offers a treatment well balanced between aesthetic appeal, degree of generality, depth, and ease of reading.

Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.

International migration has huge economic, social and political consequences and as a result there is growing demand for evidence-based policies. This has long been unfeasible due to inaccuracies in migration data, caused, for example, by different data sources employing different definitions and different collection methods. However, in recent years methods involving the use of models have been developed to derive reliable estimates of migration. International Migration in Europe draws together modern statistical approaches to provide a unified treatment of these methods, allowing a consistent and dependable set of migration flows to be developed.

The book:

Uses European-based real data to demonstrate migration estimation and modelling tools, with worldwide applications.

Explores the modelling techniques from both the frequentist and Bayesian perspectives.

Discusses vital concepts in detail, such as missing data and collection methods.

Includes chapters dedicated to the key areas of modelling asylum flows and migration forecasting.

Is authored by the leading experts working in migration data and models.

Is supported by a supplementary website featuring further reading material.

International Migration in Europe is primarily aimed at academics, undergraduate and graduate students in the fields of demography, statistics, geography, sociology, economics and political science. However, this is also an important book for government statisticians responsible for publishing migration data, as well as analysts working on migration-related topics such as planning and demography at all levels, from local to international.

Modelling Transitions shows what computational, formal and data-driven approaches can and could mean for sustainability transitions research, presenting the state-of-the-art and exploring what lies beyond. Featuring contributions from many well-known authors, this book presents the various benefits of modelling for transitions research. More than just taking stock, it also critically examines what modelling of transformative change means and could mean for transitions research and for other disciplines that study societal changes. This includes identifying a variety of approaches currently not part of the portfolios of transitions modellers. Far from only singing praise, critical methodological and philosophical introspection are key aspects of this important book. This book speaks to modellers and non-modellers alike who value the development of robust knowledge on transitions to sustainability, including colleagues in congenial fields. Be they students, researchers or practitioners, everyone interested in transitions should find this book relevant as reference, resource and guide.

Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals. With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also s

The authors of this monograph have developed a large and important class of survival analysis models that generalize most of the existing models. In a unified, systematic presentation, this monograph fully details those models and explores areas of accelerated life testing usually only touched upon in the literature. Accelerated Life Models: Modeling and Statistical Analysis presents models, methods of data collection, and statistical analysis for failure-time regression data in accelerated life testing and for degradation data with explanatory variables. In addition to the classical results, the authors devote considerable attention to models with time-varying explanatory variables and to methods of semiparametric estimation. They also examine the simultaneous analysis of degradation and failure-time data when the intensities of failure in different modes depend on the level of degradation and the values of explanatory variables. The authors avoid technical details by explaining the ideas and referring to resources where thorough analysis can be found. Whether used for teaching, research or general reference, Accelerated Life Models: Modeling and Statistical Analysis provides new and known models and modern methods of accelerated life data analysis.

The use of lasers for various applications in materials processing has grown rapidly in recent years. Lasers are by nature particularly well suited to automation, but to ensure repeatability and reliability, the engineers employing them must not simply rely on numerical analysis software. They must have a firm grasp on the physical principles involved. Mathematics of Thermal Modelling: An Introduction to the Theory of Laser Material Processing introduces the mathematics needed to formulate and exploit the physical principles important to modelling various aspects of laser material processing. The author shows how to gain insight by constructing and analyzing simple models. He demonstrates how to extract qualitative information from the models, how the underlying principles can be extended to more complex modelling, and how these principles can be applied to processes such as laser welding, surface treatment, drilling, and cutting. Written at a level accessible to graduate students, this book shows that simple mathematical investigation-- based primarily on analytical methods backed by relatively simple numerical methods--can greatly illuminate the processes being studied. Regardless of the stage of your career development, if you are confronting the modelling of thermal process in this field for the first time, Mathematics of Thermal Modelling will build the foundation you need.