Kategoria BISAC: Mathematics >> Differential Equations - Ordinary

These lectures develop simple models of complex social processes using nonlinear dynamics and mathematical biology. Dynamical analogies between seemingly disparate social and biological phenomena--revolutions and epidemics, arms races, and ecosystem dynamics--are revealed and exploited. Nonlinear Dynamics, Mathematical Biology, and Social Science invites social scientists to relax--in some cases abandon--the predominant assumption of perfectly informed utility maximization and explore social dynamics from such perspectives as epidemiology and predator-prey theory. The volume includes a...

The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.
The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.
The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics....

The book presents a systematic and compact treatment of the qualitative theory of half-linear
differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations...

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience.

These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering...

Covers all the mathematics required on the first year of a degree or diploma course in engineering.

This work is based on the International Symposium on Comparison Methods and Stability Theory held in Waterloo, Ontario, Canada. It presents advances in comparison methods and stability theory in a wide range of nonlinear problems, covering a variety of topics such as ordinary, functional, impulsive, integro-, partial, and uncertain differential equations.

Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.
This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores...

This popular self-study/supplementary textbook covers in detail all mathematical requirements common to first year engineering students of every discipline. Thoroughly revised for the second edition, the book provides more worked examples and exercises, and more material on numerical computation and gives extensive problem sets at the end of each chapter. It is organized into short sections specific to certain topics, which allows students to identify subjects of interest that they can study separately, with little background reading. The author provides numerous worked examples throughout...

Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spectrum is arbitrary. The Weyl matrix is introduced and studied as a spectral characteristic. The second part of the book is devoted to solving incomplete inverse problems when a priori information about the operator or its spectrum is available and...

An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.

Deepen students' understanding of biological phenomena

Suitable 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 modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material.

New to the Second...

The particular strength of this volume is that it unifies the abstract and topological integration theories, and is based on the vector lattice theory which makes many structures more easily understood. It uses the Daniell approach of integrating functions, rather than only measures. This textbook is aimed at undergraduates being introduced to integration theory. Extensive examples and exercises are included.

Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas.

Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary,...

There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry.

This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling.

The technique...