Introduction to Partial Differential Equations with Applications

Introduction to Partial Differential Equations with Applications
Author: E. C. Zachmanoglou,Dale W. Thoe
Publsiher: Courier Corporation
Total Pages: 432
Release: 2012-04-20
Genre: Mathematics
ISBN: 9780486132174

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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.

Nonlinear Partial Differential Equations with Applications

Nonlinear Partial Differential Equations with Applications
Author: Tomás Roubicek
Publsiher: Springer Science & Business Media
Total Pages: 405
Release: 2006-01-17
Genre: Mathematics
ISBN: 9783764373979

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This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

Theory and Applications of Partial Differential Equations

Theory and Applications of Partial Differential Equations
Author: Piero Bassanini,Alan R. Elcrat
Publsiher: Unknown
Total Pages: 456
Release: 2014-01-15
Genre: Electronic Book
ISBN: 1489918760

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Partial Differential Equations

Partial Differential Equations
Author: Victor Henner,Tatyana Belozerova,Alexander Nepomnyashchy
Publsiher: CRC Press
Total Pages: 298
Release: 2019-11-20
Genre: Mathematics
ISBN: 9780429804410

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Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor. This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book’s level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses. Highlights: Offers a complete first course on PDEs The text’s flexible structure promotes varied syllabi for courses Written with a teach-by-example approach which offers numerous examples and applications Includes additional topics such as the Sturm-Liouville problem, Fourier and Laplace transforms, and special functions The text’s graphical material makes excellent use of modern software packages Features numerous examples and applications which are suitable for readers studying the subject remotely or independently

Introduction to Partial Differential Equations with Applications

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.

Partial Differential Equations and Boundary Value Problems with Applications

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.

Stochastic Partial Differential Equations and Applications

Stochastic Partial Differential Equations and Applications
Author: Giuseppe Da Prato,Luciano Tubaro
Publsiher: CRC Press
Total Pages: 480
Release: 2002-04-05
Genre: Mathematics
ISBN: 0203910176

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Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.

Solving Partial Differential Equation Applications with PDE2D

Solving Partial Differential Equation Applications with PDE2D
Author: Granville Sewell
Publsiher: John Wiley & Sons
Total Pages: 224
Release: 2018-10-09
Genre: Mathematics
ISBN: 9781119507932

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Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author that can be applied to a wide variety of science and engineering problems. The equations studied include many time-dependent, steady-state and eigenvalue applications such as diffusion, heat conduction and convection, image processing, math finance, fluid flow, and elasticity and quantum mechanics, in one, two, and three space dimensions. The author begins with some simple "0D" problems that give the reader an opportunity to become familiar with PDE2D before proceeding to more difficult problems. The book ends with the solution of a very difficult nonlinear problem, which requires a moving adaptive grid because the solution has sharp, moving peaks. This important book: Describes a finite-element program, PDE2D, developed by the author over the course of 40 years Derives the ordinary and partial differential equations, with appropriate initial and boundary conditions, for a wide variety of applications Offers free access to the Windows version of the PDE2D software through the author’s website at www.pde2d.com Offers free access to the Linux and MacOSX versions of the PDE2D software also, for instructors who adopt the book for their course and contact the author at www.pde2d.com Written for graduate applied mathematics or computational science classes, Solving Partial Differential Equation Applications with PDE2D offers students the opportunity to actually solve interesting engineering and scientific applications using the accessible PDE2D.