Advanced Ordinary Differential Equations
Author: Athanassios G. Kartsatos
Publisher: Mancorp Publishing
Published: 1993
Total Pages: 290
ISBN-13:
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Advanced Differential Equations
Author: M.D.Raisinghania
Publisher: S. Chand Publishing
Published: 1995-03
Total Pages: 1366
ISBN-13: 8121908930
DOWNLOAD EBOOKThis book is especially prepared for B.A., B.Sc. and honours (Mathematics and Physics), M.A/M.Sc. (Mathematics and Physics), B.E. Students of Various Universities and for I.A.S., P.C.S., AMIE, GATE, and other competitve exams.Almost all the chapters have been rewritten so that in the present form, the reader will not find any difficulty in understanding the subject matter.The matter of the previous edition has been re-organised so that now each topic gets its proper place in the book.More solved examples have been added so that now each topic gets its proper place in the book. References to the latest papers of various universities and I.A.S. examination have been made at proper places.
Advanced Ordinary Differential Equations
Author: Kurt Otto Friedrichs
Publisher: CRC Press
Published: 1965
Total Pages: 224
ISBN-13: 9780677009650
DOWNLOAD EBOOKLinear Ordinary Differential Equations
Author: Earl A. Coddington
Publisher: SIAM
Published: 1997-01-01
Total Pages: 353
ISBN-13: 9781611971439
DOWNLOAD EBOOKLinear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.
A Second Course in Elementary Differential Equations
Author: Paul Waltman
Publisher: Elsevier
Published: 2014-05-10
Total Pages: 272
ISBN-13: 1483276600
DOWNLOAD EBOOKA Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics.
Ordinary Differential Equations and Stability Theory:
Author: David A. Sanchez
Publisher: Courier Dover Publications
Published: 2019-09-18
Total Pages: 179
ISBN-13: 0486837599
DOWNLOAD EBOOKThis brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.
Introduction to Ordinary Differential Equations
Author: Albert L. Rabenstein
Publisher: Academic Press
Published: 2014-05-12
Total Pages: 444
ISBN-13: 1483226220
DOWNLOAD EBOOKIntroduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.
Ordinary Differential Equations
Author: Wolfgang Walter
Publisher: Springer Science & Business Media
Published: 2013-03-11
Total Pages: 391
ISBN-13: 1461206014
DOWNLOAD EBOOKBased on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
Existence Theorems for Ordinary Differential Equations
Author: Francis J. Murray
Publisher: Courier Corporation
Published: 2013-11-07
Total Pages: 178
ISBN-13: 0486154955
DOWNLOAD EBOOKThis 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.
Ordinary Differential Equations and Dynamical Systems
Author: Thomas C. Sideris
Publisher: Springer Science & Business Media
Published: 2013-10-17
Total Pages: 230
ISBN-13: 9462390215
DOWNLOAD EBOOKThis book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
