An Introduction To Ordinary Differential Equations Cambridge Texts In Applied Mathematics

An Introduction to Ordinary Differential Equations

2004-01-08 Mathematics

Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 9780521533911

Category: Mathematics

Page: 399

This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

Stability, Instability and Chaos

1994-11-25 Mathematics

An Introduction to the Theory of Nonlinear Differential Equations

Author: Paul Glendinning

Publisher: Cambridge University Press

ISBN: 9780521425667

Category: Mathematics

Page: 388

An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.

Nonlinear PDEs: A Dynamical Systems Approach

2017-10-26 Differential equations, Nonlinear

Author: Guido Schneider,Hannes Uecker

Publisher: American Mathematical Soc.

ISBN: 1470436132

Category: Differential equations, Nonlinear

Page: 575

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

Applied Nonautonomous and Random Dynamical Systems

2017-01-31 Mathematics

Applied Dynamical Systems

Author: Tomás Caraballo,Xiaoying Han

Publisher: Springer

ISBN: 3319492470

Category: Mathematics

Page: 108

This book offers an introduction to the theory of non-autonomous and stochastic dynamical systems, with a focus on the importance of the theory in the Applied Sciences. It starts by discussing the basic concepts from the theory of autonomous dynamical systems, which are easier to understand and can be used as the motivation for the non-autonomous and stochastic situations. The book subsequently establishes a framework for non-autonomous dynamical systems, and in particular describes the various approaches currently available for analysing the long-term behaviour of non-autonomous problems. Here, the major focus is on the novel theory of pullback attractors, which is still under development. In turn, the third part represents the main body of the book, introducing the theory of random dynamical systems and random attractors and revealing how it may be a suitable candidate for handling realistic models with stochasticity. A discussion of future research directions serves to round out the coverage.

Computational Engineering

2018-05-05 Computers

Theorie und Praxis der Transportmodelle

Author: Jürgen Geiser

Publisher: Springer-Verlag

ISBN: 3658187085

Category: Computers

Page: 291

Das Buch bietet ein ausgewogenes Verhältnis zwischen Theorie und praktischen Anwendungen des berechnenden Ingenieurswesens. Es illustriert sowohl die mathematischen Modelle im Computational Engineering, wie auch die zugehörigen Simulationsmethoden für die verschiedenen Ingenieursanwendungen und benennt geeignete Softwarepakete. Die umfangreichen Beispiele aus der berechnenden Ingenieurswissenschaft, welche Wärme- und Massentransport, Plasmasimulation und hydrodynamische Transportprobleme einschließen, geben dem Leser einen Überblick zu den aktuellen Themen und deren praktische Umsetzung in spätere Simulationsprogramme. Übungsaufgaben und prüfungsrelevante Fragen schließen die einzelnen Kapitel ab.

An Introduction to Scientific Computing

2006-11-27 Mathematics

Twelve Computational Projects Solved with MATLAB

Author: Ionut Danaila,Pascal Joly,Sidi Mahmoud Kaber,Marie Postel

Publisher: Springer Science & Business Media

ISBN: 038730889X

Category: Mathematics

Page: 294

This book demonstrates scientific computing by presenting twelve computational projects in several disciplines including Fluid Mechanics, Thermal Science, Computer Aided Design, Signal Processing and more. Each follows typical steps of scientific computing, from physical and mathematical description, to numerical formulation and programming and critical discussion of results. The text teaches practical methods not usually available in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. The final section of each project contains the solutions to proposed exercises and guides the reader in using the MATLAB scripts available online.

Thinking about Ordinary Differential Equations

1997-01-13 Mathematics

Author: Robert E. O'Malley

Publisher: Cambridge University Press

ISBN: 9780521557429

Category: Mathematics

Page: 247

While mastery of these equations is essential, adhering to any one method of solving them is not. This book stresses alternative examples and analyses by means of which students can understand a number of approaches to finding solutions and understanding their behavior. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application.

Introduction to Symmetry Analysis

2002-09-23 Mathematics

Author: Brian J. Cantwell

Publisher: Cambridge University Press

ISBN: 9781139431712

Category: Mathematics

Page: N.A

Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

Practical Applied Mathematics

2005-03-24 Mathematics

Modelling, Analysis, Approximation

Author: Sam Howison

Publisher: Cambridge University Press

ISBN: 9780521842747

Category: Mathematics

Page: 326

This book illustrates how the reader's knowledge of applied mathematics can be used to describe the world around them.

Infinite-Dimensional Dynamical Systems

2001-04-23 Mathematics

An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 9780521632041

Category: Mathematics

Page: 461

This book develops the theory of global attractors for a class of parabolic PDEs which includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves 'finite-dimensional'. The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.

Nonlinear Systems

1992-06-26 Mathematics

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN: 9780521406680

Category: Mathematics

Page: 317

A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.

Partielle Differentialgleichungen

2013-08-13 Mathematics

Eine Einführung

Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.

Einführung in die Variationsrechnung

1983 Algebraiese varieteite

Author: Ursula Brechtken-Manderscheid

Publisher: N.A

ISBN: N.A

Category: Algebraiese varieteite

Page: 207

Introduction to Hydrodynamic Stability

2002-09-09 Science

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN: 1316582876

Category: Science

Page: N.A

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

Bulletin of the Belgian Mathematical Society, Simon Stevin

2002 Mathematics

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

Vorlesungen über partielle Differentialgleichungen

2006-07-16 Mathematics

Author: Vladimir I. Arnold

Publisher: Springer-Verlag

ISBN: 3540350314

Category: Mathematics

Page: 174

Nach seinem bekannten und viel verwendeten Buch über gewöhnliche Differentialgleichungen widmet sich der berühmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten Art führt er über einen geometrischen, anschaulichen Weg in das Thema ein, und ermöglicht den Lesern so ein vertieftes Verständnis der Natur der partiellen Differentialgleichungen. Für Studierende der Mathematik und Physik ist dieses Buch ein Muss. Wie alle Bücher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschränkt sich hauptsächlich auf das Cauchy-Problem und das Neumann-Problems für die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die Wärmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische Intuition wird besonders hervorgehoben. Eine große Anzahl von Problemen ist übers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende. Was dieses Buch so einzigartig macht, ist das besondere Talent Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er lüftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enthüllt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.

Differential Equations

2003-05-08 Mathematics

Linear, Nonlinear, Ordinary, Partial

Author: A. C. King,J. Billingham,S. R. Otto

Publisher: Cambridge University Press

ISBN: 9780521016872

Category: Mathematics

Page: 541

For students taking second courses; the subject is central and required at second year and above.

Lie Groups, Physics, and Geometry

2008-01-17 Science

An Introduction for Physicists, Engineers and Chemists

Author: Robert Gilmore

Publisher: Cambridge University Press

ISBN: 113946907X

Category: Science

Page: N.A

Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.