3230 



Application of the Differential Calculus 



3240 



Limits, method. Pallet, . Amiens Mm. Ac. 

 Sc. (1841) 363-. 



, proof of existence. SleSinskij, I. N. Es. 

 S. Nt. Mm. (Mth.) 8 (1888) 129- ; Fschr. 

 Mth. (1888) 200, 201. 



, questions. Laisant, C. A. As. Fr. C. E. 

 (1881) 184- . 



oo . Unferdinger, 



related to Lim. 



f or n 



13 



F. Wien Sb. 67 (1873) (Ab. 2) 355-. 



, theory. Cesdro, E. Bll. Sc. Mth. 



1889) 51-. 



, . Fubini, G. G. Mt. 38 (1900) 72-. 

 , , with examples. Leclercq, D. Liege A. 



Ac. (1820-21) 25 pp. 

 , , . Mareska, J. D. B. Liege A. 



Ac. (1823-24) 42 pp. 

 Logarithmic function, its nth differential. 



Tichomandrickij, M. A. Kharkov Mth. S. 



Com. (1886) 42-; Fschr. Mth. (1886) 373. 

 Mean, arithmetical and geometrical. Dostor, 



G. J. N. A. Mth. 10 (1851) 88-. 



Meaning of - , where n is complex. Franstn, 



A. E. Stockh. 6'fv. (1895) 481- ; Fschr. 



Mth. (1895) 307. 

 Method applicable to same purposes as Newton's 



fluxions. Tredgold, T. Tilloch Ph. Mg. 57 



(1821) 177-, 200-, 325-. 

 Multiplication of partial differential operators. 



Sylvester, J. J. Ph. Mg. 33 (1867) 48-. 



Operation x -^- . Walton, W. [1866] QJ. Mth. 



9 (1868) 18-. 

 *~. Walton, W, QJ. Mth. 9 (1868) 355-. 



Operative symbols in differential calculus. 



Crofton, M. W. L. Mth. S. P. 12 (1880-81) 



122-, 213. 

 , method, applications. Crofton, M. W. 



[1890] Ir. Ac. P. 1 (1889-91) 600-. 



Z -3- etc., transformations. 

 dx 



Operators 



Amanzio, D. G. Mt. 21 (1883) 110-. 

 Partial or apparent differentials. Ascoli, G. 



Ev. Mt. 4 (1894) 22-. 

 differentials, error in theorem. Fontana, G. 



Verona S. It. Mm. 2 (1784) 123-. 

 , property. M. Camb. Mth. J. 1 (1839) 



252-. 



of 



169-. 



. Lobatto,E. Crelle J. 11(1834) 



8 2 u 



differentiation, proof that ^ 5 = ,. _ . 



Oxdy oyox 



Whittemore, J. K. N. Y. Am. Mth. S. Bll. 

 4 (1898) 389-. 



differentiations, reversibility of order. Peano, 

 G. Mathesis 10 (1890) 153-. 



Poisson's determinants. Albeggiani, M. L. 

 Palermo Cir. Mt. Ed. 1 (1887) 6-. 



, generalisation. Albeggiani, M. L. 

 Palermo Cir. Mt. Ed. 1 (1887) 9-, 12-, 314-. 



Prime and ultimate ratios, application to 

 fluxionary calculus. Marrat, W. Tilloch 

 Ph. Mg. 36 (1810) 186-. 



Principles, doubtful points. Gyory, S. (xn) 



Mag. Ak. Ets. (Mth. Term.) 1 (1860) 287- 

 Eelative magnitude of infinities of functions. 



Du Bois-Eeymond, P. A. Mt. 4 (1870-71) 



338-; Crelle J. 74 (1872) 294-. 

 Eolle's theorem, forms. Glashan, J. C. Am. 



J. Mth. 4 (1881) 282-. 

 Second differentials and equicrescent variables. 



Webb, J. B. Am. As. P. (1886) 69-. 

 Symbolic formula, new. Faa de Bruno, F. 



C. E. 43 (1856) 725-. 

 Theorem of Cauchy. Jensen, J. L. W. V. 



Ts. Mth. 2 (1884) 81-; Fschr. Mth. (1884) 



193. 

 , generalisation. Stolz, 0. Mth. A. 



33 (1889) 237-. 

 Hesse, demonstration. Jacobi, C. G. J. 



Crelle J. 40 (1850) 318. 

 Uniform function of x and its first differential, 



relation. Schulten, N. G. of (fil.) [1843] 



Helsingf. Acta 2 (1847) 317-. 

 Vandermonde's theorem and application to 



Jacobi's theorem. Lebesgue, V. A. Liouv. 



J. Mth. 6 (1841) 17-. 

 Vector differentiation. MacFarlane, A. [1900] 



Wash. Ph. S. Bll. 14 (1906) 73-. 



3240 Taylor's series. Maxima 

 and minima; other analytical 

 applications of the differential 

 calculus. 



Analysis, formula. Gomes Teixeira, F. N. 

 A. Mth. 5 (1886) 36-. 



_, _ for -^ T/ (x) <f> f^\~\ . Halphen, G. H. 



Par. S. Mth. Bll. 8 (1880) 62-. 

 .theorems. San Martino, A. [1843] N. A. Sc. 



Nt. 4 (1845) 353-. 

 , (San-Martino). Barsotti, G. [1844] 



Lucca At. Ac. 13 (1845) 275-. 

 Approximate representation of experimental 



functions between given limits. Vallier, . 



C. E. 116 (1893) 712-. 



a function by rational fractions. 

 Fade, H. Par. EC. Norm. A. 9 (1892) 

 (Suppl.) 93 pp. 



Arbogast's expansion formulas. De Morgan, A. 

 Camb. and Dubl. Mth. J. 1 (1846) 238-; 

 Assur. Mg. 12 (*1866) 206- 



method of derivations. Donkin, W. F. 

 Camb. and Dubl. Mth. J. 6 (1851) 141-. 



. Eoberts, S. QJ. Mth. 4 (1861) 



193- ; 7 (1866) 10-. 

 . Cayley, A. Mess. Mth. 7 (1878) 



158. 

 . David, . Liouv. J. Mth. 



3 (1887) 53-. 

 . Tanner, H. W. L. Mess. Mth. 



20 (1891) 81-. 

 , application to partition of numbers 



and other problems. David, . Liouv. J. 



Mth. 8 (1882) 61-. 



, extension. Cayley, A. Phil. 

 Trans. (1861) 37-. 



259 



B 2 



