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Linear Partial Differential Equations and Fourier Theory

$60.99 (X)

  • Date Published: February 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521136594

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About the Authors
  • 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.

    • Online resources include full-colour and three-dimensional illustrations, practice problems and complete solutions for instructors
    • Includes a suggested twelve-week syllabus and lists recommended prerequisites for each section
    • Contains nearly 400 challenging theoretical exercises
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    Reviews & endorsements

    "I love this bare-handed approach to PDEs. Pivato has succeeded in creating a deeply engaging introductory PDE text; confidence building hands-on work and theory are woven together in a way that appeals to the intuition. Add to that the truly reasonable price, and you have the hands down winner in the field of introductory PDE books. The next time I teach introductory PDE's, I will use Pivato's new text."
    Kevin R. Vixie, Washington State University

    "The book comprises a well-organized exposition of a lot of useful material..."
    Gerald B. Folland, SIAM Review

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    Product details

    • Date Published: February 2010
    • format: Paperback
    • isbn: 9780521136594
    • length: 630 pages
    • dimensions: 245 x 173 x 27 mm
    • weight: 1.22kg
    • contains: 150 b/w illus. 380 exercises
    • availability: Available
  • Table of Contents

    What's good about this book?
    Suggested twelve-week syllabus
    Part I. Motivating Examples and Major Applications:
    1. Heat and diffusion
    2. Waves and signals
    3. Quantum mechanics
    Part II. General Theory:
    4. Linear partial differential equations
    5. Classification of PDEs and problem types
    Part III. Fourier Series on Bounded Domains:
    6. Some functional analysis
    7. Fourier sine series and cosine series
    8. Real Fourier series and complex Fourier series
    9. Mulitdimensional Fourier series
    10. Proofs of the Fourier convergence theorems
    Part IV. BVP Solutions Via Eigenfunction Expansions:
    11. Boundary value problems on a line segment
    12. Boundary value problems on a square
    13. Boundary value problems on a cube
    14. Boundary value problems in polar coordinates
    15. Eigenfunction methods on arbitrary domains
    Part V. Miscellaneous Solution Methods:
    16. Separation of variables
    17. Impulse-response methods
    18. Applications of complex analysis
    Part VI. Fourier Transforms on Unbounded Domains:
    19. Fourier transforms
    20. Fourier transform solutions to PDEs

  • Resources for

    Linear Partial Differential Equations and Fourier Theory

    Marcus Pivato

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  • Instructors have used or reviewed this title for the following courses

    • Advanced Mathematics
    • Selected Topics in Applied Mathematics
  • Author

    Marcus Pivato, Trent University, Peterborough, Ontario
    Marcus Pivato is Associate Professor in the Department of Mathematics at Trent University in Peterborough, Ontario.

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