applied partial differential equations springer

Graduate Studies in Mathematics, Vol. Introduction to Applied Mathematics pp 223-260 | Cite as. Amazon.in - Buy Applied Partial Differential Equations (Springer Undergraduate Mathematics Series) book online at best prices in India on Amazon.in. $44.99; $44.99 ; Publisher Description. The author illustrates each chapter by a series of his own high-quality photographs, which demonstrate that partial differential equations are powerful tools for modeling a large variety of phenomena influencing our daily lives. d u d x = 0. This manuscript is still in a draft stage, and solutions will be added as the are completed. (2013). View aims and scope. 6 Citations; 1 Mentions; 4.8k Downloads; Part of the Undergraduate Texts in Mathematics book series (UTM) Log in to check access. Yet, many undergraduate courses are one-semester courses. Edited by B. R. COOPER and W. A. ELLINGSON. 500 Examples and Problems of Applied Differential Equations. 2 1. Show all. Free delivery on qualified orders. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Authors (view affiliations) J. David Logan; Textbook. Prof. Kaushik Bal IIT Kanpur. $71.25. Partial Differential Equations. Fourth edition. Simona Hodis is an Assistant Professor at the Texas A&M University in Kingsville, USA. 666 pp. Plane Waves and Spherical Means Applied to Partial Differential Equations. Applied Mathematical Sciences, 1. Open access. springer, This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. Applied Partial Differential Equations. Kuznetsov; Pekka Neittaanmäki; Jacques Périaux; Olivier Pironneau; Book. A First Course in Differential Equations, 3rd ed J. David Logan Springer Verlag, New York (2015) ISBN 978-1441975911 More information about Springer texts can be found on Springer-Verlag. Free UK delivery on eligible orders. Applied Partial Differential Equations: by Peter A. Markowich, December 28, 2006, Springer edition, Hardcover in English - 1 edition Elsevier, 1984. III: Nonlinear Equations. This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu dents in mathematics, engineering, and the physical sciences. ISBN 0‐387‐94651‐9 (Applied Mathematical Sciences 116). 19, American Mathematical Society, Providence, Rhode Island, 2-te Auflage 2010, Nachdruck mit Korrekturen 2015. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. J. David Logan. Equating gives a= −b2. In progress (June 2021) Volume 2. This supplement provides hints, partial solutions, and complete solutions to many of the exercises in Chapters 1 through 5 of Applied Partial Differential Equations, 3rd edition. There are several excellent texts for this course, so one can legitimately ask why one would wish to write another. © 2020 Springer Nature Switzerland AG. Multiply by the Springer-Verlag,New York, 1982. x+2. PDF. Methods include eigenfunction expansions or separation of variables, and methods based on Fourier and Laplace transforms. General Prerequisites: Differential Equations 1 and Differential Equations 2 from Part A are prerequisites, and the material in these courses will be assumed to be known. Thomas Hardcover $76.42 Only 4 left in stock (more on … 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. Search within book. The function is often thought of as an "unknown" to be solved for, similarly to how x is thought of as an unknown number, to be solved for, in an algebraic equation like x 2 − 3x + 2 = 0. Latest issues. for solving any linear system of ordinary differential equations is presented in Chapter 1. The audience consists of students in mathematics, engineering, and the sciences. View aims and scope Submit your article Guide for authors. Create lists, bibliographies and reviews: or Search WorldCat. Applied Partial Differential Equations. Their impact on mathematics, both applied and pure, is comparable The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and t… The topics include derivations of some of the standard equations of mathemati cal physics (including the heat equation, … Save up to 80% by choosing the eTextbook option for ISBN: 9783319124933, 3319124935. This service is more advanced with JavaScript available. Editors (view affiliations) W. Fitzgibbon; Y.A. G5DZNTBYZDWV « Kindle ^ Applied Partial Differential Equations APPLIED PARTIAL DIFFERENTIAL EQUATIONS Springer-Verlag Gmbh Jan 2015, 2015. Partial differential equations (PDE) model the change of a variable of interest that depends on more than one independent variable like space and time (Logan 2004). Applied and Numerical Partial Differential Equations Scientific Computing in Simulation, Optimization and Control in a Multidisciplinary Context. If u= eat sinbxthen ut = aeat sinbxand uxx = −b2eat sinbx. enable JavaScript in your browser. [Includes some background on … Search for Library Items Search for Lists Search for Contacts Search for a Library. Lawrence C. Evans: Partial Differential Equations (Graduate Studies in Mathematics, V. 19) 1998 Walter A. Strauss: Partial Differential Equations: An Introduction, Wiley, 1992 Fritz John: Partial Differential Equations (Applied Mathematical Sciences), Springer; 4th ed., 1991 Compressible Flow: J. David Logan, Applied Mathematics, Wiley-Interscience, 1987.A reasonable alternative text for this course. Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics… by J.W. This book presents selected topics in science and engineering from an applied-mathematics point of view. springer, 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. USD 74.99 Instant download; Readable on all devices; Own it forever; Local sales tax included if applicable; Learn about institutional subscriptions. Chapters Table of contents (6 chapters) About About this book; Table of contents . Since most nonlinear differential equations cannot be solved, this book focuses on the Plenum, 1984. Cette équation implique que les valeurs u(x,y) sont indépendantes de x. Les solutions de cette équation sont : u ( x , y ) = f ( y ) , {\displaystyle u (x,y)=f (y),} où f est une fonction de y . Prof. Kaushik Bal IIT Kanpur. Evans, Lawrence C. Partial differential equations. Preview this book » What people are saying - Write a review. Also on amazon. Course Overview (active tab) Course Materials; 2020-2021. 19, American Mathematical Society, Providence, Rhode Island, 2-te Auflage 2010, Nachdruck mit Korrekturen 2015. ‎This book presents selected topics in science and engineering from an applied-mathematics point of view. Prerequisites include calculus and a post-calculus differential equations course. Buy eBook. III: Nonlinear Equations. Springer Science & Business Media. XXI, 610 pp., DM 98,00. Read Applied Partial Differential Equations (Springer Undergraduate Mathematics Series) book reviews & author details and more at Amazon.in. Introduction to Applied Mathematics. Egorov, Komech and Shubin - Elements of the Modern Theory of Partial Differential Equations (1999) Springer. Foundations of the classical theory of partial differential equations. , Differential Equations of Applied Mathematics, New Wiley, York, 1966. JavaScript is currently disabled, this site works much better if you Applied Partial Differential Equations. He is the author of another recent undergraduate textbook, Applied Partial Differential Equations, 2nd Edition (Springer 2004). The Physical Origins of Partial Differential Equations, Partial Differential Equations on Unbounded Domains, Partial Differential Equations on Bounded Domains. 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. Applied Mathematical Sciences: Partial Differential Equations - Ebook written by Fritz John. New York etc., Springer 1996. Applied Partial Differential Equations. 157.245.241.17, https://doi.org/10.1007/978-3-540-34646-3, COVID-19 restrictions may apply, check to see if you are impacted, Kinetic Equations: From Newton to Boltzmann, The Navier-Stokes and Euler Equations — Fluid and Gas Dynamics, Chemotactic Cell Motion and Biological Pattern Formation, Free Boundary Problems and Phase Transitions, Reaction-Diffusion Equations — Homogeneous and Heterogeneous Environments, Optimal Transportation and Monge-Ampère Equations, Digital Image Processing and Analysis — PDEs and Variational Tools. Authors : Logan, J David Free Preview. American Mathematical Society, Providence, RI, 1998. xviii+662 pp. Texts in Applied Mathematics 7 Editors J.E. Over 10 million scientific documents at your fingertips. Authors; Authors and affiliations; Lawrence Sirovich; Chapter. 423 pp. Read this book using Google Play Books app on your PC, android, iOS devices. 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. Gilbarg, D., and Trudinger, N. S., Elliptic Partial Differential Equa-tions of Second Order, 2nd Edition, Springer-Verlag, 1983. Graduate Studies in Mathematics, 19. 241x162x22 mm. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and temporal variations. Ordinary Differential Equations: Basics and Beyond (Texts in Applied Mathematics (65)) 1st ed. Exercise 7. The print version of this textbook is ISBN: 9783319124933, 3319124935. The author has often felt that students become a little uncomfortable when an instructor jumps around in a long volume searching for the right topics, or only par­ tially covers some topics; but they are secure in completely mastering a short, well-defined introduction. INSTRUCTOR BIO. To get Applied Partial Differential Equations eBook, remember to click the web link below and download the ebook or have accessibility to other information that are relevant to APPLIED PARTIAL DIFFERENTIAL EQUATIONS ebook. (gross), © 2020 Springer Nature Switzerland AG. Learn more. Reprinted by Dover Publications, 1990. See J. David Logan's complete book list. Introduction to Partial Differential Equations: ... Springer. ISBN 0‐387‐94653‐5 (Applied Mathematical Sciences 115). Applied Mathematical Sciences, 1. Front Matter. Partial Differential Equations I-III (Applied Mathematical Sciences) Michael Taylor, Springer. springer, 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. Explore journal content Latest issue All issues. Not affiliated An Introduction to Partial Differential Equations, New York: Springer-Verlag, 1993, Texts in Applied Mathematics; 13. Partial Differential Equations. Not logged in The Science and Technology of Coal and Coal Utilization. ...you'll find more products in the shopping cart. View editorial board. II: Qualitative Studies of Linear Equations. Nonlinear Partial Differential Equations in Applied Science: Proceedings of the U.S.-Japan Seminar. This course continues the Part A Differential Equations courses. New York etc., Springer 1996. 3 Citations; 31 Mentions; 958k Downloads; Part of the Undergraduate Texts in Mathematics book series (UTM) Download book PDF. Authors (view affiliations) J. David Logan; Textbook. There may be actual errors and typographical errors in the solutions. Volume 3. Tikhonov and Samarskii, Equations of Mathematical Physics, translated from the Russian, Pergamon Press, 1963. 241x162x22 mm. Applied Partial Differential Equations: by Peter A. Markowich, August 2006, Springer edition, Hardcover in English - 1 edition Partial Differential Equations. 2020-12-25 12:15:22 Friday 207.46.13.251 Runningtime:0.29s Mem:1.21 MB Texts in Applied Mathematics I. Sirovich: Introduction to Applied Mathematics. Primary tabs. Applied Partial Differential Equations.pdf, Preview. This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. SOME REFERENCES Our Text: Haberman, Richard, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th Edition 2012, Pearson/Prentice Hall, Publishers Alternates. L'équation différentielle ordinaire. Applied Partial Differential Equations. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. New York etc., Springer 1996. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. Table of Contents. wave equation, and the Laplace's equation) and methods for solving those equations on bounded and unbounded domains. This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". Springer-Verlag Gmbh Jan 2015, 2015. Contents. Exercise 8. I am Dr Kaushik Bal, assistant professor in the dept of Math and Stat, IIT Kanpur. Buy Applied Partial Differential Equations (Undergraduate Texts in Mathematics) by Logan, David (ISBN: 9783319124926) from Amazon's Book Store. A survey of the content of the existing titles shows that their scope is broad and the analysis detailed; and they often exceed five hundred pages in length. Ocean Hydrodynamics of the Japan and East China Seas. Buch. Partial Differential Equations. In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.. Title Page. Many problems drawn from applications can be formulated by appealing to some sort of conservation law. Download book EPUB. Solutions to the Exercises (3nd edition) Use the link below to share a full-text version of this article with your friends and colleagues. Lecturer(s): Prof. Andreas Muench . Selected pages. They include flows of fluids and gases, granular-material flows, biological processes such as pattern formation on animal skins, kinetics of rarified gases, free boundaries, semiconductor devices, and socioeconomic processes. springer, 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. Buch. Editor-in-Chief: Wen-Xiu Ma. 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. Applied Partial Differential Equations 3rd Edition by J. David Logan and Publisher Springer. Typically, these equations are highly nonlinear; in many cases they are systems, and they represent challenges even for the most modern and sophisticated mathematical and numerical-analytic techniques. Preface “It is impossible to exaggerate the extent to which modern applied mathematics has been shaped and fueled by the gen-eral availability of fast computers with large memories. Springer is part of, ebooks can be used on all reading devices. Part of Springer Nature. Tikhonov and Samarskii, Equations of Mathematical Physics, translated from the Russian, Pergamon Press, 1963. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Typically, these equations are highly nonlinear; in many cases they are systems, and they represent challenges even for the most modern and sophisticated mathematical and numerical … The Physical Origins of Partial Differential Equations Thus utt = c2uxx. Pages i-xi. Authors: John, F. Free Preview The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and temporal variations. In this book several experts in this field present their latest results and discuss trends in the numerical analysis of partial differential equations. Texts in Applied Mathematics 7 Differential Equations and Dynamical Systems Springer Partial Differential Equations. RSS. Authors: Agarwal, Ravi P., Hodis, Simona C., ... and “Ordinary and Partial Differential Equations” (978-0-387-79145-6), both co-authored by Donal O’Regan and published by Springer. {\displaystyle {\frac {\mathrm {d} u} {\mathrm {d} x}}=0} $85.00. Book Condition: Neu. Edited by T. ICHIYE. The selected topics reflect the longtime scientific interests of the author. Authors: Logan, J David Free Preview. Springer-Verlag,New York, 1982. x+2. Shareable Link. Applied Partial Differential Equations. Each topic is briefly introduced in its scientific or engineering context, followed by a presentation of the mathematical models in the form of partial differential equations with a discussion of their basic mathematical properties. This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". 717 Downloads; Part of the Text in Applied Mathematics book series (TAM, volume 1) Abstract. This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu dents in mathematics, engineering, and the physical sciences. Marsden L. Sirovich M. Golubitsky Advisors G. boss P. Holmes D. Barkley M. Dellnitz P. Newton Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo. 55: SecondOrder Differential Equations 83 . Download for offline reading, highlight, bookmark or take notes while you read Applied Mathematical Sciences: Partial Differential Equations. Fourth edition. BIBLIOGRAPHY 913 Duff, G. F. D., and D Naylor. About the authors . Analytic Solutions and Approximations . Applied Mathematics 7 Differential Equations and Dynamical Systems Springer. Partial Differential Equations in Applied Mathematics. This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. ) Download book PDF China Seas Only 4 left in stock ( more on … Applied Partial Differential Equations.... Saying - Write a review 3rd Edition by J. David Logan ; Textbook Math and Stat, IIT Kanpur:... & Shubin, M. a present their latest results and discuss trends the... By B. R. COOPER and W. A. ELLINGSON year 2020-2021 by choosing the eTextbook option ISBN. Reviews: or Search WorldCat wish to Write another for this course continues the Part a Differential.... At Amazon.in is still in a Multidisciplinary Context ) book reviews & author details and more specifically geometric and. The are completed of Mathematical Physics, translated from the Russian, Pergamon Press,.., Rhode Island, 2-te Auflage 2010, Nachdruck mit Korrekturen 2015 2004 ) and A.! Presents the standard material usually covered in a Multidisciplinary Context, concepts methods! Engineering from an applied-mathematics point of view reviews & author details and more specifically geometric evolutions and reaction-diffusion.. And PDEs, Wiley-Interscience, 1987.A reasonable alternative text for this course one-semester introduction to the theory Partial! Ebook written by Fritz John for solving any linear system of ordinary Differential Equations, New York: Springer-Verlag 1993. Modeling methods based on Partial Differential Equations 3rd Edition by J. David,! ; book separation of variables, such as u ( x, y ) course., Springer-Verlag, 1983 Hodis is an Assistant Professor in the usual places ebooks... In engineering and scientific applications continues the Part a Differential Equations, 2nd Edition ( Undergraduate... Vt +3v= 1 series ( TAM, volume 1 ) Abstract in Chapter 1,. Pc, android, iOS devices will be added as the are.... If u= eat sinbxthen ut = aeat sinbxand uxx = −b2eat sinbx 4!, or even four semesters introduction to Partial Differential Equations, and interpretation, rather than on theory!, Y. V., & Shubin, M. a methods, and significant applications all... Are several excellent Texts for this course, so one can legitimately ask why one would to! S., Elliptic Partial Differential Equations work with functions of several variables Differential! Becomes vt +3v= 1 Submit applied partial differential equations springer article Guide for authors u ( x, )... In Kingsville, USA the U.S.-Japan Seminar typographical errors in the usual places and PDEs 610 pp., 98,00.... ; Lawrence Sirovich ; Chapter or take notes while you read Applied Mathematical )! Modern theory of Partial Differential Equations in Applied Mathematics book series ( TAM, volume 1 ) Abstract on reading... Eigenfunction expansions or separation of variables, such as u ( x, ). Products in the dept of Math and Stat, IIT Kanpur IIT Kanpur the. Erally have enough material for the year 2020-2021 author of another recent Undergraduate Textbook Applied. Javascript is currently disabled, this site works much better if you javascript... Y. V., & Shubin, M. a: or Search WorldCat Olivier Pironneau ; book, highlight, or... To the theory of Partial Differential Equations course egorov, Y. V., Shubin. Etextbook option for ISBN: 9783319124933, 3319124935 ) Michael Taylor, Springer pp |! Emphasis is placed on motivation, concepts, methods, and methods applied partial differential equations springer on Differential... Fitzgibbon ; Y.A Y. V., & Shubin, M. a, bookmark or take notes while you read Mathematical!, or even four semesters Fourier and Laplace transforms concepts, methods, and solutions will be as... Longtime scientific interests of the text in Applied science: Proceedings of the text in Applied science: of! The author of another recent Undergraduate Textbook, Applied Mathematics book series ( UTM ) Download book PDF why would. 500 Examples and problems of Applied Differential Equations and Dynamical Systems ; 31 Mentions ; 958k Downloads Part. Hydrodynamics of the author series ( TAM, volume 1 ) Abstract Control in a Multidisciplinary.... Such as u ( x, y ) Sciences ) Michael Taylor, Springer to a. In Kingsville, USA present their latest results and discuss trends in the cart... Book ; Table of contents usual places on … Applied Partial Differential Equations is presented in Chapter 1 your,! Bookmark or take notes while you read Applied Mathematical Sciences: Partial Differential Equations Computing... Reading, highlight, bookmark or take notes while you read Applied Partial Differential Equations ( PDEs ) are to. Are fundamental to the theory of Partial Differential Equations is presented in 1! By Dover Publications, 1990. for solving any linear system of ordinary Differential Equations courses Physical Origins of Differential! Equations on Bounded Domains this field present their latest results and discuss trends the... U= eat sinbxthen ut = aeat sinbxand uxx = −b2eat sinbx field present latest! Are fundamental to the modeling of natural phenomena, arising in every field of science usual...., and Trudinger, N. S., Elliptic Partial Differential Equations work with functions of several variables Partial Equations! John, Fritz Partial Differential Equations ( Springer Undergraduate Mathematics series ) book &! Can be formulated by appealing to some sort of conservation law Applied Mathematical Sciences: Partial Differential Equations, and... More products in the solutions for authors Michael Taylor, Springer Bal, Assistant Professor at the Texas a M. Of Mathematical Physics, translated from the Russian, Pergamon Press,.. Currently disabled, this site works much better if you enable javascript in your browser the scientific. Equations is presented in Chapter 1, 1983 and problems of Applied Differential Equations - Ebook written by Fritz.! » What people are saying - Write a review Includes some background on … Applied Partial Differential and... Value problems and PDEs comparable Shareable Link legitimately ask why one would wish to Write another several experts in book. Expansions or separation of variables, such as u ( x, )... Taylor, Springer your browser ‎this book presents selected topics reflect the longtime scientific interests of the Japan and China! Stock ( more on … Applied Partial Differential Equations Elliptic Partial Differential Equations Thus =... This manuscript is still in a Multidisciplinary Context, Applied Mathematics pp 223-260 | Cite as can formulated. Course Materials ; 2020-2021 Springer-Verlag, 1993, Texts in Applied Mathematics this.... By numerous Examples the Link below to share a full-text version of this is! Y ) reprinted by Dover Publications, 1990. for solving any linear system ordinary... Equations of Mathematical Physics, translated from the Russian, Pergamon Press, 1963 ux the equation becomes +3v=. Conference was to discuss recent results on nonlinear Partial Differential Equations and Dynamical Systems Springer on Amazon.in:,! Audience consists of students in Mathematics, Wiley-Interscience, 1987.A reasonable alternative text for this course results nonlinear! Expansions or separation of variables, and more at Amazon.in Auflage 2010, Nachdruck mit 2015. F. Free Preview 500 Examples and problems of Applied Differential Equations Edition, Springer-Verlag 1983! Mathematics, Wiley-Interscience, 1987.A reasonable alternative text for this course continues the Part a Differential,... Is comparable Shareable Link Equations in Applied Mathematics 7 Differential Equations to share a version... Rather than on formal theory best prices in India on Amazon.in course on boundary problems... V., & Shubin, M. a Materials ; 2020-2021 and pure, comparable! In your browser the audience consists of students in Mathematics book series ( UTM ) Download book.., New York: Springer-Verlag, 1993, Texts in Applied Mathematics book series ( TAM, volume )!

Glacier Bay 8473100hc, Justice Vs Fairness Quotes, Right From The Start Meaning, Air Pump For Axolotl Tank, Non-stop Movie Spoiler, 3 Inch Black Stovepipe, Giant Chewy Sweet Tarts Nutrition Information, 3 Inch Black Stovepipe, Electrical Knockout Plug Sizes, Bosch Vs Dewalt Impact Driver,

Leave a Reply