Partial Differential Equations I PDF Download

Author: Michael E. Taylor
Publisher: Springer Science & Business Media
ISBN: 144197055X
Category : Mathematics
Languages : en
Pages : 673

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Book Description
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.

Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467

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Book Description
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.

Author: Stanley J. Farlow
Publisher: Courier Corporation
ISBN: 0486134733
Category : Mathematics
Languages : en
Pages : 414

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Book Description
Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.

Author: Jürgen Jost
Publisher: Springer Science & Business Media
ISBN: 1461448093
Category : Mathematics
Languages : en
Pages : 416

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Book Description
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.

Author: David. Bleecker
Publisher: CRC Press
ISBN: 1351086987
Category : Mathematics
Languages : en
Pages : 1010

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Book Description
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.

Author: I. G. Petrovsky
Publisher: Courier Corporation
ISBN: 0486155080
Category : Mathematics
Languages : en
Pages : 261

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Book Description
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.

Author: Peter V. O'Neil
Publisher: John Wiley & Sons
ISBN: 1118629981
Category : Mathematics
Languages : en
Pages : 456

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Book Description
A broad introduction to PDEs with an emphasis on specializedtopics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics,Beginning Partial Differential Equations, Third Editionprovides a challenging, yet accessible, combination of techniques,applications, and introductory theory on the subjectof partialdifferential equations. The new edition offers nonstandardcoverageon material including Burger’s equation, thetelegraph equation, damped wavemotion, and the use ofcharacteristics 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 andproperties of solutions; and the use of software to experiment withgraphics and carry out computations. With a primary focus on waveand diffusion processes, Beginning Partial DifferentialEquations, Third Edition also includes: Proofs of theorems incorporated within the topicalpresentation, such as the existence of a solution for the Dirichletproblem The incorporation of Maple™ to perform computations andexperiments 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 importantproblems Beginning of Partial Differential Equations, ThirdEdition is an ideal textbook for upper-undergraduate andfirst-year graduate-level courses in analysis and appliedmathematics, science, and engineering.

Author: William O. Bray
Publisher: Jones & Bartlett Publishers
ISBN: 0763772569
Category : Mathematics
Languages : en
Pages : 334

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Book Description
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.

Author: David Colton
Publisher: Courier Corporation
ISBN: 0486138437
Category : Mathematics
Languages : en
Pages : 322

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Book Description
This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Features coverage of integral equations and basic scattering theory. Includes exercises, many with answers. 1988 edition.

Author: Thomas Hillen
Publisher: John Wiley & Sons
ISBN: 1118438434
Category : Mathematics
Languages : en
Pages : 533

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Book Description
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.