Skip to content
Register Sign in Wishlist

Advanced Mathematics for Applications


  • Date Published: January 2011
  • availability: In stock
  • format: Paperback
  • isbn: 9780521735872

£ 47.99

Add to cart Add to wishlist

Other available formats:
Hardback, eBook

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.

    • Its modular structure makes the book suitable for a variety of uses and users
    • Homework sets are available from
    • Appendix provides material that is usually covered in mathematical analysis courses (e.g. the Lebesgue integral) but is often unfamiliar to the applied mathematician
    Read more

    Reviews & endorsements

    'This carefully written book by a well-known expert in the area is also an excellent guide to the present literature, recommended as well to graduate students as to experts in the area. This volume will help the reader in getting acquainted with some mathematical aspects of the modern theory of linear and non-linear phenomena arising in relevant applications to mathematical physics.' Zentralblatt MATH

    'A truly wonderful book … The author succeeded in creating a new type of book, that many will put on their desks, and they should: beginners, physicists, advanced learners, instructors, users of maths in the sciences … A modern work, showing new ways, unusually multi-layered, applicable in many contexts and at many levels, an exciting book.' Siegfried Großmann, Philipps-Universität Marburg

    'This book admirably lays down physical and mathematical groundwork, provides motivating examples, gives access to the relevant deep mathematics, and unifies components of many mathematical areas. This sophisticated topics text, which interweaves and connects subjects in a meaningful way, gives readers the satisfaction and the pleasure of putting two and two together.' Laura K. Gross, SIAM Review

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: January 2011
    • format: Paperback
    • isbn: 9780521735872
    • length: 742 pages
    • dimensions: 247 x 173 x 36 mm
    • weight: 1.32kg
    • contains: 80 b/w illus.
    • availability: In stock
  • Table of Contents

    To the reader
    List of tables
    Part I. General Remarks and Basic Concepts:
    1. The classical field equations
    2. Some simple preliminaries
    Part II. Applications:
    3. Fourier series: applications
    4. Fourier transform: applications
    5. Laplace transform: applications
    6. Cylindrical systems
    7. Spherical systems
    Part III. Essential Tools:
    8. Sequences and series
    9. Fourier series: theory
    10. The Fourier and Hankel transforms
    11. The Laplace transform
    12. The Bessel equation
    13. The Legendre equation
    14. Spherical harmonics
    15. Green's functions: ordinary differential equations
    16. Green's functions: partial differential equations
    17. Analytic functions
    18. Matrices and finite-dimensional linear spaces
    Part IV. Some Advanced Tools:
    19. Infinite-dimensional spaces
    20. Theory of distributions
    21. Linear operators in infinite-dimensional spaces

  • Resources for

    Advanced Mathematics for Applications

    Andrea Prosperetti

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact

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

    • Advanced Calculus
    • Math Methods in Physics
    • Mathematics for Engineers and Physcists
    • Mechanical Engineering Analysis
    • Methods of Applied Math
    • Methods of Engineering Evaluation
    • Transport Phenomena
    • Visualizing Diffusion (tutorial)
  • Author

    Andrea Prosperetti, The Johns Hopkins University and University of Twente
    Andrea Prosperetti is the Charles A. Miller, Jr Professor in the Department of Mechanical Engineering at The Johns Hopkins University. He also holds the Berkhoff Chair in the Department of Applied Sciences at the University of Twente, Enschede, Netherlands.

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.