A Treatise on Differential Equations

Front Cover
Courier Dover Publications, 1929 - Mathematics - 583 pages
0 Reviews
Sixth edition (1928) of classic 19th-century work considered one of the finest treatments of the topic. Differential equations of the 1st order, general linear equations with constant coefficients, integration in series, hypergeometric series, solution by definite integrals, many other topics. Over 800 examples. Index.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

CHAPTER I
1
Lemma relating to functional dependence
11
CHAPTER II
17
one variable absent
27
Derivation of the Singular Solution from the primitive
37
An equation of the ntb degree haa not necessarily a Singular
43
Its primitive consists of two parts
63
Derivation of the Particular Integral in some typical forma
71
Total equations in n variables conditions to be satisfied that such
324
Modified method for the process in 152
331
SIMULTANEOUS EQUATIONS cases in which they arise
342
Simultaneous equations with variable coefficients sufficient to con
350
Jacobis Multipliers
356
Integration of the equations of motion of a particle moving under
370
included in some one of the three general classes
379
18L The Complete Integral
382

Solationof
85
CHAPTER IV
87
Equations possessing generalised homogeneity
94
General linear equation of second order i iutegrable when any single
101
Solution of particular cases of the linear equation by change of inde
108
Solution in case of particular form of the invariant
118
122123 Division of the 24 aohuions into six classes of four each 216
124
Derivation of the Particular Integral by Variation of Parometera
127
AST PAOE
151
LEGEXDREs equation
159
Different cases to be considered
165
Differential relation oetween Pnand Qn
171
Properties of the functions J
180
Deduction of Bessels equation from Legendres equation
186
Reduction of Riccatia equation to Bessels equation
195
CHAPTER VI
207
Six values of the variable element
213
these integrals
218
Gausss 11 function
221
126129 Determination of the constants in the linear relations of 124
224
The Schwarzian derivative for the differential equation to be applied to obtain the cases of integration in a finite form
230
ART FAOE
231
Case I ic + la4
232
Case II i c 2s s3 ia + 2 Jf I
233
References to original memoirs
239
Miscellaneous Examples
240
SUPPLXMSNTARY NOTZS I Integration of linear equations in series by the method of Frobenius with examples of application to BessePs equations...
243
Equations having all their integrals regular
258
Equations having some but not all integrals regular
265
Equations having no regular integrals normal integrals subnormal integrals
275
SOLUTION BY DEFINITE INTEGRALS 135 Applicable to linear equations
277
General method of determination of the limits
279
Particular form of this method usually applied
280
Proposition relating to the solution by definite integrals of the general linear equation
283
Special cases of this proposition
286
Form of solution suitable for y xy
288
Application to the differential equation of the hypergeometric series
290
Primitive of this equation in the definiteintegral form
292
References to memoirs
294
ORDINARY EQUATIONS WITH MORE THAN TWO VARIABLES 146 ETLEKS equation Richelots method of integration
299
Method of integration when this relation is satisfied
314
Geometrical interpretation in the case in which there are two independent variables
384
Derivation of the Singular Integral if it exists from the differen tial equation with test of existence
387
Derivation of integral of Pp + QqR
393
189190 This integral provides all the integrals that are not special
394
Particular solutions of the equation
401
Homogeneous linear equation in n variables
407
xzp ? 0 and geometrical interpretation
410
iIx p y q
412
zpx + qy + ipp q
414
Duality of partial differential equations
415
This duality corresponds to the principle of duality in geometry
417
Determination in special cases of the arbitrary function which occurs in the General Integral
418
Principle of CHAHPITS METHOD for the integration of the general equation containing two independent variables
420
Eeenunciation of the result of 206
421
The Standard forms are particular cases in which Charpits method is immediately effective
426
Lagranges linear equation is a particular case
427
211213 Proof that Standards I II and III are particular cases
430
Principle of the method naed by JACOSI for the integration of the general equation
431
Deduction of the necessary subsidiary equations
432
These subsidiary equations are sufficient
434
Formulation of the rule to which the method leads
436
Lemma on functions connected with the subsidiary equations
437
221227 Integration of the subsidiary equations
439
List of authorities on partial differential equations
447
Examples of Jacobis method
448
SIMULTANROUS PARTIAL EQUATIONS
453
CHAPTER X
470
Cauchys method of integration 301
473
Deduction of intermediate integral of Rr + Ss+ Tt+ Urtt2V
476
Summary of the method of solution
484
General method for the construction of an intermediate integral
493
Principle of duality
503
POISBOSS method for a special form of the homogeneous equation 609
511
Modification of the complementary function in special cases
517
Class of homogeneous equations
520
Solution also by a symbolical method
526
AuptREs METHOD for equations of the second order
533
GENERAL EXAMPLES
558
INDEX
581
Generalisation of Eiders equation method of integration due to Jacobi 303
582
Copyright

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information