Partial Differential Equations And Boundary Value Problems With Applications
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Partial Differential Equations and Boundary Value Problems with Applications
Author | : Mark A. Pinsky |
Publsiher | : American Mathematical Soc. |
Total Pages | : 545 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9780821868898 |
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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.
Introduction to Partial Differential Equations with Applications
Author | : E. C. Zachmanoglou,Dale W. Thoe |
Publsiher | : Courier Corporation |
Total Pages | : 434 |
Release | : 1986-01-01 |
Genre | : Mathematics |
ISBN | : 9780486652511 |
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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.
Boundary Value Problems
Author | : David L. Powers |
Publsiher | : Academic Press |
Total Pages | : 516 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 9780125637381 |
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Preface -- Chapter 0. Ordinary Differential Equations -- Chapter 1. Fourier Series and Integrals -- Chapter 2. The Heat Equation -- Chapter 3. The Wave Equation -- Chapter 4. The Potential Equation -- Chapter 5. Higher Dimensions & Other Coordinates.
Partial Differential Equations and Boundary Value Problems
Author | : Nakhlé H. Asmar |
Publsiher | : Unknown |
Total Pages | : 616 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : STANFORD:36105119754997 |
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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.
Partial Differential Equations
Author | : T. Hillen,I.E. Leonard,H. van Roessel |
Publsiher | : FriesenPress |
Total Pages | : 683 |
Release | : 2019-05-15 |
Genre | : Mathematics |
ISBN | : 9781525550249 |
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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.
Boundary Value Problems for Partial Differential Equations and Applications
Author | : Jacques-Louis Lions,C. Baiocchi |
Publsiher | : Elsevier Masson |
Total Pages | : 480 |
Release | : 1993 |
Genre | : Boundary value problems |
ISBN | : UOM:39015049315693 |
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Student Solutions Manual Boundary Value Problems
Author | : David L. Powers |
Publsiher | : Academic Press |
Total Pages | : 152 |
Release | : 2009-07-13 |
Genre | : Science |
ISBN | : 9780123756640 |
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Student Solutions Manual, Boundary Value Problems
Differential Equations with Boundary Value Problems
Author | : James R. Brannan |
Publsiher | : John Wiley & Sons |
Total Pages | : 450 |
Release | : 2010-11-08 |
Genre | : Mathematics |
ISBN | : 9780470595350 |
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Unlike other books in the market, this second edition presents differential equations consistent with the way scientists and engineers use modern methods in their work. Technology is used freely, with more emphasis on modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. It also refers to larger-scale computations that computer algebra systems and DE solvers make possible. And more exercises and examples involving working with data and devising the model provide scientists and engineers with the tools needed to model complex real-world situations.