عنوان

Introduction to partial differential equations /

(Number (ISBN

3319020986

(Number (ISBN

3319020994

(Number (ISBN

9783319020983

(Number (ISBN

9783319020990

Erroneous ISBN

9783319020983

Number

b623845

Title Proper

Introduction to partial differential equations /

General Material Designation

[Book]

First Statement of Responsibility

Peter J. Olver.

Specific Material Designation and Extent of Item

1 online resource (xxv, 635 pages) :

Other Physical Details

illustrations

Series Title

Undergraduate Texts in Mathematics,

ISSN of Series

0172-6056

Text of Note

Includes bibliographical references and indexes.

Text of Note

What are Partial Differential Equations? -- Linear and Nonlinear Waves -- Fourier Series -- Separation of Variables -- Finite Differences -- Generalized Functions and Green's Functions -- Complex Analysis and Conformal Mapping -- Fourier Transforms -- Linear and Nonlinear Evolution Equations -- A General Framework for Linear Partial Differential Equations -- Finite Elements and Weak Solutions -- Dynamics of Planar Media -- Partial Differential Equations in Space.

0

Text of Note

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 solitons, 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.

Source for Acquisition/Subscription Address

Springer

International Standard Book Number

9783319020983

Differential equations, Partial-- Numerical solutions.

Mathematics.

Models, Theoretical.

Differential equations, Partial-- Numerical solutions.

MAT007000

PBKJ

Number

Edition

Class number

Class number

Olver, Peter J.

Date of Transaction

20201221082935.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

270410

Y