Applied partial differential equations

Bibliographic Information

Applied partial differential equations

John Ockendon ... [et al.]

Oxford University Press, 1999

  • : hard
  • : pbk

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Note

Bibliography: p. [413]-415

Includes index

Description and Table of Contents

Volume

: pbk ISBN 9780198532439

Description

Partial differential equations (PDEs) are a central concept in mathematics. Their power lies in their universality: there is a huge and ever-growing range of real-world phenomena to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This is an enthusiastically and clearly written guide to the theory and applications of PDEs. Its central aim is to set out, in an informal yet rigorous manner, a mathematical framework within which to assess any given PDE. Space is devoted as much to explicit methods of solution as to more general qualitative ideas, the most important of which is the concept of well-posedness. This attribute is vital in deciding the accuracy to which the problem can be solved numerically, and it becomes increasingly important as the power of computer software grows. Prerequisites here have been kept to a minimum: some familiarity with ordinary differential equations, functions of a single complex variable, and the calculus of functions of several real variables are all that is needed. This book is intended for final year undergraduates and graduate students in applied mathematics and engineering.

Table of Contents

  • 1. First-order scalar quasilinear equations
  • 2. First-order quasilinear systems
  • 3. Introduction to second-order scalar equations
  • 4. Hyperbolic equations
  • 5. Elliptic equations
  • 6. Parabolic equations
  • 7. Free boundary problems
  • 8. Non-quasilinear eqeuations
  • 9. Miscellaneous
Volume

: hard ISBN 9780198532446

Description

Partial differential equations are a central concept in mathematics. They arise in mathematical models whose dependent variables vary continuously as functions of several independent variables (usually space and time). Their power lies in their universality: there is a huge and ever-growing range of real-world problems to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This is an enthusiastic and clear guide to the theory and applications of PDEs. It deals with questions such as the well-posedness of a PDE problem: when is there a unique solution that changes only slightly when the input data is slightly changed? This is connected to the problem of establishing the accuracy of a numerical solution to a PDE, a problem that becomes increasingly important as the power of computer software to produce numerical solutions grows. This book is intended for final year undergraduates and graduate students in applied mathematics and engineering.

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Details

  • NCID
    BA43064825
  • ISBN
    • 019853244X
    • 0198532431
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Oxford ; New York
  • Pages/Volumes
    xi, 427 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
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