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| walter a strauss 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. |
| walter a strauss partial differential equations: An Introduction to Partial Differential Equations Michael Renardy, Robert C. Rogers, 2006-04-18 Partial differential equations are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis and algebraic topology. Like algebra, topology, and rational mechanics, partial differential equations are a core area of mathematics. This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses. This new edition features new problems throughout and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with Young-measure solutions appears. The reference section has also been expanded. |
| walter a strauss partial differential equations: Partial Differential Equations Lawrence C. Evans, 2022-03-22 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 |
| walter a strauss partial differential equations: Introduction to Partial Differential Equations Gerald B. Folland, 2020-05-05 The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout. The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics. The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators. |
| walter a strauss partial differential equations: Basic Partial Differential Equations David. Bleecker, 2018-01-18 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. |
| walter a strauss 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. |
| walter a strauss partial differential equations: Partial Differential Equations: An Introduction, 2e Student Solutions Manual Julie L. Levandosky, Steven P. Levandosky, Walter A. Strauss, 2008-02-25 Practice partial differential equations with this student solutions manual Corresponding chapter-by-chapter with Walter Strauss's Partial Differential Equations, this student solutions manual consists of the answer key to each of the practice problems in the instructional text. Students will follow along through each of the chapters, providing practice for areas of study including waves and diffusions, reflections and sources, boundary problems, Fourier series, harmonic functions, and more. Coupled with Strauss's text, this solutions manual provides a complete resource for learning and practicing partial differential equations. |
| walter a strauss 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. |
| walter a strauss partial differential equations: Partial Differential Equations Paul Garabedian, 1964 This book is intended to fill the gap between the standard introductory material on partial differential equations: separation of variables, the basics of the second-order equations from mathematical physics and the advanced methods such as Sobolev spaces and fixed point theorems. |
| walter a strauss partial differential equations: Partial Differential Equations Mark S. Gockenbach, 2010-12-02 A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis. |
| walter a strauss partial differential equations: Partial Differential Equations Abdul-Majid Wazwaz, 2002-01-01 This text gathers, revises and explains the newly developed Adomian decomposition method along with its modification and some traditional techniques. |
| walter a strauss partial differential equations: A Very Applied First Course in Partial Differential Equations Michael K. Keane, 2002 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. |
| walter a strauss partial differential equations: Finite Difference Schemes and Partial Differential Equations John C. Strikwerda, 1989-09-28 |
| walter a strauss partial differential equations: Elementary Partial Differential Equations with Boundary Value Problems Larry C. Andrews, 1986 |
| walter a strauss partial differential equations: Computational Differential Equations Kenneth Eriksson, 1996-09-05 This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications. |
| walter a strauss partial differential equations: Nonlinear Wave Equations Walter A. Strauss, 1990-01-12 The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course. |
| walter a strauss partial differential equations: Numerical Analysis of Partial Differential Equations Charles A. Hall, Thomas A. Porsching, 1990 |
| walter a strauss partial differential equations: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems Richard Haberman, 2013-10-03 This text emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Greenês functions, and transform methods. This text is ideal for students in science, engineering, and applied mathematics. |
| walter a strauss partial differential equations: Global Dynamics Above the Ground State Energy for the Combined Power-Type Nonlinear Schrödinger Equations with Energy-Critical Growth at Low Frequencies Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, Hayato Nawa, 2021-11-16 View the abstract. |
| walter a strauss partial differential equations: Recent Advances in Scientific Computing and Applications Jichun Li, Hongtao Yang, Eric Alexander Machorro, 2013-04-24 This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications. |
| walter a strauss partial differential equations: Partial Differential Equations Robert C. McOwen, 1996 Designed to bridge the gap between graduate-level texts in partial differential equations and the current literature in research journals, this text introduces students to a wide variety of more modern methods - especially the use of functional analysis - which has characterized much of the recent development of PDEs. *Covers the modern, functional analytic methods in use today -- especially as they pertain to nonlinear equations. *Maintains mathematical rigor and generality whenever possible -- but not at the expense of clarity or concreteness. *Offers a rapid pace -- with some proofs and applications relegated to exercises. *Unlike other texts -- which start with the treatment of second-order equations -- begins with the method of characteristics and first-order equations, with an emphasis in its constructive aspects. *Introduces the methods by emphasizing important applications. *Illustrates topics with many figures. *Contains nearly 400 exercises, most with hints or solutions. *Provides chapter summaries. *Lists references for further reading. |
| walter a strauss partial differential equations: Partial Differential Equations and Boundary Value Problems Nakhlé H. Asmar, 2000 For introductory courses in PDEs taken by majors in engineering, physics, and mathematics. Packed with examples, this text provides a smooth transition from a course in elementary ordinary differential equations to more advanced concepts in a first course in partial differential equations. Asmar's relaxed style and emphasis on applications make the material understandable even for students with limited exposure to topics beyond calculus. This computer-friendly text encourages the use of computer resources for illustrating results and applications, but it is also suitable for use without computer access. Additional specialized topics are included that are covered independently of each other and can be covered by instructors as desired. |
| walter a strauss partial differential equations: Partial Differential Equations of Mathematical Physics Tyn Myint U., 1980 |
| walter a strauss partial differential equations: Differential Equations: From Calculus to Dynamical Systems Virginia W. Noonburg, 2019-01-24 A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme. Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature. |
| walter a strauss partial differential equations: Elementary Applied Partial Differential Equations Richard Haberman, 1998 |
| walter a strauss partial differential equations: Singular and Degenerate Cauchy Problems , 1977-01-13 In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering |
| walter a strauss partial differential equations: Numerical Methods for Ordinary Differential Equations J. C. Butcher, 2004-08-20 This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. This book is...an indispensible reference for any researcher.-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography. |
| walter a strauss partial differential equations: Solutions Manual to accompany Ordinary Differential Equations Michael D. Greenberg, 2012-10-09 Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. |
| walter a strauss 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. |
| walter a strauss partial differential equations: Introduction to Ordinary Differential Equations Albert L. Rabenstein, 2014-05-12 Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation. |
| walter a strauss 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. |
| walter a strauss partial differential equations: Schaum's Outline of Theory and Problems of Partial Differential Equations Paul Du Chateau, 1986 |
| walter a strauss partial differential equations: Nonlinear Evolution Equations Michael G. Crandall, 1978 This volume constitutes the proceedings of the Symposium on Nonlinear Evolution Equations held in Madison, October 17-19, 1977. The thirteen papers presented herein follow the order of the corresponding lectures. This symposium was sponsored by the Army Research Office, the National Science Foundation, and the Office of Naval Research. |
| walter a strauss partial differential equations: Elementary Differential Equations and Boundary Value Problems William E. Boyce, Richard C. DiPrima, 2015 |
| walter a strauss partial differential equations: Elements of Partial Differential Equations Ian N. Sneddon, 1988 |
| walter a strauss partial differential equations: Partial Differential Equations: An Introduction, 2e Student Solutions Manual Julie L. Levandosky, Steven P. Levandosky, Walter A. Strauss, 2008-02-25 Practice partial differential equations with this student solutions manual Corresponding chapter-by-chapter with Walter Strauss's Partial Differential Equations, this student solutions manual consists of the answer key to each of the practice problems in the instructional text. Students will follow along through each of the chapters, providing practice for areas of study including waves and diffusions, reflections and sources, boundary problems, Fourier series, harmonic functions, and more. Coupled with Strauss's text, this solutions manual provides a complete resource for learning and practicing partial differential equations. |
| walter a strauss partial differential equations: Partial Differential Equations András Vasy, 2015-12-21 This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the features one wants without the overhead of measure theory. There is additional material provided for readers who would like to learn more than the core material, and there are numerous exercises to help solidify one's understanding. The text should be suitable for advanced undergraduates or for beginning graduate students including those in engineering or the sciences. |
| walter a strauss partial differential equations: Transforms and Partial Differential Equations M. S. VIJAYARAJ, S. SURESHSUGUMAR, G. AYYANAR, 2025-03-31 This book covers the various mathematical techniques and tools, to solve partial differential equations in a simple manner. The Fourier series, Fourier transform and Z transforms are also covered. The book helps to solve complex problems in engineering, physics and various scientific disciplines. |
| walter a strauss partial differential equations: Elements of Partial Differential Equations Pavel Drábek, Gabriela Holubová, 2008-07-16 This textbook presents a first introduction to 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. An elementary introduction to the basic principles of partial differential equations. With many illustrations. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics. |
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