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| elementary partial differential equations: Elementary Partial Differential Equations with Boundary Value Problems Larry C. Andrews, 1986 |
| elementary partial differential equations: Elementary partial differential equations Paul W. Berg, James L. MacGregor, 1980 |
| elementary partial differential equations: Elementary Partial Differential Equations Paul W. Berg, 1969 |
| elementary partial differential equations: Solution Techniques for Elementary Partial Differential Equations Christian Constanda, 2022-08-10 In my opinion, this is quite simply the best book of its kind that I have seen thus far. —Professor Peter Schiavone, University of Alberta, from the Foreword to the Fourth Edition Praise for the previous editions An ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses. —Marian Aron, Plymouth University, UK This is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended. —CHOICE Solution Techniques for Elementary Partial Differential Equations, Fourth Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). It provides a streamlined, direct approach to developing students’ competence in solving PDEs, and offers concise, easily understood explanations and worked examples that enable students to see the techniques in action. New to the Fourth Edition Two additional sections A larger number and variety of worked examples and exercises A companion pdf file containing more detailed worked examples to supplement those in the book, which can be used in the classroom and as an aid to online teaching |
| elementary partial differential equations: Elementary Partial Differential Equations Paul W. Berg, James L. McGregor, 1966 |
| elementary partial differential equations: An Elementary Course in Partial Differential Equations T. Amaranath, 2003 The long awaited second edition of this very successful textbook for graduate students covers the study of first and second order of Partial Differential Equations. New to this edition: Improved presentation Exercises and worked examples at the end of each chapter with solutions Also useful for students of Engineering and Physics |
| elementary partial differential equations: An Elementary Treatise on Partial Differential Equations George Biddell Airy, 1873 |
| elementary partial differential equations: Elementary Partial Differential Equations R. J. Gribben, 1975 |
| elementary partial differential equations: Elementary Partial Differential Equations Paul Berg, James L. McGregor, 1966 |
| elementary partial differential equations: Solution Techniques for Elementary Partial Differential Equations Christian Constanda, 2022-08-10 In my opinion, this is quite simply the best book of its kind that I have seen thus far. —Professor Peter Schiavone, University of Alberta, from the Foreword to the Fourth Edition Praise for the previous editions An ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses. —Marian Aron, Plymouth University, UK This is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended. —CHOICE Solution Techniques for Elementary Partial Differential Equations, Fourth Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). It provides a streamlined, direct approach to developing students’ competence in solving PDEs, and offers concise, easily understood explanations and worked examples that enable students to see the techniques in action. New to the Fourth Edition Two additional sections A larger number and variety of worked examples and exercises A companion pdf file containing more detailed worked examples to supplement those in the book, which can be used in the classroom and as an aid to online teaching |
| elementary partial differential equations: Solution Techniques for Elementary Partial Differential Equations Christian Constanda, Ronald B Guenther, Kuo-Ching Ma, 2002-03 |
| elementary partial differential equations: Principles of Partial Differential Equations Alexander Komech, Andrew Komech, 2009-10-05 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. |
| elementary partial differential equations: An Elementary Treatise on Partial Differential Equations Designed for the Use of Students in the University by George Biddell Airy George Biddell Airy, 1873 |
| elementary partial differential equations: Introduction to Partial Differential Equations Peter J. Olver, 2013-11-08 This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements. |
| elementary partial differential equations: Ordinary and Partial Differential Equations Victor Henner, Tatyana Belozerova, Mikhail Khenner, 2013-01-29 Covers ODEs and PDEs—in One Textbook Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software. Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques. Guides Students through the Problem-Solving Process Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students’ analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps. |
| elementary partial differential equations: Elementary Partial Differential Equations Robert Ranulph Marett, 1966 |
| elementary partial differential equations: Introduction to Partial Differential Equations Aslak Tveito, Ragnar Winther, 2008-01-21 Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some projects suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering. |
| elementary partial differential equations: Elements of Partial Differential Equations Pavel Drábek, Gabriela Holubová, 2014-08-19 This textbook is an elementary introduction to the basic principles of partial differential equations. With many illustrations it introduces PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics. |
| elementary partial differential equations: Finite Difference Methods for Ordinary and Partial Differential Equations Randall J. LeVeque, 2007-01-01 This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. |
| elementary partial differential equations: Elementary Partial Differential Equations and Applications , |
| elementary partial differential equations: Introduction To Partial Differential Equations (With Maple), An: A Concise Course Zhilin Li, Larry Norris, 2021-09-23 The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations.The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm-Liouville eigenvalue problems and series solutions.The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area. |
| elementary partial differential equations: Elementary Partial Differential Equations Macgregor Berg, 1966 |
| elementary partial differential equations: Mathematical Physics with Partial Differential Equations James Kirkwood, 2011-12-01 Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments. The text presents some of the most important topics and methods of mathematical physics. The premise is to study in detail the three most important partial differential equations in the field – the heat equation, the wave equation, and Laplace's equation. The most common techniques of solving such equations are developed in this book, including Green's functions, the Fourier transform, and the Laplace transform, which all have applications in mathematics and physics far beyond solving the above equations. The book's focus is on both the equations and their methods of solution. Ordinary differential equations and PDEs are solved including Bessel Functions, making the book useful as a graduate level textbook. The book's rigor supports the vital sophistication for someone wanting to continue further in areas of mathematical physics. - Examines in depth both the equations and their methods of solution - Presents physical concepts in a mathematical framework - Contains detailed mathematical derivations and solutions— reinforcing the material through repetition of both the equations and the techniques - Includes several examples solved by multiple methods—highlighting the strengths and weaknesses of various techniques and providing additional practice |
| elementary partial differential equations: Elements of Partial Differential Equations Ian N. Sneddon, 1988 |
| elementary partial differential equations: Introduction to Partial Differential Equations with Applications E. C. Zachmanoglou, Dale W. Thoe, 2012-04-20 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. |
| elementary partial differential equations: Elementary Applied Partial Differential Equations Richard Haberman, 1987 This text is designed for engineers, scientists, and mathematicians with a background in elementary ordinary differential equations and calculus. |
| elementary partial differential equations: Partial Differential Equations in Action Sandro Salsa, 2015-04-24 The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems. |
| elementary partial differential equations: Ordinary Differential Equations Morris Tenenbaum, Harry Pollard, 1985-10-01 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. |
| elementary partial differential equations: Elementary Partial Differential Equations for Engineers and Scientists J. C. Wilhoit, 1978 |
| elementary partial differential equations: Partial Differential Equations T. Hillen, I.E. Leonard, H. van Roessel, 2019-05-15 Provides more than 150 fully solved problems for linear partial differential equations and boundary value problems. Partial Differential Equations: Theory and Completely Solved Problems offers a modern introduction into the theory and applications of linear partial differential equations (PDEs). It is the material for a typical third year university course in PDEs. The material of this textbook has been extensively class tested over a period of 20 years in about 60 separate classes. The book is divided into two parts. Part I contains the Theory part and covers topics such as a classification of second order PDEs, physical and biological derivations of the heat, wave and Laplace equations, separation of variables, Fourier series, D’Alembert’s principle, Sturm-Liouville theory, special functions, Fourier transforms and the method of characteristics. Part II contains more than 150 fully solved problems, which are ranked according to their difficulty. The last two chapters include sample Midterm and Final exams for this course with full solutions. |
| elementary partial differential equations: An Introduction to Nonlinear Partial Differential Equations J. David Logan, 2008-04-11 Praise for the First Edition: This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds. —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases An expanded bibliography that facilitates further investigation into specialized topics With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs. |
| elementary partial differential equations: Hyperbolic Partial Differential Equations Serge Alinhac, 2009-06-17 This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as do it yourself instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher. |
| elementary partial differential equations: Linear Partial Differential Equations and Fourier Theory Marcus Pivato, 2010-01-07 This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation. |
| elementary partial differential equations: Partial Differential Equations Walter A. Strauss, 2007-12-21 Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics. |
| elementary partial differential equations: Notes on Diffy Qs Jiri Lebl, 2019-11-13 Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions. |
| elementary partial differential equations: An Elementary Treatise on Partial Differential Equations George Biddell Airy, 2007 |
| elementary partial differential equations: Elementary Differential Equations and Boundary Value Problems William E. Boyce, Richard C. DiPrima, Douglas B. Meade, 2017-08-21 Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. |
| elementary partial differential equations: Functional Analysis, Sobolev Spaces and Partial Differential Equations Haim Brezis, 2010-11-10 This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list. |
| elementary partial differential equations: Partial Differential Equations I Michael E. Taylor, 2010-10-29 The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. |
| elementary partial differential equations: Partial Differential Equations with Numerical Methods Stig Larsson, Vidar Thomee, 2008-12-05 The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. |
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