Non Linear Mathematics Vol I

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Invitation to Nonlinear Algebra

Mateusz Michałek,Bernd Sturmfels
Invitation to Nonlinear Algebra Book PDF

Author : Mateusz Michałek,Bernd Sturmfels
Publisher : American Mathematical Society
Page : 226 pages
File Size : 45,7 Mb
Release : 2021-03-05
Category : Mathematics
ISBN : 9781470453671

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Invitation to Nonlinear Algebra by Mateusz Michałek,Bernd Sturmfels Pdf

Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.

It's a Nonlinear World

Richard H. Enns
It s a Nonlinear World Book PDF

Author : Richard H. Enns
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 42,8 Mb
Release : 2010-10-14
Category : Mathematics
ISBN : 9780387753409

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It's a Nonlinear World by Richard H. Enns Pdf

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations. No prior knowledge of Maple is assumed. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world", or for self-study by practicing scientists and engineers.

Iterative Methods for Linear and Nonlinear Equations

C. T. Kelley
Iterative Methods for Linear and Nonlinear Equations Book PDF

Author : C. T. Kelley
Publisher : SIAM
Page : 179 pages
File Size : 46,7 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 1611970946

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

Nonlinear Systems and Their Remarkable Mathematical Structures

Taylor & Francis Group
Nonlinear Systems and Their Remarkable Mathematical Structures Book PDF

Author : Taylor & Francis Group
Publisher : CRC Press
Page : 582 pages
File Size : 55,9 Mb
Release : 2020-12-18
Category : Electronic
ISBN : 0367732432

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Nonlinear Systems and Their Remarkable Mathematical Structures by Taylor & Francis Group Pdf

Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems

Nonlinear Potential Theory on Metric Spaces

Anders Björn,Jana Björn
Nonlinear Potential Theory on Metric Spaces Book PDF

Author : Anders Björn,Jana Björn
Publisher : European Mathematical Society
Page : 422 pages
File Size : 41,7 Mb
Release : 2011
Category : Harmonic functions
ISBN : 303719099X

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Nonlinear Potential Theory on Metric Spaces by Anders Björn,Jana Björn Pdf

The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.

Analysis and Control of Nonlinear Infinite Dimensional Systems

Barbu
Analysis and Control of Nonlinear Infinite Dimensional Systems Book PDF

Author : Barbu
Publisher : Academic Press
Page : 490 pages
File Size : 43,5 Mb
Release : 1992-11-26
Category : Computers
ISBN : 9780080958767

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Analysis and Control of Nonlinear Infinite Dimensional Systems by Barbu Pdf

Analysis and Control of Nonlinear Infinite Dimensional Systems

Methods in Nonlinear Analysis

Kung-Ching Chang
Methods in Nonlinear Analysis Book PDF

Author : Kung-Ching Chang
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 52,6 Mb
Release : 2005-11-21
Category : Mathematics
ISBN : 9783540292326

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Methods in Nonlinear Analysis by Kung-Ching Chang Pdf

This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.

Non-Linear Differential Equations

G. Sansone,R. Conti
Non Linear Differential Equations Book PDF

Author : G. Sansone,R. Conti
Publisher : Elsevier
Page : 550 pages
File Size : 44,6 Mb
Release : 2016-06-06
Category : Mathematics
ISBN : 9781483135960

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Non-Linear Differential Equations by G. Sansone,R. Conti Pdf

International Series of Monographs in Pure and Applied Mathematics, Volume 67: Non-Linear Differential Equations, Revised Edition focuses on the analysis of the phase portrait of two-dimensional autonomous systems; qualitative methods used in finding periodic solutions in periodic systems; and study of asymptotic properties. The book first discusses general theorems about solutions of differential systems. Periodic solutions, autonomous systems, and integral curves are explained. The text explains the singularities of Briot-Bouquet theory. The selection takes a look at plane autonomous systems. Topics include limiting sets, plane cycles, isolated singular points, index, and the torus as phase space. The text also examines autonomous plane systems with perturbations and autonomous and non-autonomous systems with one degree of freedom. The book also tackles linear systems. Reducible systems, periodic solutions, and linear periodic systems are considered. The book is a vital source of information for readers interested in applied mathematics.

Non Linear Mathematics Vol. I

Thomas L., Saaty ,Joseph, Bram
Non Linear Mathematics Vol I Book PDF

Author : Thomas L., Saaty ,Joseph, Bram
Publisher : RWS Publications
Page : 396 pages
File Size : 40,7 Mb
Release : 2014-12-22
Category : Business & Economics
ISBN : 9781888603385

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Non Linear Mathematics Vol. I by Thomas L., Saaty ,Joseph, Bram Pdf

"We are surrounded and deeply involved, in the natural world, with non- linear events which are not necessarily mathematical," the authors write. "For example . . . the nonlinear problem of pedalling a bicycle up and down a hillside. On a grand scale . . . the struggle for existence between two species, one of which preys exclusively on the other." This book is' for mathematicians and researchers who believe that "nonlinear mathematics is' the mathematics of today"; it is also for economists, engineers, operations analysts, "the reader who has been thus bemused into an artificially linear conception of the universe." Nonlinear Mathematics is the first attempt to consider the widest range of nonlinear topics found in the -scattered literature. Accessible to non- mathematics professionals as well as college seniors and graduates, it offers a discussion both particular and broad enough to stimulate research towards a unifying theory of nonlinear mathematics. Ideas are presented "according to existence and uniqueness theorems, characterization (e.g., stability and asymptotic behavior), construction of solutions, convergence, approximation and errors."

Introduction to Non-linear Mechanics

Nikolai Mitrofanovich Krylov,Nikolai Nikolaevich Bogoliubov
Introduction to Non linear Mechanics Book PDF

Author : Nikolai Mitrofanovich Krylov,Nikolai Nikolaevich Bogoliubov
Publisher : Princeton University Press
Page : 126 pages
File Size : 52,9 Mb
Release : 1950-01-20
Category : Mathematics
ISBN : 0691079854

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Introduction to Non-linear Mechanics by Nikolai Mitrofanovich Krylov,Nikolai Nikolaevich Bogoliubov Pdf

The description for this book, Introduction to Non-Linear Mechanics. (AM-11), Volume 11, will be forthcoming.

Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

V.L. Kocic,G. Ladas
Global Behavior of Nonlinear Difference Equations of Higher Order with Applications Book PDF

Author : V.L. Kocic,G. Ladas
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 52,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401717038

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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by V.L. Kocic,G. Ladas Pdf

Nonlinear difference equations of order greater than one are of paramount impor tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention.

Nonlinear Dispersive Equations

Terence Tao
Nonlinear Dispersive Equations Book PDF

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 49,7 Mb
Release : 2006
Category : Differential equations, Partial
ISBN : 9780821841433

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Nonlinear Dispersive Equations by Terence Tao Pdf

"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Nonlinear Methods in Numerical Analysis

A. Cuyt,L. Wuytack
Nonlinear Methods in Numerical Analysis Book PDF

Author : A. Cuyt,L. Wuytack
Publisher : Elsevier
Page : 277 pages
File Size : 54,8 Mb
Release : 1987-03-01
Category : Mathematics
ISBN : 0080872476

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Nonlinear Methods in Numerical Analysis by A. Cuyt,L. Wuytack Pdf

While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.

Nonlinear Systems and Their Remarkable Mathematical Structures

Norbert Euler,Maria Clara Nucci
Nonlinear Systems and Their Remarkable Mathematical Structures Book PDF

Author : Norbert Euler,Maria Clara Nucci
Publisher : CRC Press
Page : 541 pages
File Size : 45,5 Mb
Release : 2019-12-06
Category : Mathematics
ISBN : 9780429554308

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Nonlinear Systems and Their Remarkable Mathematical Structures by Norbert Euler,Maria Clara Nucci Pdf

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics

Nonlinear Systems, Vol. 1

Victoriano Carmona,Jesús Cuevas-Maraver,Fernando Fernández-Sánchez,Elisabeth García- Medina
Nonlinear Systems Vol 1 Book PDF

Author : Victoriano Carmona,Jesús Cuevas-Maraver,Fernando Fernández-Sánchez,Elisabeth García- Medina
Publisher : Springer
Page : 424 pages
File Size : 52,6 Mb
Release : 2018-09-15
Category : Science
ISBN : 9783319667669

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Nonlinear Systems, Vol. 1 by Victoriano Carmona,Jesús Cuevas-Maraver,Fernando Fernández-Sánchez,Elisabeth García- Medina Pdf

This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.