Problems And Examples In Differential Equations

Author : Ravi P. Agarwal,Simona Hodis,Donal O’Regan
Publisher : Springer Nature
Page : 388 pages
File Size : 52,5 Mb
Release : 2019-09-24
Category : Mathematics
ISBN : 9783030263843

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500 Examples and Problems of Applied Differential Equations by Ravi P. Agarwal,Simona Hodis,Donal O’Regan Pdf

This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge–Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more. Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

Author : Piotr Biler,Tadeusz Nadzieja
Publisher : CRC Press
Page : 261 pages
File Size : 41,6 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9781000104752

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Problems and Examples in Differential Equations by Piotr Biler,Tadeusz Nadzieja Pdf

This book presents original problems from graduate courses in pure and applied mathematics and even small research topics, significant theorems and information on recent results. It is helpful for specialists working in differential equations.

Author : Piotr Biler,Tadeusz Nadzieja
Publisher : CRC Press
Page : 264 pages
File Size : 47,5 Mb
Release : 2020-08-12
Category : Mathematics
ISBN : 9781000147964

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Problems and Examples in Differential Equations by Piotr Biler,Tadeusz Nadzieja Pdf

This book presents original problems from graduate courses in pure and applied mathematics and even small research topics, significant theorems and information on recent results. It is helpful for specialists working in differential equations.

Author : J. L. Brenner
Publisher : Courier Corporation
Page : 176 pages
File Size : 55,8 Mb
Release : 2013-11-06
Category : Mathematics
ISBN : 9780486782829

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Problems in Differential Equations by J. L. Brenner Pdf

More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.

Author : Chin-Yuan Lin
Publisher : World Scientific
Page : 555 pages
File Size : 44,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814307123

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Theory and Examples of Ordinary Differential Equations by Chin-Yuan Lin Pdf

This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered in this book with clear proofs for the theoretical results and with detailed solutions for the examples and problems. This book is intended for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra. Additionally, the comprehensive coverage of the theory with a wide array of examples and detailed solutions, would appeal to mathematics graduate students and researchers as well as graduate students in majors of other disciplines. As a handy reference, advanced knowledge is provided in this book with details developed beyond the basics; optional sections, where main results are extended, offer an understanding of further applications of ordinary differential equations.

Author : Alekseĭ Fedorovich Filippov,Joel Lee Brenner
Publisher : Unknown
Page : 196 pages
File Size : 53,9 Mb
Release : 1966
Category : Differential equations
ISBN : STANFORD:36105033283149

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Problems in Differential Equations by Alekseĭ Fedorovich Filippov,Joel Lee Brenner Pdf

Author : John M. Rassias
Publisher : World Scientific
Page : 198 pages
File Size : 45,7 Mb
Release : 1991
Category : Mathematics
ISBN : 9810204612

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Counter Examples in Differential Equations and Related Topics by John M. Rassias Pdf

Based on a semester course taught in Greece for many years to science, engineering, and mathematics students. Discusses continuity and linearity, differentiability and analyticity, extrema, existence, uniqueness, stability, and other topics. The examples are drawn from the literature of the field. Acidic paper. Annotation copyrighted by Book News, Inc., Portland, OR

Author : William F. Trench
Publisher : Thomson Brooks/Cole
Page : 766 pages
File Size : 48,5 Mb
Release : 2001
Category : Mathematics
ISBN : UCSC:32106015134783

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Elementary Differential Equations with Boundary Value Problems by William F. Trench Pdf

Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.

Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Page : 1767 pages
File Size : 44,5 Mb
Release : 2017-11-15
Category : Mathematics
ISBN : 9781351643917

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Handbook of Ordinary Differential Equations by Andrei D. Polyanin,Valentin F. Zaitsev Pdf

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.

Author : Deng Yuefan
Publisher : World Scientific
Page : 572 pages
File Size : 45,6 Mb
Release : 2017-08-11
Category : Mathematics
ISBN : 9789813226159

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Lectures, Problems and Solutions for Ordinary Differential Equations by Deng Yuefan Pdf

This unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples. The initial draft was used to teach more than 10,000 advanced undergraduate students in engineering, physics, economics, as well as applied mathematics. It is a good source for students to learn problem-solving skills and for educators to find problems for homework assignments and tests. The 2nd edition, with at least 100 more examples and five added subsections, has been restructured to flow more pedagogically.

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 53,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821868898

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Partial Differential Equations and Boundary-Value Problems with Applications by Mark A. Pinsky Pdf

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

Author : Alexander Komech,Andrew Komech
Publisher : Springer Science & Business Media
Page : 165 pages
File Size : 54,5 Mb
Release : 2009-10-05
Category : Mathematics
ISBN : 9781441910950

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Principles of Partial Differential Equations by Alexander Komech,Andrew Komech Pdf

This concise book covers the classical tools of Partial Differential Equations Theory in today’s science and engineering. The rigorous theoretical presentation includes many hints, and the book contains many illustrative applications from physics.

Author : Thomas Hillen,I. E. Leonard,Henry van Roessel
Publisher : John Wiley & Sons
Page : 610 pages
File Size : 55,6 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118438435

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Partial Differential Equations by Thomas Hillen,I. E. Leonard,Henry van Roessel Pdf

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.

Author : M. V. Makarets,V. Yu Reshetnyak
Publisher : World Scientific
Page : 385 pages
File Size : 42,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9789810221911

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Ordinary Differential Equations and Calculus of Variations by M. V. Makarets,V. Yu Reshetnyak Pdf

This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practicing engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students ? much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, and expanded treatment of applications.

Author : P. Mohana Shankar
Publisher : CRC Press
Page : 448 pages
File Size : 46,7 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9781351385749

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Differential Equations by P. Mohana Shankar Pdf

The book takes a problem solving approach in presenting the topic of differential equations. It provides a complete narrative of differential equations showing the theoretical aspects of the problem (the how's and why's), various steps in arriving at solutions, multiple ways of obtaining solutions and comparison of solutions. A large number of comprehensive examples are provided to show depth and breadth and these are presented in a manner very similar to the instructor's class room work. The examples contain solutions from Laplace transform based approaches alongside the solutions based on eigenvalues and eigenvectors and characteristic equations. The verification of the results in examples is additionally provided using Runge-Kutta offering a holistic means to interpret and understand the solutions. Wherever necessary, phase plots are provided to support the analytical results. All the examples are worked out using MATLAB® taking advantage of the Symbolic Toolbox and LaTex for displaying equations. With the subject matter being presented through these descriptive examples, students will find it easy to grasp the concepts. A large number of exercises have been provided in each chapter to allow instructors and students to explore various aspects of differential equations.