Introduction To Differential Equations An Deterministic Modeling Methods And Analysis Volume 1

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Introduction To Differential Equations, An: Deterministic Modeling, Methods And Analysis (Volume 1)

Author : Anilchandra G Ladde
Publisher : World Scientific Publishing Company
ISBN 13 : 9813100605
Total Pages : 542 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Introduction To Differential Equations, An: Deterministic Modeling, Methods And Analysis (Volume 1) by : Anilchandra G Ladde

Download or read book Introduction To Differential Equations, An: Deterministic Modeling, Methods And Analysis (Volume 1) written by Anilchandra G Ladde and published by World Scientific Publishing Company. This book was released on 2012-05-31 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2: Stochastic Modeling, Methods, and Analysis This is a twenty-first century book designed to meet the challenges of understanding and solving interdisciplinary problems. The book creatively incorporates “cutting-edge” research ideas and techniques at the undergraduate level. The book also is a unique research resource for undergraduate/graduate students and interdisciplinary researchers. It emphasizes and exhibits the importance of conceptual understandings and its symbiotic relationship in the problem solving process. The book is proactive in preparing for the modeling of dynamic processes in various disciplines. It introduces a “break-down-the problem” type of approach in a way that creates “fun” and “excitement”. The book presents many learning tools like “step-by-step procedures (critical thinking)”, the concept of “math” being a language, applied examples from diverse fields, frequent recaps, flowcharts and exercises. Uniquely, this book introduces an innovative and unified method of solving nonlinear scalar differential equations. This is called the “Energy/Lyapunov Function Method”. This is accomplished by adequately covering the standard methods with creativity beyond the entry level differential equations course.

Introduction To Differential Equations, An: Stochastic Modeling, Methods And Analysis (Volume 2)

Author : Anilchandra G Ladde
Publisher : World Scientific Publishing Company
ISBN 13 : 9814397393
Total Pages : 634 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Introduction To Differential Equations, An: Stochastic Modeling, Methods And Analysis (Volume 2) by : Anilchandra G Ladde

Download or read book Introduction To Differential Equations, An: Stochastic Modeling, Methods And Analysis (Volume 2) written by Anilchandra G Ladde and published by World Scientific Publishing Company. This book was released on 2013-01-11 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)

Random Differential Equations in Scientific Computing

Author : Tobias Neckel
Publisher : Walter de Gruyter
ISBN 13 : 8376560263
Total Pages : 650 pages
Book Rating : 4.3/5 (765 download)

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Book Synopsis Random Differential Equations in Scientific Computing by : Tobias Neckel

Download or read book Random Differential Equations in Scientific Computing written by Tobias Neckel and published by Walter de Gruyter. This book was released on 2013-12-17 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Stochastic Versus Deterministic Systems Of Iterative Processes

Author : Gangaram S Ladde
Publisher : World Scientific
ISBN 13 : 981128749X
Total Pages : 355 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Stochastic Versus Deterministic Systems Of Iterative Processes by : Gangaram S Ladde

Download or read book Stochastic Versus Deterministic Systems Of Iterative Processes written by Gangaram S Ladde and published by World Scientific. This book was released on 2024-04-22 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.

Applied Stochastic Differential Equations

Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 1316510085
Total Pages : 327 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä

Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Mathematics for Reliability Engineering

Author : Mangey Ram
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110725592
Total Pages : 274 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Mathematics for Reliability Engineering by : Mangey Ram

Download or read book Mathematics for Reliability Engineering written by Mangey Ram and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reliability is a fundamental criterium in engineering systems. This book shows innovative concepts and applications of mathematics in solving reliability problems. The contents address in particular the interaction between engineers and mathematicians, as well as the cross-fertilization in the advancement of science and technology. It bridges the gap between theory and practice to aid in practical problem-solving in various contexts.

An Introduction to Computational Stochastic PDEs

Author : Gabriel J. Lord
Publisher : Cambridge University Press
ISBN 13 : 0521899907
Total Pages : 516 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Computational Stochastic PDEs by : Gabriel J. Lord

Download or read book An Introduction to Computational Stochastic PDEs written by Gabriel J. Lord and published by Cambridge University Press. This book was released on 2014-08-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.

An Introduction to Mathematical Epidemiology

Author : Maia Martcheva
Publisher : Springer
ISBN 13 : 1489976124
Total Pages : 462 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis An Introduction to Mathematical Epidemiology by : Maia Martcheva

Download or read book An Introduction to Mathematical Epidemiology written by Maia Martcheva and published by Springer. This book was released on 2015-10-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.

Partial Differential Equations: Modeling, Analysis and Numerical Approximation

Author : Hervé Le Dret
Publisher : Birkhäuser
ISBN 13 : 3319270672
Total Pages : 403 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Partial Differential Equations: Modeling, Analysis and Numerical Approximation by : Hervé Le Dret

Download or read book Partial Differential Equations: Modeling, Analysis and Numerical Approximation written by Hervé Le Dret and published by Birkhäuser. This book was released on 2016-02-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

Mathematics Applied to Deterministic Problems in the Natural Sciences

Author : C. C. Lin
Publisher : SIAM
ISBN 13 : 9780898712292
Total Pages : 646 pages
Book Rating : 4.7/5 (122 download)

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Book Synopsis Mathematics Applied to Deterministic Problems in the Natural Sciences by : C. C. Lin

Download or read book Mathematics Applied to Deterministic Problems in the Natural Sciences written by C. C. Lin and published by SIAM. This book was released on 1988-12-01 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.

An Introduction to Stochastic Modeling

Author : Howard M. Taylor
Publisher : Academic Press
ISBN 13 : 1483269272
Total Pages : 410 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis An Introduction to Stochastic Modeling by : Howard M. Taylor

Download or read book An Introduction to Stochastic Modeling written by Howard M. Taylor and published by Academic Press. This book was released on 2014-05-10 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1460 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 1460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Stochastic Differential Equations

Author : Michael J. Panik
Publisher : John Wiley & Sons
ISBN 13 : 1119377404
Total Pages : 362 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Stochastic Differential Equations by : Michael J. Panik

Download or read book Stochastic Differential Equations written by Michael J. Panik and published by John Wiley & Sons. This book was released on 2017-03-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.

Science By Simulation - Volume 1: A Mezze Of Mathematical Models

Author : Andrew French
Publisher : World Scientific
ISBN 13 : 1800611099
Total Pages : 276 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Science By Simulation - Volume 1: A Mezze Of Mathematical Models by : Andrew French

Download or read book Science By Simulation - Volume 1: A Mezze Of Mathematical Models written by Andrew French and published by World Scientific. This book was released on 2022-05-30 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mezze of Mathematical Methods is Volume 1 of Science by Simulation. It is a recipe book of mathematical models that can be enlivened by the transmutation of equations into computer code. In this volume, the examples chosen are an eclectic mix of systems and stories rooted in common experience, rather than those normally associated with constrained courses on Physics, Chemistry or Biology which are taught in isolation and susceptible to going out of date in a few years. Rather than a 'what' of Science, this book is aimed at the 'how', readily applied to projects by students and professionals. Written in a friendly style based upon the author's expertise in teaching and pedagogy, this mathematically rigorous book is designed for readers to follow arguments step-by-step with stand-alone chapters which can be read independently. This approach will provide a tangible and readily accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science.

Chronobioengineering

Author : Donald McEachron
Publisher : Springer Nature
ISBN 13 : 303101653X
Total Pages : 264 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Chronobioengineering by : Donald McEachron

Download or read book Chronobioengineering written by Donald McEachron and published by Springer Nature. This book was released on 2022-06-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first in a two-volume set on biological rhythms. This volume focuses on supporting the claim that biological rhythms are universal and essential characteristics of living organisms, critical for proper functioning of any living system. The author begins by examining the potential reasons for the evolution of biological rhythms: (1) the need for complex, goal-oriented devices to control the timing of their activities; (2) the inherent tendency of feedback control systems to oscillate; and (3) the existence of stable and powerful geophysical cycles to which all organisms must adapt. To investigate the second reason, the author enlists the help of biomedical engineering students to develop mathematical models of various biological systems. One such model involves a typical endocrine feedback system. By adjusting various model parameters, it was found that creating a oscillation in any component of the model generated a rhythmic cascade that made the entire system oscillate. This same approach was used to show how daily light/dark cycles could cascade rhythmic patterns throughout ecosystems and within organisms. Following up on these results, the author discusses how the twin requirements of internal synchronization (precise temporal order necessary for the proper functioning of organisms as complex, goal-oriented devices) and external synchronization (aligning organisms' behavior and physiology with geophysical cycles) supported the evolution of biological clocks. The author then investigates the clock systems that evolved using both conceptual and mathematical models, with the assistance of Dr. Bahrad Sokhansanj, who contributes a chapter on mathematical formulations and models of rhythmic phenomena. With the ubiquity of biological rhythms established, the author suggests a new classification system: the F4LM approach (Function; Frequency; waveForm; Flexibility; Level of biological system expressing rhythms; and Mode of rhythm generation) to investigate biological rhythms. This approach is first used on the more familiar cardiac cycle and then on neural rhythms as exemplified and measured by the electroencephalogram. During the process of investigating neural cycles, the author finds yet another reason for the evolution of biological rhythms: physical constraints, such as those imposed upon long distance neural signaling. In addition, a common theme emerges of a select number of autorhythmic biological oscillators imposing coherent rhythmicity on a larger network or system. During the course of the volume, the author uses a variety of observations, models, experimental results, and arguments to support the original claim of the importance and universality of biological rhythms. In Volume 2, the author will move from the establishment of the critical nature of biological rhythms to how these phenomena may be used to improve human health, well-being, and productivity. In a sense, Volume 1 focuses on the chronobio aspect of chronobioengineering while Volume 2 investigates methods of translating this knowledge into applications, the engineering aspect of chronobioengineering. Table of Contents: Time and Time Again / Walking on Air: An Empirical Proof-of-Concept / Clock Tech, Part 1 / Clock Tech II From External to Internal Timers / Clock Tech III Rise of the CircaRhythms / The Circle Game: Mathematics, Models, and Rhythms / The Power of Circular Reasoning

Solving Differential Equations in R

Author : Karline Soetaert
Publisher : Springer Science & Business Media
ISBN 13 : 3642280706
Total Pages : 258 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Solving Differential Equations in R by : Karline Soetaert

Download or read book Solving Differential Equations in R written by Karline Soetaert and published by Springer Science & Business Media. This book was released on 2012-06-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Mathematical Modeling

Author : Christof Eck
Publisher : Springer
ISBN 13 : 3319551612
Total Pages : 519 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Mathematical Modeling by : Christof Eck

Download or read book Mathematical Modeling written by Christof Eck and published by Springer. This book was released on 2017-04-11 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.