A Treatise on Differential EquationsCambridge University Press, 21.08.2014 - 518 Seiten 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. |
Inhalt
CHAPTER I | 1 |
Species Order and Degree 3 General solution Com | 20 |
General equation de+Nolyo 23 Complete primitive f x yc | 41 |
CHAPTER IV | 52 |
or THE GENERAL DETERMINATION or THE INTEGRATING | 69 |
CHAPTER VI | 91 |
can 1 a fila + by3 cm 2 Solution | 103 |
CHAPTER VII | 113 |
Meaning of de+Qoly+Rdzo 267 Condition of derivation from | 277 |
Meaning of a determinate system 287 General theory of simultaneous | 311 |
CHAPTER XIV | 313 |
Primary modes of genesis 315 Solution when all | 319 |
CHAPTER XV | 351 |
The equation Rr+Ss+Tt V 35 Condition of its admitting a first | 365 |
CHAPTER XVI | 371 |
Laws of direct expressions 371374 Inverse forms 375 Linear | 388 |
Typical form U3 General theory of its solution 115 Relation | 125 |
CHAPTER VIII | 139 |
Primary definitionpositiveand negative marks I 39 14c Derivation | 177 |
Relation to complete primitive 187 Solution by deVelopment | 189 |
EQUATIONS or AN ORDER HIGHER THAN THE FIRST CONTINUED | 208 |
tions 61 Exact equations 219 Miscellaneous methods and | 235 |
Diflerent problems 23524I Trajectories 242 Curves of Pursuit | 251 |
CHAPTER XVII | 402 |
Symbolical form of diflerential equations with variable coeflicients | 408 |
CHAPTER XVIII | 451 |
Laplaces method 451 Partial diflerential equations 465 Parsevals | 476 |
| 492 | |
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according admit application arbitrary constant arbitrary function assume becomes changing Chap CHAPTER complete primitive condition connected considered consists contain corresponding curve deduce definite dependent derived determined developed difi'erential direct effected eliminating equa equal exact differential example exist expressed final find finite first integral first member first order given equation gives Hence homogeneous homogeneous functions illustration important independent variable infinite integral integrating factor involving latter lead limit linear means method multiplying observed obtained operation ordinary original partial differential equation particular positive possible present problem Prop proposed question ratio reduced referred regarding relation represent respect result satisfied satisfy second member second order shew singular solution solve substituting suppose symbolical theorem tion transformation variables whence