Books in Partial differential equations

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Partial Differential Equations and Applications

• 1st Edition
• June 28, 2023
• Hong-Ming Yin
• English
• Paperback 978-0-443-18705-6

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• eBook 978-0-443-18706-3

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Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics. Beginning with very elementary PDEs, such as classical heat equations, wave equations and Laplace equations, the book focuses on concrete examples. It gives students basic skills and techniques to find explicit solutions for partial differential equations. As it progresses, the book covers more advanced topics such as the maximum principle and applications, Green’s representation, Schauder’s theory, finite-time blowup, and shock waves. By exploring these topics, students gain the necessary tools to deal with research topics in their own fields, whether proceeding in math or engineering areas.

Differential Equations with Mathematica

• 5th Edition
• January 18, 2022
• Martha L. Abell + 1 more
• English
• Paperback 978-0-12-824160-8

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• eBook 978-0-323-98436-2

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Differential Equations with Mathematica, Fifth Edition uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica’s diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica’s built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, Mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica’s outstanding graphics capabilities.

Introductory Differential Equations

• 5th Edition
• April 16, 2018
• Martha L. Abell + 1 more
• English
• eBook 978-0-12-814949-2

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Introductory Differential Equations, Fifth Edition provides accessible explanations and new, robust sample problems. This valuable resource is appropriate for a first semester course in introductory ordinary differential equations (including Laplace transforms), but is also ideal for a second course in Fourier series and boundary value problems, and for students with no background on the subject. The book provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies.

Mathematical Physics with Partial Differential Equations

• 2nd Edition
• February 26, 2018
• James Kirkwood
• English
• Paperback 978-0-12-814759-7

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• eBook 978-0-12-814760-3

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Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics—the heat equation, the wave equation and Laplace’s equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green’s functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods.

Differential Equations with Mathematica

• 4th Edition
• September 13, 2016
• Martha L. Abell + 1 more
• English
• eBook 978-0-12-804777-4

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Differential Equations with Mathematica, Fourth Edition is a supplementing reference which uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica’s diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica’s built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica’s outstanding graphics capabilities.

Analytical Solution Methods for Boundary Value Problems

• 1st Edition
• July 15, 2016
• A.S. Yakimov
• English
• Hardback 978-0-12-804289-2

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• eBook 978-0-12-804363-9

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Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods.

Nonlinear Partial Differential Equations in Engineering

• 1st Edition
• February 16, 2016
• W. F. Ames
• Richard Bellman
• English
• eBook 978-1-4832-2292-9

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Nonlinear Partial Differential Equations in Engineering discusses methods of solution for nonlinear partial differential equations, particularly by using a unified treatment of analytic and numerical procedures. The book also explains analytic methods, approximation methods (such as asymptotic processes, perturbation procedures, weighted residual methods), and specific numerical procedures associated with these equations. The text presents exact methods of solution including the quasi-linear theory, the Poisson-Euler-Darboux equation, a general solution for anisentropic flow, and other solutions obtained from ad hoc assumptions. The book explores analytic methods such as an ad hoc solution from magneto-gas dynamics. Noh and Protter have found the Lagrange formulation to be a convenient vehicle for obtaining "soft" solutions of the equations of gas dynamics. The book notes that developing solutions in two and three dimensions can be achieved by employing Lagrangian coordinates. The book explores approximate methods that use analytical procedures to obtain solutions in the form of functions approximating solutions of nonlinear problems. Approximate methods include integral equations, boundary theory, maximum operation, and equations of elliptic types. The book can serve and benefit mathematicians, students of, and professors of calculus, statistics, or advanced mathematics.

Numerical Methods for Partial Differential Equations

• 1st Edition
• December 1, 2015
• Sandip Mazumder
• English
• Paperback 978-0-12-849894-1

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• eBook 978-0-12-803504-7

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Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses.

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations

• 1st Edition
• October 1, 2015
• Johnny Henderson + 1 more
• English
• Paperback 978-0-12-803652-5

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• eBook 978-0-12-803679-2

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Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.

Introductory Differential Equations

• 4th Edition
• July 22, 2014
• Martha L. Abell + 1 more
• English
• eBook 978-0-12-417282-1

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Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. The book provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. It follows a traditional approach and includes ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide array of exercises ranging from straightforward to challenging. There are also new applications and extended projects made relevant to everyday life through the use of examples in a broad range of contexts. This book will be of interest to undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering.