Partial differential equations
著者
書誌事項
Partial differential equations
（Theory of differential equations, pt. 4）
Cambridge University Press, 2011, c1906
1st pbk. ed
- v. 5 : pbk
- v. 6 : pbk
大学図書館所蔵 件 / 全8件
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v. 5 : pbk413.6||FOR 9||3-5200024923247,
v. 6 : pbk413.6||FOR 9||3-6200024923256 -
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注記
"Paperback reissue"--P. [4] of cover
"First published 1906, first paperback edition 2011"--T.p. verso
Vol. 6 includes index
内容説明・目次
- 巻冊次
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v. 5 : pbk ISBN 9781107660144
内容説明
Andrew Russell Forsyth (1858-1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1906, this book constitutes the fifth of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on partial differential equations. The text contains detailed information on the development of this area and substantial contributions made to it. All sources are quoted in their proper connection and a few fresh investigations are added. Examples are given, where necessary, in order to provide illustrations of various methods. This book will be of value to anyone with an interest in differential equations and the history of mathematics.
目次
- 1. Introduction: two existence-theorems
- 2. Cauchy's theorem
- 3. Linear equations and complete linear systems
- 4. Non-linear equations: Jacobi's second method, with Mayer's developments
- 5. Classes of integrals possessed by equations of the first order: generalisation of integrals
- 6. The method of characteristics for equations in two independent variables: geometrical relations of the various integrals
- 7. Singular integrals and their geometrical properties: singularities of the characteristics
- 8. The method of characteristics in any number of independent variables
- 9. Lie's methods applied to equations of the first order
- 10. The equations of theoretical dynamics
- 11. Simultaneous equations of the first order.
- 巻冊次
-
v. 6 : pbk ISBN 9781107692749
内容説明
Andrew Russell Forsyth (1858-1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1906, this book constitutes the sixth and final volume in Forsyth's Theory of Differential Equations series, concentrating specifically on partial differential equations. The text contains detailed information on the development of this area and substantial contributions made to it. All sources are quoted in their proper connection and a few fresh investigations are added. Examples are given, where necessary, in order to provide illustrations of various methods. This book will be of value to anyone with an interest in differential equations and the history of mathematics.
目次
- 12. General integrals of equations of orders higher than the first
- 13. Linear equations of the second order in two independent variables: the Laplace-transformations
- 14. Adjoint equations: linear equations having equal invariants
- 15. Forms of equations of the second order in two independent variables having their general integrals in explicit finite form
- 16. Equations of the second order in two independent variables having an intermediate integral
- 17. Ampere's method applied to equations of the second order in two independent variables
- 18. Darboux's method and other methods for equations of the second order in two independent variables
- 19. Generalisation of integrals
- 20. Characteristics of equations of second order: intermediate integrals
- 21. General transformation of equations of the second order
- 22. Equations of the third and higher orders, in two independent variables
- 23. Equations of the second order in more than two independent variables, having an intermediate integral
- 24. Equations of the second order in three independent variables, not necessarily having an intermediate integral
- Index to Part IV.
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