A treatise on differential equations
著者
書誌事項
A treatise on differential equations
（Cambridge library collection, . mathematics）
Cambridge University Press, c2014
- : pbk.
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注記
"This degitally printed version 2014"--T.p. verso
Reprint. Original published by Macmillan in 1859
内容説明・目次
内容説明
The need to support his family meant that George Boole (1815-64) was a largely self-educated mathematician. Widely recognised for his ability, he became the first professor of mathematics at Cork. Boole belonged to the British school of algebra, which held what now seems to modern mathematicians to be an excessive belief in the power of symbolism. However, in Boole's hands symbolic algebra became a source of novel and lasting mathematics. Also reissued in this series, his masterpiece was An Investigation of the Laws of Thought (1854), and his two later works A Treatise on Differential Equations (1859) and A Treatise on the Calculus of Finite Differences (1860) exercised an influence which can still be traced in many modern treatments of differential equations and numerical analysis. The beautiful and mysterious formulae that Boole obtained are among the direct ancestors of the theories of distributions and of operator algebras.
目次
- Preface
- 1. Of the nature and origin of differential equations
- 2. On differential equations of the first order and degree between two variables
- 3. Exact differential equations of the first degree
- 4. On the integrating factors of the differential equation
- 5. On the general determination of the integrating factors of the equation
- 6. On some remarkable equations of the first order and degree
- 7. On differential equations of the first order, but not of the first degree
- 8. On the singular solutions of differential equations of the first order
- 9. On differential equations of an order higher than the first
- 10. Equations of an order higher than the first (cont.)
- 11. Geometrical applications
- 12. Ordinary differential equations with more than two variables
- 13. Simultaneous differential equations
- 14. Of partial differential equations
- 15. Partial differential equations of the second order
- 16. Symbolical methods
- 17. Symbolical methods (cont.)
- 18. Solution of linear differential equations by definite integrals
- Answers
- Appendix
- Corrections.
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