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Author: William E. Schiesser
Publisher: Cambridge University Press
Published: 2009-03-16
Total Pages: 491
ISBN-13: 0521519861
DOWNLOAD EBOOKPresents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
Author: Alfio Borzì
Publisher: CRC Press
Published: 2020-04-13
Total Pages: 339
ISBN-13: 1351190377
DOWNLOAD EBOOKModelling 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
Author: Glenn Fulford
Publisher: Cambridge University Press
Published: 1997-06-12
Total Pages: 420
ISBN-13: 9780521446181
DOWNLOAD EBOOKAny student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.
Author: Paul W. Davis
Publisher:
Published: 2009
Total Pages: 685
ISBN-13: 9780558371562
DOWNLOAD EBOOKAuthor: E. Allen
Publisher: Springer Science & Business Media
Published: 2007-03-08
Total Pages: 239
ISBN-13: 1402059531
DOWNLOAD EBOOKThis book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.
Author: Robert L. Borrelli
Publisher: Wiley
Published: 2004-01-02
Total Pages: 736
ISBN-13: 9780471433323
DOWNLOAD EBOOKThis effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs.
Author: Courtney Brown
Publisher: SAGE
Published: 2007-05-18
Total Pages: 121
ISBN-13: 1412941083
DOWNLOAD EBOOK'Differential Equations: A Modeling Approach' explains the mathematics and theory of differential equations. Graphical methods of analysis are emphasized over formal proofs, making the text even more accessible for newcomers to the subject matter.
Author: Nail H. Ibragimov
Publisher: World Scientific
Published: 2009
Total Pages: 365
ISBN-13: 9814291951
DOWNLOAD EBOOKA Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author?s own theoretical developments. The book ? which aims to present new mathematical curricula based on symmetry and invariance principles ? is tailored to develop analytic skills and ?working knowledge? in both classical and Lie?s methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author?s extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collge de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.
Author: Hervé Le Dret
Publisher: Birkhäuser
Published: 2016-02-11
Total Pages: 403
ISBN-13: 3319270672
DOWNLOAD EBOOKThis 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.
Author: Martin Braun
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 390
ISBN-13: 1461254272
DOWNLOAD EBOOKThe purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.
