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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations

Global Affine Differential Geometry of Hypersurfaces (Hardcover, 2nd revised and extended edition): An-Min Li, Udo Simon,... Global Affine Differential Geometry of Hypersurfaces (Hardcover, 2nd revised and extended edition)
An-Min Li, Udo Simon, Guosong Zhao, Zejun Hu
R4,435 Discovery Miles 44 350 Ships in 12 - 17 working days

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry - as differential geometry in general - has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces. The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.

Advanced Applications of Fractional Differential Operators to Science and Technology (Hardcover): Ahmed Ezzat Matouk Advanced Applications of Fractional Differential Operators to Science and Technology (Hardcover)
Ahmed Ezzat Matouk
R7,290 Discovery Miles 72 900 Ships in 12 - 17 working days

Fractional-order calculus dates to the 19th century but has been resurrected as a prevalent research subject due to its provision of more adequate and realistic descriptions of physical aspects within the science and engineering fields. What was once a classical form of mathematics is currently being reintroduced as a new modeling technique that engineers and scientists are finding modern uses for. There is a need for research on all facets of these fractional-order systems and studies of its potential applications. Advanced Applications of Fractional Differential Operators to Science and Technology provides emerging research exploring the theoretical and practical aspects of novel fractional modeling and related dynamical behaviors as well as its applications within the fields of physical sciences and engineering. Featuring coverage on a broad range of topics such as chaotic dynamics, ecological models, and bifurcation control, this book is ideally designed for engineering professionals, mathematicians, physicists, analysts, researchers, educators, and students seeking current research on fractional calculus and other applied mathematical modeling techniques.

Nonlinear Reaction-Diffusion Processes for Nanocomposites - Anomalous Improved Homogenization (Hardcover): Jesus Ildefonso... Nonlinear Reaction-Diffusion Processes for Nanocomposites - Anomalous Improved Homogenization (Hardcover)
Jesus Ildefonso Diaz, David Gomez-Castro, Tatiana A Shaposhnikova
R3,361 Discovery Miles 33 610 Ships in 12 - 17 working days

The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.

Topological Dynamical Systems - An Introduction to the Dynamics of Continuous Mappings (Hardcover, Digital original): Jan Vries Topological Dynamical Systems - An Introduction to the Dynamics of Continuous Mappings (Hardcover, Digital original)
Jan Vries
R4,451 Discovery Miles 44 510 Ships in 12 - 17 working days

There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.

Stochastically Forced Compressible Fluid Flows (Hardcover): Dominic Breit, Eduard Feireisl, Martina Hofmanova Stochastically Forced Compressible Fluid Flows (Hardcover)
Dominic Breit, Eduard Feireisl, Martina Hofmanova
R3,724 Discovery Miles 37 240 Ships in 12 - 17 working days

This book contains a first systematic study of compressible fluid flows subject to stochastic forcing. The bulk is the existence of dissipative martingale solutions to the stochastic compressible Navier-Stokes equations. These solutions are weak in the probabilistic sense as well as in the analytical sense. Moreover, the evolution of the energy can be controlled in terms of the initial energy. We analyze the behavior of solutions in short-time (where unique smooth solutions exists) as well as in the long term (existence of stationary solutions). Finally, we investigate the asymptotics with respect to several parameters of the model based on the energy inequality. Contents Part I: Preliminary results Elements of functional analysis Elements of stochastic analysis Part II: Existence theory Modeling fluid motion subject to random effects Global existence Local well-posedness Relative energy inequality and weak-strong uniqueness Part III: Applications Stationary solutions Singular limits

Oscillations and Resonances (Hardcover): Sergey G Glebov, Oleg M Kiselev, Nikolai N. Tarkhanov Oscillations and Resonances (Hardcover)
Sergey G Glebov, Oleg M Kiselev, Nikolai N. Tarkhanov
R4,435 Discovery Miles 44 350 Ships in 12 - 17 working days

This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators

Periodic Differential Equations in the Plane - A Topological Perspective (Hardcover): Rafael Ortega Periodic Differential Equations in the Plane - A Topological Perspective (Hardcover)
Rafael Ortega
R3,706 Discovery Miles 37 060 Ships in 12 - 17 working days

Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincare-Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.

Numerical Methods for Delay Differential Equations (Hardcover, New): Alfredo Bellen, Marino Zennaro Numerical Methods for Delay Differential Equations (Hardcover, New)
Alfredo Bellen, Marino Zennaro
R6,312 R5,324 Discovery Miles 53 240 Save R988 (16%) Ships in 12 - 17 working days

This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.

Richardson Extrapolation - Practical Aspects and Applications (Hardcover): Zahari Zlatev, Ivan Dimov, Istvan Farago, Agnes... Richardson Extrapolation - Practical Aspects and Applications (Hardcover)
Zahari Zlatev, Ivan Dimov, Istvan Farago, Agnes Havasi
R4,428 Discovery Miles 44 280 Ships in 12 - 17 working days

Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book. Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations. Contents The basic properties of Richardson extrapolation Richardson extrapolation for explicit Runge-Kutta methods Linear multistep and predictor-corrector methods Richardson extrapolation for some implicit methods Richardson extrapolation for splitting techniques Richardson extrapolation for advection problems Richardson extrapolation for some other problems General conclusions

Mathematical Elasticity, Volume II - Theory of Plates (Paperback): Philippe G. Ciarlet Mathematical Elasticity, Volume II - Theory of Plates (Paperback)
Philippe G. Ciarlet
R2,753 R2,432 Discovery Miles 24 320 Save R321 (12%) Ships in 12 - 17 working days

The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems (Paperback): John R. Graef,... Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems (Paperback)
John R. Graef, Johnny L. Henderson, Lingju Kong, Sherry Xueyan Liu
R1,606 Discovery Miles 16 060 Ships in 10 - 15 working days

The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.

Handbook of Differential Equations: Ordinary Differential Equations, Volume 3 (Hardcover, 3rd edition): A Canada, P. Drabek, A... Handbook of Differential Equations: Ordinary Differential Equations, Volume 3 (Hardcover, 3rd edition)
A Canada, P. Drabek, A Fonda
R6,786 Discovery Miles 67 860 Ships in 10 - 15 working days

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 a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume.
- Covers a variety of problems in ordinary differential equations
- Pure mathematical and real world applications
- Written for mathematicians and scientists of many related fields

Selected Topics in Almost Periodicity (Hardcover): Marko Kostic Selected Topics in Almost Periodicity (Hardcover)
Marko Kostic
R5,961 Discovery Miles 59 610 Ships in 12 - 17 working days

Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.

Partial Differential Equations - Theory and Completely Solved Problems (Hardcover, 2nd ed.): T Hillen, I E Leonard, H Van... Partial Differential Equations - Theory and Completely Solved Problems (Hardcover, 2nd ed.)
T Hillen, I E Leonard, H Van Roessel
R1,205 Discovery Miles 12 050 Ships in 12 - 17 working days
Combinatorial Functional Equations - Advanced Theory (Hardcover): Yanpei Liu Combinatorial Functional Equations - Advanced Theory (Hardcover)
Yanpei Liu
R6,565 Discovery Miles 65 650 Ships in 12 - 17 working days

This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The second volume mainly presents several kinds of meson functional equations which are divided into three types: outer, inner and surface. It is suited for a wide readership, including pure and applied mathematicians, and also computer scientists.

Concentration Compactness - Functional-Analytic Theory of Concentration Phenomena (Hardcover): Cyril Tintarev Concentration Compactness - Functional-Analytic Theory of Concentration Phenomena (Hardcover)
Cyril Tintarev
R3,613 Discovery Miles 36 130 Ships in 12 - 17 working days

Concentration compactness methods are applied to PDE's that lack compactness properties, typically due to the scaling invariance of the underlying problem. This monograph presents a systematic functional-analytic presentation of concentration mechanisms and is by far the most extensive and systematic collection of mathematical tools for analyzing the convergence of functional sequences via the mechanism of concentration.

Handbook of Differential Equations: Evolutionary Equations, Volume 2 (Hardcover, New): C.M. Dafermos, Eduard Feireisl Handbook of Differential Equations: Evolutionary Equations, Volume 2 (Hardcover, New)
C.M. Dafermos, Eduard Feireisl
R5,554 Discovery Miles 55 540 Ships in 12 - 17 working days

The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.
. Volume I of this Handbook does focus on the abstract theory of evolutionary equations.
. Volume 2 considers more concrete problems relating to specific applications.
. Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

Handbook of Differential Equations: Stationary Partial Differential Equations, Volume 3 (Hardcover, New): Michel Chipot, Pavol... Handbook of Differential Equations: Stationary Partial Differential Equations, Volume 3 (Hardcover, New)
Michel Chipot, Pavol Quittner
R5,362 Discovery Miles 53 620 Ships in 12 - 17 working days

This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics.

Key features:


- Written by well-known experts in the field
- Self-contained volume in series covering one of the most rapid developing topics in mathematics
- Written by well-known experts in the field
- Self-contained volume in series covering one of the most rapid developing topics in mathematics

Meanders - Sturm Global Attractors, Seaweed Lie Algebras and Classical Yang-Baxter Equation (Hardcover): Anna Karnauhova Meanders - Sturm Global Attractors, Seaweed Lie Algebras and Classical Yang-Baxter Equation (Hardcover)
Anna Karnauhova
R3,703 Discovery Miles 37 030 Ships in 12 - 17 working days

This unique book's subject is meanders (connected, oriented, non-self-intersecting planar curves intersecting the horizontal line transversely) in the context of dynamical systems. By interpreting the transverse intersection points as vertices and the arches arising from these curves as directed edges, meanders are introduced from the graphtheoretical perspective. Supplementing the rigorous results, mathematical methods, constructions, and examples of meanders with a large number of insightful figures, issues such as connectivity and the number of connected components of meanders are studied in detail with the aid of collapse and multiple collapse, forks, and chambers. Moreover, the author introduces a large class of Morse meanders by utilizing the right and left one-shift maps, and presents connections to Sturm global attractors, seaweed and Frobenius Lie algebras, and the classical Yang-Baxter equation. Contents Seaweed Meanders Meanders Morse Meanders and Sturm Global Attractors Right and Left One-Shifts Connection Graphs of Type I, II, III and IV Meanders and the Temperley-Lieb Algebra Representations of Seaweed Lie Algebras CYBE and Seaweed Meanders

Handbook of Differential Equations:Stationary Partial Differential Equations, Volume 2 (Hardcover): Michel Chipot, Pavol... Handbook of Differential Equations:Stationary Partial Differential Equations, Volume 2 (Hardcover)
Michel Chipot, Pavol Quittner
R5,362 Discovery Miles 53 620 Ships in 12 - 17 working days

A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.


Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.


Key features:


- Self-contained volume in series covering one of the most rapid developing topics in mathematics.
- 7 Chapters, enriched with numerous figures originating from numerical simulations.
- Written by well known experts in the field.
- Self-contained volume in series covering one of the most rapid developing topics in mathematics.
- 7 Chapters, enriched with numerous figures originating from numerical simulations.
- Written by well known experts in the field.

Fractional Signals and Systems (Hardcover): Manuel Duarte Ortigueira, Duarte Valerio Fractional Signals and Systems (Hardcover)
Manuel Duarte Ortigueira, Duarte Valerio
R4,279 Discovery Miles 42 790 Ships in 12 - 17 working days

The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.

Mathematical Elasticity, Volume III - Theory of Shells (Paperback): Philippe G. Ciarlet Mathematical Elasticity, Volume III - Theory of Shells (Paperback)
Philippe G. Ciarlet
R2,786 R2,626 Discovery Miles 26 260 Save R160 (6%) Ships in 12 - 17 working days

The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Handbook of Differential Equations: Stationary Partial Differential Equations, Volume 6 (Hardcover, Revised): Michel Chipot Handbook of Differential Equations: Stationary Partial Differential Equations, Volume 6 (Hardcover, Revised)
Michel Chipot
R5,933 Discovery Miles 59 330 Ships in 10 - 15 working days

This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems.
* Collection of self-contained, state-of-the-art surveys
* Written by well-known experts in the field
* Informs and updates on all the latest developments

Non-Self-Adjoint Boundary Eigenvalue Problems, Volume 192 (Hardcover, 1st ed): R. Mennicken, M. Moeller Non-Self-Adjoint Boundary Eigenvalue Problems, Volume 192 (Hardcover, 1st ed)
R. Mennicken, M. Moeller
R4,853 Discovery Miles 48 530 Ships in 12 - 17 working days

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and "n"-th order ordinary differential equations.
In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every "n"-th order differential equation is equivalent
to a first order system, the main techniques are developed for systems. Asymptotic fundamental
systems are derived for a large class of systems of differential equations. Together with boundary
conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.
The contour integral method and estimates of the resolvent are used to prove expansion theorems.
For Stone regular problems, not all functions are expandable, and again relatively easy verifiable
conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.
Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as
the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.


Key features:
Expansion Theorems for Ordinary Differential Equations
Discusses Applications to Problems from Physics and Engineering
Thorough Investigation of Asymptotic Fundamental Matrices and Systems
Provides a Comprehensive Treatment
Uses the Contour Integral Method
Represents the Problems as Bounded Operators
Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions
"

Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations (Hardcover): Ravi P. Agarwal, Vangipuram... Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations (Hardcover)
Ravi P. Agarwal, Vangipuram Lakshmikantham
R3,206 Discovery Miles 32 060 Ships in 12 - 17 working days

This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.

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