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Differentiability in Banach Spaces, Differential Forms and Applications
by Celso Melchiades DoriaThis book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.
Differential and Differential-Algebraic Systems for the Chemical Engineer
by Flavio Manenti Guido Buzzi-FerrarisThis fourth in a suite of five practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows in a step-by-step fashion how to use them.The volume focuses on differential and differential-algebraic systems, providing numerous real-life industrial case studies to illustrate this complex topic. It describes the methods, innovative techniques and strategies that are all implemented in a freely available toolbox called BzzMath, which is developed and maintained by the authors and provides up-to-date software tools for all the methods described in the book. Numerous examples, sample codes, programs and applications are taken from a wide range of scientific and engineering fields, such as chemical engineering, electrical engineering, physics, medicine, and environmental science. As a result, engineers and scientists learn how to optimize processes even before entering the laboratory.With additional online material including the latest version of BzzMath Library, installation tutorial, all examples and sample codes used in the book and a host of further examples.
Differential Antennas: Theory and Practice
by Yueping ZhangA comprehensive introduction to the theory and practice of differential antennas The first antennas ever created were differential antennas, in the dipole and loop constructions, before the subsequent creation of the single-ended or monopole antenna. Dozens of basic antenna configurations have been invented since then, the majority of them differential. The theory and design of differential antennas therefore has an impact on a huge range of fields which make use of electromagnetic waves. Differential Antennas contains a thorough, comprehensive overview of these antennas, their theory, and their practical applications. It details the relationship between differential and single-ended antennas, which may act as tools for determining the properties of one when the other is known. This book offers an analysis of the role differential antennas play in wireless communication and sensing. Overall, it stands as an essential contribution to a key area of communications technology. Differential Antennas readers will also find: Chapters covering topics including microstrip antennas, shorted patch antennas, grid array antennas, and other designs Tables and figures illustrating key data, antenna structures, and more Instructions for measuring differential antennas for characterization and specification purposes Differential Antennas is ideal for senior and graduate level students, researchers, and radio frequency engineers.
Differential Equation Analysis in Biomedical Science and Engineering
by William E. SchiesserFeatures a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fieldsWith a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations.The author's primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes:R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEsModels as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiologyNumerical solutions of the presented model equations with a discussion of the important features of the solutionsAspects of general PDE computation through various biomedical science and engineering applicationsDifferential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Differential Equation Analysis in Biomedical Science and Engineering
by William E. SchiesserFeatures a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fieldsWith a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear ordinary differential equations.The author's primary focus is on models expressed as systems of ODEs, which generally result by neglecting spatial effects so that the ODE dependent variables are uniform in space. Therefore, time is the independent variable in most applications of ODE systems. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes:R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for ODEsModels as systems of ODEs with explanations of the associated chemistry, physics, biology, and physiology as well as the algebraic equations used to calculate intermediate variablesNumerical solutions of the presented model equations with a discussion of the important features of the solutionsAspects of general ODE computation through various biomolecular science and engineering applicationsDifferential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Differential Equations: Practice Problems, Methods, and Solutions
by Mehdi Rahmani-AndebiliThis study guide is designed for students taking courses in differential equations. The textbook includes examples, questions, and exercises that will help engineering students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve student’s problem-solving skills and basic and advanced understanding of the topics covered in electric circuit analysis courses.
Differential Equations: For Scientists and Engineers
by Allan Struthers Merle PotterThis book is designed to serve as a textbook for a course on ordinary differential equations, which is usually a required course in most science and engineering disciplines and follows calculus courses. The book begins with linear algebra, including a number of physical applications, and goes on to discuss first-order differential equations, linear systems of differential equations, higher order differential equations, Laplace transforms, nonlinear systems of differential equations, and numerical methods used in solving differential equations. The style of presentation of the book ensures that the student with a minimum of assistance may apply the theorems and proofs presented. Liberal use of examples and homework problems aids the student in the study of the topics presented and applying them to numerous applications in the real scientific world. This textbook focuses on the actual solution of ordinary differential equations preparing the student to solve ordinary differential equations when exposed to such equations in subsequent courses in engineering or pure science programs. The book can be used as a text in a one-semester core course on differential equations, alternatively it can also be used as a partial or supplementary text in intensive courses that cover multiple topics including differential equations.
Differential Equations and Data Analysis (Synthesis Lectures on Mathematics & Statistics)
by Aleksei BeltukovThis book is focused on modeling with linear differential equations with constant coefficients. The author starts with the elementary natural growth equation and ends with the heat equation on the real line. The emphasis is on linear algebra, Fourier theory, and specifically data analysis, which is given a very prominent role and is often the book's main driving force. All aspects of modeling with linear differential equations are illustrated by analyzing real and simulated data in MATLAB®. These modeling case studies are of particular interest to students who anticipate having to use differential equations in their fields. The book is self-contained and is appropriate as a supplement for a first course in differential equations whose prerequisites include proficiency in multivariate calculus and MATLAB literacy.
Differential Equations of My Young Years
by Vladimir Maz'YaVladimir Maz'ya (born 1937) is an outstanding mathematician who systematically made fundamental contributions to a wide array of areas in mathematical analysis and in the theory of partial differential equations. In this fascinating book he describes the first thirty years of his life. He starts with the story of his family, speaks about his childhood, high school and university years, describe his formative years as a mathematician. Behind the author's personal recollections, with his own joys, sorrows and hopes, one sees a vivid picture of the time. He speaks warmly about his friends, both outside and inside mathematics. The author describes the awakening of his passion for mathematics and his early achievements. He mentions a number of mathematicians who influenced his professional life. The book is written in a readable and inviting way sometimes with a touch of humor. It can be of interest for a very broad readership.
Differential Evolution Algorithm with Type-2 Fuzzy Logic for Dynamic Parameter Adaptation with Application to Intelligent Control (SpringerBriefs in Applied Sciences and Technology)
by Oscar Castillo Patricia Ochoa Jose SoriaThis book focuses on the fields of fuzzy logic, bio-inspired algorithm, especially the differential evolution algorithm and also considering the fuzzy control area. The main idea is that these two areas together can help solve various control problems and to find better results. In this book, the authors test the proposed method using five benchmark control problems. First, the water tank, temperature, mobile robot, and inverted pendulum controllers are considered. For these 4 problems, experimentation was carried out using a Type-1 fuzzy system and an Interval Type-2 system. The last control problem was the D.C. motor, for which the experiments were performed with Type-1, Interval Type-2, and Generalized Type-2 fuzzy systems. When we use fuzzy systems combined with the differential evolution algorithm, we can notice that the results obtained in each of the controllers are better and with increasing uncertainty, the results are even better. For this reason, the authors consider in this book the proposed method using fuzzy systems and the differential evolution algorithm to improve the fuzzy controllers’ behavior in complex control problems.
Differential Evolution: From Theory to Practice (Studies in Computational Intelligence #1009)
by Diego Oliva B. Vinoth Kumar P. N. SuganthanThis book addresses and disseminates state-of-the-art research and development of differential evolution (DE) and its recent advances, such as the development of adaptive, self-adaptive and hybrid techniques. Differential evolution is a population-based meta-heuristic technique for global optimization capable of handling non-differentiable, non-linear and multi-modal objective functions. Many advances have been made recently in differential evolution, from theory to applications. This book comprises contributions which include theoretical developments in DE, performance comparisons of DE, hybrid DE approaches, parallel and distributed DE for multi-objective optimization, software implementations, and real-world applications. The book is useful for researchers, practitioners, and students in disciplines such as optimization, heuristics, operations research and natural computing.
Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance
by Farhan A. FaruqiDifferential Game Theory with Applications to Missiles and Autonomous Systems explains the use of differential game theory in autonomous guidance and control systems. The book begins with an introduction to the basic principles before considering optimum control and game theory. Two-party and multi-party game theory and guidance are then covered and, finally, the theory is demonstrated through simulation examples and models and the simulation results are discussed. Recent developments in the area of guidance and autonomous systems are also presented. Key features: Presents new developments and how they relate to established control systems knowledge. Demonstrates the theory through simulation examples and models. Covers two-party and multi-party game theory and guidance. Accompanied by a website hosting MATLAB® code. The book is essential reading for researchers and practitioners in the aerospace and defence industries as well as graduate students in aerospace engineering.
Differential Linear Matrix Inequalities: In Sampled-Data Systems Filtering and Control
by José C. GeromelThis book is entirely devoted to sampled-data control systems analysis and design from a new point of view, which has at its core a mathematical tool named Differential Linear Matrix Inequality - DLMI, a natural generalization of Linear Matrix Inequality - LMI, that had an important and deep impact on systems and control theory almost thirty years ago. It lasts until now. It is shown that the DLMI is well adapted to deal with the important class of sampled-data control systems in both theoretical and numerical contexts. All design conditions are expressed by convex programming problems, including when robustness against parameter uncertainty is assessed and imposed through state feedback control.Special attention is given to filter, dynamic output feedback and model predictive control design, as well as nonlinear systems of Lur’e class and Markov jump linear systems. The subject is treated with mathematical rigor, at the same time, trying to keep the reading agreeable and fruitful for colleagues and students. To this respect, the book contains together with the theoretical developments, many solved illustrative examples and the formulation of some open problems that could be faced and hopefully solved by interested readers.
Differential Privacy for Dynamic Data (SpringerBriefs in Electrical and Computer Engineering)
by Jerome Le NyThis Springer brief provides the necessary foundations to understand differential privacy and describes practical algorithms enforcing this concept for the publication of real-time statistics based on sensitive data. Several scenarios of interest are considered, depending on the kind of estimator to be implemented and the potential availability of prior public information about the data, which can be used greatly to improve the estimators' performance. The brief encourages the proper use of large datasets based on private data obtained from individuals in the world of the Internet of Things and participatory sensing. For the benefit of the reader, several examples are discussed to illustrate the concepts and evaluate the performance of the algorithms described. These examples relate to traffic estimation, sensing in smart buildings, and syndromic surveillance to detect epidemic outbreaks.
Differential Scanning Calorimetry: Applications in Fat and Oil Technology
by Emma ChiavaroDifferential Scanning Calorimetry: Applications in Fat and Oil Technology provides a complete summary of the scientific literature about differential scanning calorimetry (DSC), a well-known thermo-analytical technique that currently has a large set of applications covering several aspects of lipid technology. The book is divided into three major s
Differentially Flat Systems (Automation and Control Engineering #Vol. 17)
by Hebertt Sira-Ramírez Sunil K. AgrawalIllustrating the power, simplicity, and generality of the concept of flatness, this reference explains how to identify, utilize, and apply flatness in system planning and design. The book includes a large assortment of exercises and models that range from elementary to complex classes of systems. Leading students and professionals through a vast array of designs, simulations, and analytical studies on the traditional uses of flatness, Differentially Flat Systems contains an extensive amount of examples that showcase the value of flatness in system design, demonstrate how flatness can be assessed in the context of perturbed systems and apply static and dynamic feedback controller design techniques.
Differentiated Instruction for the Middle School Science Teacher
by Joan D'Amico Kate GallawayAn indispensable guide for middle school science teachers who have inclusive classrooms The third volume in the Differentiated Instruction series, Differentiated Instruction for the Middle School Science Teacher offers teachers proven techniques for designing and delivering effective science instruction, measuring success, getting students to work together, and collaborating with other professionals. The ready-to-use activities are tied to core curriculum standards for middle school students and each lesson incorporates adaptations for students with different learning needs. Includes strategies for teaching a standards-based science curriculum Contains a wealth of activities that can be adapted for learners of all abilities Offers information for delivering effective instruction, measuring success, and student collaboration The authors, both experienced teachers, offer a range of techniques, such as station/group activities, enrichment activities, and modifications for students with specific disabilities.
Differentiated Layout Styles for MOSFETs: Electrical Behavior in Harsh Environments
by Salvador Pinillos Gimenez Egon Henrique GalembeckThis book describes in detail the semiconductor physics and the effects of the high temperatures and ionizing radiations in the electrical behavior of the Metal-OxideSemiconductor Field Effect Transistors (MOSFETs), implemented with the first and second generations of the differentiated layout styles. The authors demonstrate a variety of innovative layout styles for MOSFETs, enabling readers to design analog and RF MOSFETs that operate in a high-temperature wide range and an ionizing radiation environment with high electrical performance and reduced die area.
Differentiated Resourceful Utilization of Rural Organic Wastes
by Mingxiao Li Xuan Jia Beidou Xi Jiaqi Hou Dongming Liu Yan HaoThis book systematically introduces the key technologies for differentiated resourceful utilization of rural organic wastes based on high-efficiency anaerobic fermentation and bio-augmented composting, and discusses differentiating sources of organic wastes, integrating recycling technologies, developing key equipment, and researching management mechanisms. In addition, it describes the development of viable techniques and low-pollution, low-cost, and low-maintenance equipment. It also includes the technical specifications for the differentiated resourceful utilization of rural organic wastes and presents the energy-fertilizer integrated resourceful utilization method for rural organic wastes. Providing technological insights into improving the resourceful utilization level of rural organic wastes, this book is a valuable reference resource for administrative staff, researchers in the field of environmental protection, and technicians in enterprises involved in the treatment and disposal of solid wastes.
Differentiated Science Inquiry
by Douglas J. LlewellynIgnite science learning with differentiated instruction One type of science instruction does not fit all. Best-selling author Douglas Llewellyn gives teachers standards-based strategies for differentiating science education to more effectively meet the needs of all students. This book takes the concept of inquiry-based science instruction to a deeper level, includes a compelling case study, and demonstrates: Methods for determining when and how to provide students with more choices, thereby increasing their ownership and motivation Ways to implement differentiated science inquiry in the main areas of science instruction Strategies for successfully managing the classroom
Differentiating Instruction With Menus: Science (Grades 6-8)
by Laurie E. WestphalThe best-selling Differentiating Instruction With Menus series has helped teachers nationwide differentiate instruction for their high-ability learners with easy-to-use menus and exciting tools to challenge and reach gifted and advanced students in the classroom. Each book includes an updated, student-friendly rubric that can assess different types of products, free choice proposal forms to encourage independent study, and new and favorite challenging menus to meet the needs of these diverse higher level learners. Readers will also be able to save time by using updated guidelines that reflect changes in technology for each of the products included in the menus and find direct alignment with standards approved in recent years. Topics addressed in Differentiating Instruction With Menus: Science (Grades 6-8, 2nd ed.) include process skills, physical sciences, life sciences, and Earth and space sciences.Grades 6-8
Differentiating Instruction With Menus: Biology (Grades 9-12)
by Laurie E. WestphalDifferentiating Instruction With Menus: Biology offers teachers everything needed to create a student-centered learning environment based on choice. This book presents six different types of menus that students can use to select exciting advanced-level products that they will develop so teachers can assess what has been learned, instead of using a traditional worksheet format. Topics addressed include biology basics, biodiversity and environments, genetics, human body systems, and the different phyla typically included in the biology curriculum. Differentiating Instruction With Menus: Biology contains attractive reproducible menus, each based on the levels of Bloom's revised taxonomy as well as incorporating different learning styles. These menus can be used to guide students in making decisions as to which products they will develop after studying a major concept or unit.Grades 9-12
Differentiating Instruction With Menus: Science (Grades 3-5)
by Laurie E. WestphalThe best-selling Differentiating Instruction With Menus series has helped teachers nationwide differentiate instruction for their high-ability learners with easy-to-use menus and exciting tools to challenge and reach gifted and advanced students in the classroom. Each book includes an updated, student-friendly rubric that can assess different types of products, free choice proposal forms to encourage independent study, and new and favorite challenging menus to meet the needs of these diverse higher level learners. Readers will also be able to save time by using updated guidelines that reflect changes in technology for each of the products included in the menus and find direct alignment with standards approved in recent years. Topics addressed in Differentiating Instruction With Menus: Science (Grades 3-5, 2nd ed.) include physical science, biological science, Earth science, and scientists and the tools they use.Grades 3-5
Differentiating Instruction With Menus: Science (Grades K-2)
by Laurie E. WestphalThe Differentiating Instruction With Menus series offers teachers exciting tools to challenge and reach both gifted and advanced students in the classroom. Whether these students need enrichment, choice in independent practice, or even additional academic options resulting from curriculum compacting, these books provide teachers a complete ready-to-use resource. Each book includes a rubric that can assess different types of products, free choice proposal forms to encourage independent study, specific guidelines for each of the products included in the menus to save the teacher time, and challenging menus to meet the needs of these diverse higher level learners.Differentiating Instruction With Menus: Science (Grades K-2) contains attractive reproducible menus, based on the levels of Bloom's revised taxonomy, that students can use as a guide when making decisions about which products they will develop after they study a major concept or unit. Topics addressed include life science, Earth science, and physical science.The products included on the menu are carefully selected from various learning styles to build students' excitement and so that teachers can more accurately assess the depth of what has been learned. Using creative and challenging choices found in Three-Shape Menus, Tic-Tac-Toe Menus, Meal Menus, Give Me Five Menus, 2-5-8 Menus, and List Menus, students will look forward to sharing their newfound knowledge throughout the year!Grades K-2
Differentiating Instruction With Menus: Chemistry (Grades 9-12)
by Laurie E. WestphalDifferentiating Instruction With Menus: Chemistry offers teachers everything needed to create a student-centered learning environment based on choice. This book uses different types of menus that students can use to select exciting advanced-level products that they will develop so teachers can assess what has been learned—instead of using a traditional worksheet format. Topics addressed include chemistry basics, measurements, atoms, chemical bonding and reactions, gas laws, energy, acids and bases, and nuclear and organic chemistry. Differentiating Instruction With Menus: Chemistry contains attractive reproducible menus, each based on the levels of Bloom's revised taxonomy as well as incorporating different learning styles. These menus can be used to guide students in making decisions as to which products they will develop after studying a major concept or unit.Grades 9-12