Applied partial differential equations
著者
書誌事項
Applied partial differential equations
Oxford University Press, 1999
- : hard
- : pbk
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注記
Bibliography: p. [413]-415
Includes index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780198532439
内容説明
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.
目次
- 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
- 巻冊次
-
: hard ISBN 9780198532446
内容説明
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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