Download or read book A Course on Partial Differential Equations written by Walter Craig and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Does entropy really increase no matter what we do? Can light pass through a Big Bang? What is certain about the Heisenberg uncertainty principle? Many laws of physics are formulated in terms of differential equations, and the questions above are about the nature of their solutions. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view. In addition to the three principal examples of the wave equation, the heat equation, and Laplace's equation, the book has chapters on dispersion and the Schrödinger equation, nonlinear hyperbolic conservation laws, and shock waves. The book covers material for an introductory course that is aimed at beginning graduate or advanced undergraduate level students. Readers should be conversant with multivariate calculus and linear algebra. They are also expected to have taken an introductory level course in analysis. Each chapter includes a comprehensive set of exercises, and most chapters have additional projects, which are intended to give students opportunities for more in-depth and open-ended study of solutions of partial differential equations and their properties.
Download or read book A Basic Course in Partial Differential Equations written by Qing Han and published by American Mathematical Soc.. This book was released on 2011 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory graduate course on partial differential equations. Han focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In particular, Han emphasizes a priori estimates throughout the text, even for those equations that can be solved explicitly. Such estimates are indispensable tools for proving the existence and uniqueness of solutions to PDEs, being especially important for nonlinear equations. The estimates are also crucial to establishing properties of the solutions, such as the continuous dependence on parameters. Han's book is suitable for students interested in the mathematical theory of partial differential equations, either as an overview of the subject or as an introduction leading to further study.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Partial Differential Equations written by Lawrence C. Evans and published by American Mathematical Society. This book was released on 2022-03-22 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. … Evans' book is evidence of his mastering of the field and the clarity of presentation. —Luis Caffarelli, University of Texas It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations … Every graduate student in analysis should read it. —David Jerison, MIT I usePartial Differential Equationsto prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's … I am very happy with the preparation it provides my students. —Carlos Kenig, University of Chicago Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge … An outstanding reference for many aspects of the field. —Rafe Mazzeo, Stanford University
Download or read book A Very Applied First Course in Partial Differential Equations written by Michael K. Keane and published by . This book was released on 2002 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Journey Into Partial Differential Equations written by William O. Bray and published by Jones & Bartlett Publishers. This book was released on 2012 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the International Series in Mathematics Ideal for the 1-term course, A Journey into Partial Differential Equations provides a solid introduction to PDEs for the undergraduate math, engineering, or physics student. Discussing underlying physics, concepts and methodologies, the text focuses on the classical trinity of equations: the wave equation, heat/diffusion equation, and Laplace's equation. Bray provides careful treatment of the separation of variables and the Fourier method, motivated by the geometrical notion of symmetries and places emphasis on both the qualitative and quantitative methods, as well as geometrical perspectives. With hundred of exercises and a wealth of figures, A Journey into Partial Differential Equations proves to be the model book for the PDE course.
Download or read book A Concise Course on Stochastic Partial Differential Equations written by Claudia Prévôt and published by Springer. This book was released on 2007-05-26 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material is included in appendices.
Download or read book An Introduction to Partial Differential Equations written by Michael Renardy and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.
Download or read book Partial Differential Equations and Boundary Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Partial Differential Equations in Action written by Sandro Salsa and published by Springer. This book was released on 2015-04-24 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Partial Differential Equations for Environmental Scientists and Engineers written by Daniel R. Lynch and published by Springer Science & Business Media. This book was released on 2006-06-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.
Download or read book Beginning Partial Differential Equations written by Peter V. O'Neil and published by John Wiley & Sons. This book was released on 2014-05-07 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible, combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger’s equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is organized around four themes: methods of solution for initial-boundary value problems; applications of partial differential equations; existence and properties of solutions; and the use of software to experiment with graphics and carry out computations. With a primary focus on wave and diffusion processes, Beginning Partial Differential Equations, Third Edition also includes: Proofs of theorems incorporated within the topical presentation, such as the existence of a solution for the Dirichlet problem The incorporation of MapleTM to perform computations and experiments Unusual applications, such as Poe’s pendulum Advanced topical coverage of special functions, such as Bessel, Legendre polynomials, and spherical harmonics Fourier and Laplace transform techniques to solve important problems Beginning of Partial Differential Equations, Third Edition is an ideal textbook for upper-undergraduate and first-year graduate-level courses in analysis and applied mathematics, science, and engineering.
Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou and published by Courier Corporation. This book was released on 2012-04-20 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Partial Differential Equations written by I. G. Petrovsky and published by Courier Corporation. This book was released on 2012-12-13 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.
Download or read book Ordinary and Partial Differential Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2008-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
Download or read book Linear Partial Differential Equations for Scientists and Engineers written by Tyn Myint-U and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.
Download or read book Basic Partial Differential Equations written by David. Bleecker and published by CRC Press. This book was released on 2018-01-18 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.
