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Especially among Japanese mathematicians Mitio Nagumo (1905-1995) is regarded as one of the greatest pioneers in research on differential equations. However, so far most of his papers have only been published in Japanese journals and were unavailable in the West. This Collected Papers volume contains practically all mathematical papers Nagumo wrote in languages other than Japanese and will be a basic reference volume and essential working tool for every library and for many active mathematicians...

REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES ...168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups...169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation ...173 10...

Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately, there's Schaum's. This all-in-one-package includes more than 550 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highe...

This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDE's to biology. The text differs from other texts in its brevity...

Stochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.

How to solve partial differential systems by completing the square. This could well have been the title of this monograph as it grew into a project to develop a s- tematic approach for associating suitable nonnegative energy functionals to a large class of partial differential equations (PDEs) and evolutionary systems. The minima of these functionals are to be the solutions we seek, not because they are critical points (i. e. , from the corresponding Euler-Lagrange equations) but from also - ing...

This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of analytic behaviour of solutions. It presents basic facts of the subject and includes recent results, emphasizing the method of integral operators and the method of differential operators. The first chapter gives a motivation for and the underlying ideas of, the later chapters. Chapters 2 to 7 give a detailed exposition of the basic concepts and fundamental theorems,...

V ? V ?K? , 3 2 2 R ? /?x K i i g V T G g ?T , ? G g g 4 ? R ? ? G ? T g g ? h h ? 2 2 2 2 ? ? ? ? ? ? ? h ?S , ?? ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 S T S T? T?. ? ~ T S 2 2 2 2 ? ? ? ? ? ? ? h . ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 g h h ?? g T T g vacuum M n R n R Acknowledgements n R Chapter I Pseudo-Riemannian Manifolds I.1 Connections M C n X M C M F M C X M F M connection covariant derivative M ? X M xX M ?? X M X,Y ?? Y X ? Y ? Y ? Y X +X X X 1 2 1 2 ? Y Y ? Y ? Y X 1 2 X 1 X 2 ? Y f? Y f?F M...

The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, t...

The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical f...

Dieses vierfarbige Lehrbuch bietet in einem Band ein lebendiges Bild der "gesamten" Mathematik fur Anwender. Angehende Ingenieure und Naturwissenschaftler finden hier die wichtigen Konzepte und Begriffe ausfuhrlich und mit vielen Beispielen erklart. Im Mittelpunkt stehen das Verstandnis der Zusammenhange und die Beherrschung der Rechentechniken. Herausragende Merkmale sind: durchgangig vierfarbiges Layout mit mehr als 1500 Abbildungen pragnant formulierte Kerngedanken bilden die Abschnittsubersc...

Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh's point of view. The second part expounds 1-summability and Ecalle's theory of resurgence under fairly general conditions. It contains numerous...

For Differential Equation and Linear Algebra courses at a sophomore level.Using a unique, student-friendly approach to teaching differential equations, this text encourages students to think both quantitatively and qualitatively when approaching differential equations. Before finding the analytical solution of a differential equation, the text presents the qualitative aspects of the problem--the directional field, the bounded solutions, their range, the presence of constant solutions and so on--...