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Author: Raimond A. Struble
Publisher: Courier Dover Publications
Published: 2018-01-16
Total Pages: 289
ISBN-13: 0486817547
DOWNLOAD EBOOK →Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.
Author: Ferdinand Verhulst
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 287
ISBN-13: 3642971490
DOWNLOAD EBOOK →Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.
Author: Feliz Manuel Minhós
Publisher: MDPI
Published: 2021-04-15
Total Pages: 158
ISBN-13: 3036507108
DOWNLOAD EBOOK →This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Author: R. Grimshaw
Publisher: Routledge
Published: 2017-10-19
Total Pages: 276
ISBN-13: 135142808X
DOWNLOAD EBOOK →Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.
Author: Dominic Jordan
Publisher: OUP Oxford
Published: 2007-08-24
Total Pages: 540
ISBN-13: 0191525995
DOWNLOAD EBOOK →This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007). Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.
Author: Andrei D. Polyanin
Publisher: CRC Press
Published: 2004-06-02
Total Pages: 835
ISBN-13: 1135440816
DOWNLOAD EBOOK →The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Author: Mi-Ho Giga
Publisher: Springer Science & Business Media
Published: 2010-05-30
Total Pages: 307
ISBN-13: 0817646515
DOWNLOAD EBOOK →This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.
Author: R. E. Gaines
Publisher: Springer
Published: 2006-11-15
Total Pages: 267
ISBN-13: 3540375015
DOWNLOAD EBOOK →Author: Dominic Jordan
Publisher: Oxford University Press
Published: 2007-08-23
Total Pages: 594
ISBN-13: 0199212031
DOWNLOAD EBOOK →An ideal companion to the student textbook Nonlinear Ordinary Differential Equations 4th Edition (OUP, 2007) this text contains over 500 problems and solutions in nonlinear differential equations, many of which can be adapted for independent coursework and self-study.
