Applied Partial Differential Equations

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J. R. Ockendon
Oxford University Press, 1999 - Mathematics - 427 pages
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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- growingrange 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 aunique 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 become increasingly important as the power of computer software to produce numerical solutionsgrows.

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Contents

Introduction
1
Firstorder quasilinear systems
35
Introduction to secondorder scalar equations
75
Copyright

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About the author (1999)

John Ockendon, Lecturer, Centre for Industrial and Applied Mathematics, University of Oxford. Andrew Lacey, Department of Mathematics, Heriot-Watt University. Alexander Movchan, Department of Mathematics, University of Bath.

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