A First Course In Ordinary Differential Equations

Author : Martin Hermann,Masoud Saravi
Publisher : Springer Science & Business
Page : 300 pages
File Size : 41,5 Mb
Release : 2014-04-22
Category : Mathematics
ISBN : 9788132218357

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A First Course in Ordinary Differential Equations by Martin Hermann,Masoud Saravi Pdf

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

Author : Suman Kumar Tumuluri
Publisher : CRC Press
Page : 338 pages
File Size : 47,8 Mb
Release : 2021-03-24
Category : Mathematics
ISBN : 9781000356717

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A First Course in Ordinary Differential Equations by Suman Kumar Tumuluri Pdf

A First course in Ordinary Differential Equations provides a detailed introduction to the subject focusing on analytical methods to solve ODEs and theoretical aspects of analyzing them when it is difficult/not possible to find their solutions explicitly. This two-fold treatment of the subject is quite handy not only for undergraduate students in mathematics but also for physicists, engineers who are interested in understanding how various methods to solve ODEs work. More than 300 end-of-chapter problems with varying difficulty are provided so that the reader can self examine their understanding of the topics covered in the text. Most of the definitions and results used from subjects like real analysis, linear algebra are stated clearly in the book. This enables the book to be accessible to physics and engineering students also. Moreover, sufficient number of worked out examples are presented to illustrate every new technique introduced in this book. Moreover, the author elucidates the importance of various hypotheses in the results by providing counter examples. Features Offers comprehensive coverage of all essential topics required for an introductory course in ODE. Emphasizes on both computation of solutions to ODEs as well as the theoretical concepts like well-posedness, comparison results, stability etc. Systematic presentation of insights of the nature of the solutions to linear/non-linear ODEs. Special attention on the study of asymptotic behavior of solutions to autonomous ODEs (both for scalar case and 2✕2 systems). Sufficient number of examples are provided wherever a notion is introduced. Contains a rich collection of problems. This book serves as a text book for undergraduate students and a reference book for scientists and engineers. Broad coverage and clear presentation of the material indeed appeals to the readers. Dr. Suman K. Tumuluri has been working in University of Hyderabad, India, for 11 years and at present he is an associate professor. His research interests include applications of partial differential equations in population dynamics and fluid dynamics.

Author : J. David Logan
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 54,7 Mb
Release : 2006-05-20
Category : Mathematics
ISBN : 9780387299303

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A First Course in Differential Equations by J. David Logan Pdf

Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying di?erential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts.

Author : Stephen A. Wirkus,Randall J. Swift
Publisher : CRC Press
Page : 689 pages
File Size : 51,8 Mb
Release : 2006-10-23
Category : Mathematics
ISBN : 9781420010411

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A Course in Ordinary Differential Equations by Stephen A. Wirkus,Randall J. Swift Pdf

The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB, Mathematica, and Maple A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics student's field o

Author : Antonio Ambrosetti,Shair Ahmad
Publisher : Walter de Gruyter GmbH & Co KG
Page : 435 pages
File Size : 45,7 Mb
Release : 2023-12-18
Category : Mathematics
ISBN : 9783111185781

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Differential Equations by Antonio Ambrosetti,Shair Ahmad Pdf

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 481 pages
File Size : 45,5 Mb
Release : 2008-11-27
Category : Mathematics
ISBN : 9781139473767

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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles Pdf

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.

Author : Dennis G. Zill
Publisher : Unknown
Page : 552 pages
File Size : 41,9 Mb
Release : 1979
Category : Differential equations
ISBN : STANFORD:36105031599900

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A First Course in Differential Equations with Applications by Dennis G. Zill Pdf

An introduction to differential equations; First-order differential equations; Applications of first-order differential equations; Linear equations of higher order; Applications of second-order differential equations: vibrational models; Differential equations with variable coefficients; The laplace transform; Linear systems of differencial equations; Numerial methods; Partial differential equations.

Author : D. Somasundaram
Publisher : CRC Press
Page : 324 pages
File Size : 54,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0849309883

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Ordinary Differential Equations by D. Somasundaram Pdf

Though ordinary differential equations is taught as a core course to students in mathematics and applied mathematics, detailed coverage of the topics with sufficient examples is unique. Written by a mathematics professor and intended as a textbook for third- and fourth-year undergraduates, the five chapters of this publication give a precise account of higher order differential equations, power series solutions, special functions, existence and uniqueness of solutions, and systems of linear equations. Relevant motivation for different concepts in each chapter and discussion of theory and problems-without the omission of steps-sets Ordinary Differential Equations: A First Course apart from other texts on ODEs. Full of distinguishing examples and containing exercises at the end of each chapter, this lucid course book will promote self-study among students.

Author : Fred Brauer,John A. Nohel
Publisher : Addison Wesley Longman
Page : 492 pages
File Size : 40,7 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015017330500

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Ordinary Differential Equations by Fred Brauer,John A. Nohel Pdf

Author : Carlos A. Smith,Scott W. Campbell
Publisher : CRC Press
Page : 344 pages
File Size : 54,8 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9781439850886

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A First Course in Differential Equations, Modeling, and Simulation by Carlos A. Smith,Scott W. Campbell Pdf

Emphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for

Author : Rudolph Ernest Langer
Publisher : Unknown
Page : 272 pages
File Size : 53,6 Mb
Release : 1954
Category : Differential equations
ISBN : UOM:39015004507557

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A First Course in Ordinary Differential Equations by Rudolph Ernest Langer Pdf

Author : Gerald Teschl
Publisher : American Mathematical Society
Page : 370 pages
File Size : 43,8 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9781470476410

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Ordinary Differential Equations and Dynamical Systems by Gerald Teschl Pdf

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 Poincaré–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.

Author : Mayer Humi,William Miller
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461238324

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Second Course in Ordinary Differential Equations for Scientists and Engineers by Mayer Humi,William Miller Pdf

The world abounds with introductory texts on ordinary differential equations and rightly so in view of the large number of students taking a course in this subject. However, for some time now there is a growing need for a junior-senior level book on the more advanced topics of differential equations. In fact the number of engineering and science students requiring a second course in these topics has been increasing. This book is an outgrowth of such courses taught by us in the last ten years at Worcester Polytechnic Institute. The book attempts to blend mathematical theory with nontrivial applications from varipus disciplines. It does not contain lengthy proofs of mathemati~al theorems as this would be inappropriate for its intended audience. Nevertheless, in each case we motivated these theorems and their practical use through examples and in some cases an "intuitive proof" is included. In view of this approach the book could be used also by aspiring mathematicians who wish to obtain an overview of the more advanced aspects of differential equations and an insight into some of its applications. We have included a wide range of topics in order to afford the instructor the flexibility in designing such a course according to the needs of the students. Therefore, this book contains more than enough material for a one semester course.

Author : Michael K. Keane
Publisher : Unknown
Page : 536 pages
File Size : 43,7 Mb
Release : 2002
Category : Mathematics
ISBN : UCSC:32106016867183

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A Very Applied First Course in Partial Differential Equations by Michael K. Keane Pdf

This extremely readable book illustrates how mathematics applies directly to different fields of study. Focuses on problems that require physical to mathematical translations, by showing readers how equations have actual meaning in the real world. Covers fourier integrals, and transform methods, classical PDE problems, the Sturm-Liouville Eigenvalue problem, and much more. For readers interested in partial differential equations.

Author : David A. Sanchez
Publisher : Courier Dover Publications
Page : 179 pages
File Size : 54,6 Mb
Release : 2019-09-18
Category : Mathematics
ISBN : 9780486837598

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Ordinary Differential Equations and Stability Theory: by David A. Sanchez Pdf

This 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.