Schedule of Classification 



4430 Polymorphic functions. Other 

 functions which may be de- 

 fined by definite integrals. 



(See also 4860.) 349 



4440 Automorphic functions. (See 



also 1210, 4050.) 350 



Fuchsian functions 350-351 

 4450 Other functions which may 

 be defined by linear 

 differential equations. 

 Lame's functions ... 351 



Lame's functions 352 



4460 Functions which may be de- 

 fined by functional equa- 

 tions. (See also 6030.) ... 353 



4470 Integral functions 353 



Differential Equations. 

 4800 General. (See also 8080 Con- 



nexes.) 354 



4810 Existence theorems for 

 ordinary and partial 

 differential equations ... 356 



Integrability 356 



4820 Methods of solution and re- 

 duction of ordinary differen - 

 tial equations ... ... 357 



Equations 358 



Integrals 359 



Integration ... 359-362 



Solution 362-363 



4830 Methods of solution and re- 

 duction of partial differen- 

 tial equations of first order, 

 including the differential 

 equations of theoretical 

 dynamics ... ... ... 364 



Equations ... ... 364 



Integration ... 365-367 



Solution ... 367-368 



Theory 368 



4840 Methods of solution and re- 

 duction of partial differen- 

 tial equations of the second 

 and higher orders . . . 368 



Equations ... 369-371 



Integrals 371 



Integration ... 371-373 



Solution, ... ... ... 374 



4850 General theory of ordinary 

 linear equations. (See also 



4450.) 375 



Equations ... 377-380 



Integrals ... 381-382 



Integration . . . 383-386 



Solution 386-387 



4860 Integration of ordinary linear 

 equations by definite inte- 

 grals. (See also 4430.) ... 388 

 4870 General theory of ordinary 

 equations, not linear, of 

 the first order 389 



Riccatts equation 390-391 



Solutions ... 391-392 



4880 General theory of ordinary 

 equations, not linear, of 

 order higher than first ... 392 



Differential Forms and Differential 

 Invariants. 



5200 General 393 



5210 Linear differential forms; 



Pfaffians 394 



5220 Differential forms of the 

 second and higher orders. 



(See also 8450.) 396 



5230 Transformation of differential 

 forms, including tangen- 

 tial (or contact) trans- 

 formations ... ... 396 



Transformation ... 397-398 



5240 Differential invariants. (See 



also 1230.) 398 



Analytical Methods connected with 

 Physical Problems. 



5600 General 400 



5610 Harmonic Analysis ; Fourier's 



series. (See also 3220.) 400 

 Fourier's series ... 400-401 



5620 Harmonic Analysis ; series 

 other than Fourier's. 

 Spherical and ellipsoidal 

 harmonics. (See also 3220.) 403 



5630 Generalities on the differen- 

 tial equations of mathe- 

 matical physics ... ... 404 



5640 Integration of the differential 

 equations of mathematical 

 physics by series ... ... 406 



5650 Integration of the differential 

 equations of mathematical 

 physics by definite integrals 407 



5660 Dirichlet's problem and ana- 

 logous problems affected by 

 boundary conditions ... 407 



Difference Equations and Functional 

 Equations. 



6000 General 409 



6020 Solution of equations of finite 



differences 409 



6030 Solution of functional equa- 

 tions. (See also 4460.) ... 411 



GEOMETRY. 



6390 General 



412 



Foundations. 



6400 General 412 



6410 Principles of geometry ; non- 

 Euclidean geometries ; 

 hyperspace ... ... 413 



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