Ordinary Differential Equations in the Complex Domain


Author: Einar Hille
Publisher: Courier Corporation
ISBN: 9780486696201
Category: Mathematics
Page: 484
View: 5725

Continue Reading →

Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.

Ordinary Differential Equations


Author: Edward L. Ince
Publisher: Courier Corporation
ISBN: 0486158217
Category: Mathematics
Page: 576
View: 5132

Continue Reading →

Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.

Ordinary Differential Equations

An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences
Author: Morris Tenenbaum,Harry Pollard
Publisher: Courier Corporation
ISBN: 0486649407
Category: Mathematics
Page: 808
View: 6208

Continue Reading →

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

A First Course in Partial Differential Equations

with Complex Variables and Transform Methods
Author: H. F. Weinberger
Publisher: Courier Corporation
ISBN: 0486132048
Category: Mathematics
Page: 480
View: 4807

Continue Reading →

Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.

Ordinary Differential Equations and Dynamical Systems


Author: Gerald Teschl
Publisher: American Mathematical Soc.
ISBN: 0821883283
Category: Mathematics
Page: 356
View: 4860

Continue Reading →

This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Introduction to Nonlinear Differential and Integral Equations


Author: Harold Thayer Davis
Publisher: Courier Corporation
ISBN: 9780486609713
Category: Mathematics
Page: 566
View: 1882

Continue Reading →

Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

Lectures on Analytic Differential Equations


Author: I͡U. S. Ilʹi͡ashenko,S. Yakovenko
Publisher: American Mathematical Soc.
ISBN: 0821836676
Category: Mathematics
Page: 625
View: 2615

Continue Reading →

The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text. The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.

Introduction to Partial Differential Equations with Applications


Author: E. C. Zachmanoglou,Dale W. Thoe
Publisher: Courier Corporation
ISBN: 048613217X
Category: Mathematics
Page: 432
View: 2401

Continue Reading →

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Lectures on Ordinary Differential Equations


Author: Witold Hurewicz
Publisher: Courier Corporation
ISBN: 048679721X
Category: Mathematics
Page: 144
View: 4995

Continue Reading →

Introductory treatment explores existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. "A rigorous and lively introduction." — The American Mathematical Monthly. 1958 edition.

Existence Theorems for Ordinary Differential Equations


Author: Francis J. Murray,Kenneth S. Miller
Publisher: Courier Corporation
ISBN: 0486154955
Category: Mathematics
Page: 176
View: 8759

Continue Reading →

This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.

Partial Differential Equations

Theory and Completely Solved Problems
Author: Thomas Hillen,I. E. Leonard,Henry van Roessel
Publisher: John Wiley & Sons
ISBN: 1118438434
Category: Mathematics
Page: 696
View: 815

Continue Reading →

Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

Asymptotic Expansions for Ordinary Differential Equations


Author: Wolfgang Wasow
Publisher: Courier Dover Publications
ISBN: 0486824586
Category: Mathematics
Page: 384
View: 991

Continue Reading →

This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

Asymptotic Expansions of Integrals


Author: Norman Bleistein,Richard A. Handelsman
Publisher: Courier Corporation
ISBN: 0486650820
Category: Mathematics
Page: 425
View: 7652

Continue Reading →

Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Ordinary Differential Equations and Their Solutions


Author: George Moseley Murphy
Publisher: Courier Corporation
ISBN: 0486485919
Category: Mathematics
Page: 451
View: 8716

Continue Reading →

This treatment presents most of the methods for solving ordinary differential equations and systematic arrangements of more than 2,000 equations and their solutions. The material is organized so that standard equations can be easily found. Plus, the substantial number and variety of equations promises an exact equation or a sufficiently similar one. 1960 edition.

Advanced Calculus

Revised
Author: Lynn Harold Loomis,Shlomo Sternberg
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category: Mathematics
Page: 596
View: 702

Continue Reading →

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Linear Differential Equations in the Complex Domain

Problems of Analytic Continuation
Author: Yasutaka Sibuya
Publisher: American Mathematical Soc.
ISBN: 0821846760
Category: Mathematics
Page: 267
View: 6812

Continue Reading →

This book is a translation of a 1976 book originally written in Japanese. The main attention is paid to intrinsic aspects of problems related to linear ordinary differential equations in complex domains. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. Since the original book was published, many new ideas have developed, such as applications of D-modules, Gevrey asymptotics, cohomological methods, $k$-summability, and studies of differential equations containing parameters. Five appendices, added in the present edition, briefly cover these new ideas. In addition, more than 100 references have been added. This book introduces the reader to the essential facts concerning the structure of solutions of linear differential equations in the complex domain and illuminates the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar.

The Qualitative Theory of Ordinary Differential Equations

An Introduction
Author: Fred Brauer,John A. Nohel
Publisher: Courier Corporation
ISBN: 0486151514
Category: Mathematics
Page: 320
View: 9871

Continue Reading →

Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.

Mathematics

Its Content, Methods and Meaning
Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev
Publisher: Courier Corporation
ISBN: 0486157873
Category: Mathematics
Page: 1120
View: 5354

Continue Reading →

Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type
Author: Kai Diethelm
Publisher: Springer
ISBN: 3642145744
Category: Mathematics
Page: 247
View: 736

Continue Reading →

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.