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Differential Algebras in Topology
by David AnikThis research monograph in the field of algebraic topology contains many thought-provoking discussions of open problems and promising research directions.
Differential Calculus and Its Applications (Dover Books on Mathematics)
by Prof. Michael J. FieldThis text offers a synthesis of theory and application related to modern techniques of differentiation. Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. Suitable for advanced undergraduate courses in pure and applied mathematics, it forms the basis for graduate-level courses in advanced calculus and differential manifolds. Starting with a brief resume of prerequisites, including elementary linear algebra and point set topology, the self-contained approach examines liner algebra and normed vector spaces, differentiation and calculus on vector spaces, and the inverse- and implicit-function theorems. A final chapter is dedicated to a consolidation of the theory as stated in previous chapters, in addition to an introduction to differential manifolds and differential equations.
Differential Calculus in Several Variables: A Learning-by-Doing Approach (Textbooks in Mathematics)
by Marius GherguThe aim of this book is to lead the reader out from the ordinary routine of computing and calculating by engaging in a more dynamic process of learning. This Learning-by-Doing Approach can be traced back to Aristotle, who wrote in his Nicomachean Ethics that “For the things we have to learn before we can do them, we learn by doing them”. The theory is illustrated through many relevant examples, followed by a large number of exercises whose requirements are rendered by action verbs: find, show, verify, check and construct. Readers are compelled to analyze and organize analytical skills. Rather than placing the exercises in bulk at the end of each chapter, sets of practice questions after each theoretical concept are included. The reader has the possibility to check their understanding, work on the new topics and gain confidence during the learning activity. As the theory unfolds, the exercises become more complex – sometimes they span over several topics. Hints have been added in order to guide the reader in the process. This book stems from the Differential Calculus course which the author taught for many years. The goal of this book is to immerse the reader in the subtleties of Differential Calculus through an active perspective. Particular attention was paid to continuity and differentiability topics, presented in a new course of action.
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 Equation Based Solutions for Emerging Real-Time Problems (Computational Intelligence in Engineering Problem Solving)
by Biswajit Sarkar Manash Chanda Papiya DebnathModeling with differential equations is an effective tool to provide methodical and quantitative solutions to real-world phenomena including investigating measurable features, consolidation and processing of data, and designing and developing complex engineering systems. This book describes differential equations correlation with qualitative and quantitative analysis, and mathematical modeling in the engineering and applied sciences. Given equations are explained from multidimensional characterizations with MATLAB® codes. Features: Addresses differential equation-based approaches to solve varied engineering problems Discusses derivation and solution of major equations of engineering and applied science Reviews qualitative and quantitative (numerical) analysis and mathematical modelling Includes mathematical models of the discussed problems Discusses MATLAB® codes Features: code and online materials related to the differential equations. This book is aimed at researchers graduate students in electrical and electronics engineering, control systems, electron devices society, applied physics, and engineering design.
Differential Equations
by Christian ConstandaDifferential Equations for Scientists and Engineers is a book designed with students in mind. It attempts to take a concise, simple, and no-frills approach to differential equations. The approach used in this text is to give students extensive experience in main solution techniques with a lighter emphasis on the physical interpretation of the results. With a more manageable page count than comparable titles, and over 400 exercises that can be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct fashion. At the end of each worked example, the author provides the Mathematica commands that can be used to check the results and where applicable, to generate graphical representations. It can be used independently by the average student, while those continuing with the subject will develop a fundamental framework with which to pursue more advanced material. This book is designed for undergraduate students with some basic knowledge of precalculus algebra and a first course in calculus.
Differential Equations
by Christian ConstandaDifferential Equations for Scientists and Engineers is a book designed with students in mind. It attempts to take a concise, simple, and no-frills approach to differential equations. The approach used in this text is to give students extensive experience in main solution techniques with a lighter emphasis on the physical interpretation of the results. With a more manageable page count than comparable titles, and over 400 exercises that can be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct fashion. At the end of each worked example, the author provides the Mathematica commands that can be used to check the results and where applicable, to generate graphical representations. It can be used independently by the average student, while those continuing with the subject will develop a fundamental framework with which to pursue more advanced material. This book is designed for undergraduate students with some basic knowledge of precalculus algebra and a first course in calculus.
Differential Equations
by Harry HochstadtModern approach to differential equations presents subject in terms of ideas and concepts rather than special cases and tricks which traditional courses emphasized. No prerequisites needed other than a good calculus course. Certain concepts from linear algebra used throughout. Problem section at end of each chapter.
Differential Equations
by O.A. OleinikPart II of the Selected Works of Ivan Georgievich Petrowsky, contains his major papers on second order Partial differential equations, systems of ordinary. Differential equations, the theory, of Probability, the theory of functions, and the calculus of variations. Many of the articles contained in this book have Profoundly, influenced the development of modern mathematics. Of exceptional value is the article on the equation of diffusion with growing quantity of the substance. This work has found extensive application in biology, genetics, economics and other branches of natural science. Also of great importance is Petrowsky's work on a Problem which still remains unsolved - that of the number of limit cycles for ordinary differential equations with rational right-hand sides.
Differential Equations
by Viorel BarbuThis textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Differential Equations (Dover Books on Mathematics)
by F. G. Tricomi Elizabeth A. McHargBased on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and differential equations in the complex field. The author discusses only ordinary differential equations, excluding coverage of the methods of integration and stressing the importance of reading the properties of the integrals directly from the equations. An extensive bibliography and helpful indexes conclude the text.
Differential Equations And Control Theory
by Nicolae H. Pavel Sergiu AizicoviciProvides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equations over non-Archimedean fields in relation to Markov processes.
Differential Equations I Essentials
by The Editors of REAREA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
Differential Equations Problem Solver
by David ArterbumREA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies. The Differential Equations Problem Solver is the perfect resource for any class, any exam, and any problem.
Differential Equations With Applications
by Paul D. Ritger Nicholas J. RoseCoherent introductory text focuses on initial- and boundary-value problems, general properties of linear equations, and differences between linear and nonlinear systems. Answers to most problems.
Differential Equations With Boundary-value Problems
by Dennis ZillMaster differential equations and succeed in your course DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS with accompanying CD-ROM and technology! Straightfoward and readable, this mathematics text provides you with tools such as examples, explanations, definitions, and applications designed to help you succeed. The accompanying DE Tools CD-ROM makes helps you master difficult concepts through twenty-one demonstration tools such as Project Tools and Text Tools. Studying is made easy with iLrn Tutorial, a text-specific, interactive tutorial software program that gives the practice you need to succeed.
Differential Equations and Control Theory
by Zongqi Deng; Zhaojun Liang; Gang Lu; Shigui RuanThis work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic 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 and Dynamical Systems: 2 USUZCAMP, Urgench, Uzbekistan, August 8–12, 2017 (Springer Proceedings in Mathematics & Statistics #268)
by Leonid Bunimovich Abdulla Azamov Akhtam Dzhalilov Hong-Kun ZhangThis book features papers presented during a special session on dynamical systems, mathematical physics, and partial differential equations. Research articles are devoted to broad complex systems and models such as qualitative theory of dynamical systems, theory of games, circle diffeomorphisms, piecewise smooth circle maps, nonlinear parabolic systems, quadtratic dynamical systems, billiards, and intermittent maps. Focusing on a variety of topics from dynamical properties to stochastic properties of dynamical systems, this volume includes discussion on discrete-numerical tracking, conjugation between two critical circle maps, invariance principles, and the central limit theorem. Applications to game theory and networks are also included. Graduate students and researchers interested in complex systems, differential equations, dynamical systems, functional analysis, and mathematical physics will find this book useful for their studies. The special session was part of the second USA-Uzbekistan Conference on Analysis and Mathematical Physics held on August 8-12, 2017 at Urgench State University (Uzbekistan). The conference encouraged communication and future collaboration among U.S. mathematicians and their counterparts in Uzbekistan and other countries. Main themes included algebra and functional analysis, dynamical systems, mathematical physics and partial differential equations, probability theory and mathematical statistics, and pluripotential theory. A number of significant, recently established results were disseminated at the conference’s scheduled plenary talks, while invited talks presented a broad spectrum of findings in several sessions. Based on a different session from the conference, Algebra, Complex Analysis, and Pluripotential Theory is also published in the Springer Proceedings in Mathematics & Statistics Series.
Differential Equations and Mathematical Biology (Chapman & Hall/CRC Mathematical Biology Series)
by Michael Plank B.D. Sleeman D.S. JonesDeepen students' understanding of biological phenomenaSuitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeli
Differential Equations and Numerical Analysis
by Valarmathi Sigamani John J. H. Miller Ramanujam Narasimhan Paramasivam Mathiazhagan Franklin VictorThis book offers an ideal introduction to singular perturbation problems, and a valuable guide for researchers in the field of differential equations. It also includes chapters on new contributions to both fields: differential equations and singular perturbation problems. Written by experts who are active researchers in the related fields, the book serves as a comprehensive source of information on the underlying ideas in the construction of numerical methods to address different classes of problems with solutions of different behaviors, which will ultimately help researchers to design and assess numerical methods for solving new problems. All the chapters presented in the volume are complemented by illustrations in the form of tables and graphs.
Differential Equations and Their Applications: An Introduction to Applied Mathematics (Fourth Edition)
by F. John Jerrold E. Marsden Martin Golubitsky W. Jager Lawrence Sirovich Martin BraunUsed in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book distinguishes itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Fortran are presented throughout the text to show readers how to apply differential equations towards quantitative problems.
Differential Equations for Engineers and Scientists (Dover Books on Mathematics)
by C. G. Lambe C. J. TranterThis concise applications-oriented text is intended for undergraduate students in engineering, mathematics, and other areas of science. The first chapters focus on solutions of first order equations, linear equations with constant coefficients, and simultaneous equations and reducible equations. Subsequent chapters explore the method of solution by infinite series and the more important special functions of mathematical physics. The treatment examines the solution of partial differential equations as well as numerical methods of solution, including that of relaxation. Readers also receive an introduction to the theory of nonlinear differential equations. Nearly 900 worked examples and exercises include complete solutions, making this volume ideal for self-study as well as an excellent classroom text.
Differential Equations in Banach Spaces
by Giovanni Dore; Angelo Favini; Enrico Obrecht; Alberto VenniThis reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.