Linear partial differential equations and Fourier theory / Marcus Pivato.

Format:

Book

Author/Creator:

Pivato, Marcus, 1974- author.

Language:

English

Subjects (All):

Differential equations, Partial.

Differential equations, Linear.

Fourier transformations.

Physical Description:

1 online resource (xxvii, 601 pages) : digital, PDF file(s).

Other Title:

Linear Partial Differential Equations & Fourier Theory

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

Summary:

Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to abstraction - the most powerful tool for solving problems - rather than simply drilled in the practice of imitating solutions to given examples. The book is therefore ideal for students in mathematics and physics who require a more theoretical treatment than given in most introductory texts. Also designed with lecturers in mind, the fully modular presentation is easily adapted to a course of one-hour lectures, and a suggested 12-week syllabus is included to aid planning. Downloadable files for the hundreds of figures, hundreds of challenging exercises, and practice problems that appear in the book are available online, as are solutions.

Contents:

Suggested 12-week syllabus

Heat and diffusion

Waves and signals

Quantum mechanics

Linear partial differential equations

Classification of PDEs and problem types

Some functional analysis

Fourier sine series and cosine series

Real Fourier series and complex Fourier series

Multidimensional Fourier series

Proofs of the Fourier convergence theorems

Boundary value problems on a line segment

Boundary value problems on a square

Boundary value problems on a cube

Boundary value problems in polar coordinates

Eigenfunction methods on arbitrary domains

Separation of variables

Impulse-response methods

Applications of complex analysis

Fourier transforms

Fourier transform solutions to PDEs

Appendix A: Sets and functions

Appendix B: Derivatives

notation

Appendix C: Complex numbers

Appendix D: Coordinate systems and domains

Appendix E: Vector calculus

Appendix F: Differentiation of function series

Appendix G: Differentiation of integrals

Appendix H: Taylor polynomials.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 581-583) and indexes.

ISBN:

1-107-20571-9

1-282-65311-3

0-511-76908-3

9786612653117

0-511-81018-0

0-511-76992-X

0-511-76685-8

0-511-76546-0

0-511-76824-9

0-511-76461-8

OCLC:

645098190