Partial Differential Equations: An Essay Towards an Entirely New Method of Integrating Them |
From inside the book
Results 1-5 of 13
Page 2
... constants ; and so on . It is here proposed to express this briefly by the use of the word quasi - constant . Thus ... arbitrary function of x , y , z , ... its quasi - constants : and this principle is general and may be thus stated ...
... constants ; and so on . It is here proposed to express this briefly by the use of the word quasi - constant . Thus ... arbitrary function of x , y , z , ... its quasi - constants : and this principle is general and may be thus stated ...
Page 4
... constants ) of the set to be determined , one of them ( t ) being already fixed upon in using this equa- tion . 8 ... arbitrary hypotheses if we use equation ( 1 ) of Art . 4 ; but only ( n − 1 ) arbitrary hypotheses if we employ ...
... constants ) of the set to be determined , one of them ( t ) being already fixed upon in using this equa- tion . 8 ... arbitrary hypotheses if we use equation ( 1 ) of Art . 4 ; but only ( n − 1 ) arbitrary hypotheses if we employ ...
Page 12
... arbitrary functions of § , the left - hand members must also be arbitrary functions of each other ; -1 2 ... u = ( t + x ) F ( tan = ' ( tan12 — log √t + x2 ) . Ex . 13. To integrate - ( bu — cx ) du + ( ct — au ) d ̧u = ax – bt ...
... arbitrary functions of § , the left - hand members must also be arbitrary functions of each other ; -1 2 ... u = ( t + x ) F ( tan = ' ( tan12 — log √t + x2 ) . Ex . 13. To integrate - ( bu — cx ) du + ( ct — au ) d ̧u = ax – bt ...
Page 20
... constant coefficients . 16. In a similar way it may be shewn that if F , G , H be any symbols whatever of integration , F.G.H.O = F.O + G.O + H.0 , provided the proper number of arbitrary functions be fur- nished by the right - hand ...
... constant coefficients . 16. In a similar way it may be shewn that if F , G , H be any symbols whatever of integration , F.G.H.O = F.O + G.O + H.0 , provided the proper number of arbitrary functions be fur- nished by the right - hand ...
Page 33
... arbitrary constants we are at liberty to assume ( a — b ) 2 m = B — Aa , and ( a - b ) 2 n = B − Ab ; .. DA ~ + { C + ( B - Aa ) ( B – Ab ) ) ( a - b ) 3 v = We ̃m§ ' - n§ ̧ Consequently when W = 0 , the form I. can be reduced to the ...
... arbitrary constants we are at liberty to assume ( a — b ) 2 m = B — Aa , and ( a - b ) 2 n = B − Ab ; .. DA ~ + { C + ( B - Aa ) ( B – Ab ) ) ( a - b ) 3 v = We ̃m§ ' - n§ ̧ Consequently when W = 0 , the form I. can be reduced to the ...
Other editions - View all
Common terms and phrases
A₁ ad¸u Algebra arbitrary constants arbitrary functions ARITHMETIC beginners BROOKE FOSS WESTCOTT Cambridge Chapter CLASS-BOOK cloth coefficients commutative complete integral Crown 8vo d¸³u D₁ D₁u D₁x D₂ d³u Differential Calculus EDWARD THRING ELEMENTARY TREATISE English equa equivalent Essay Examination Papers Extra fcap F₁ Fcap final integral finite terms form of H ƒ Dr ƒ dt GEOMETRY gives Grammar Greek ht+kx independent variables integral in finite John's College kx)² Latin liberty to assume Mathematical method MIXED MATHEMATICS Multiply numerous Examples obtained partial differential equation preceding example principle proposed equation quasi-constants render revised root-integral Schools Second Edition second order shew student substitute symbolical integral symbols of operation tion Trigonometry utª write
Popular passages
Page 10 - Astronomer Royal :— ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS. Designed for the Use of Students in the Universities. With Diagrams.
Page 16 - ... ELEMENTARY TREATISE ON DETERMINANTS, with their Application to Simultaneous Linear Equations and Algebraical Geometry. By CHARLES L. DODGSON, MA, Student and Mathematical Lecturer of Christ Church, Oxford. Small 4to. cloth.
Page 12 - ... the discussion of such deeper questions of principle as are likely to present themselves to the reflective student in connexion with the methods and processes of his previous course.
Page 3 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Page 3 - CICERO— THE SECOND PHILIPPIC ORATION. From the German of Karl Halm. Edited, with Corrections and Additions, by JOHN EB MAYOR, Professor of Latin in the University of Cambridge, and Fellow of St.
Page 7 - Map. By the Rev. PERCIVAL FROST, MA, late Fellow of St. John's College, Cambridge. Fcap. 8vo.
Page 45 - WILSON— THE BIBLE STUDENT'S GUIDE to the more Correct Understanding of the English Translation of the Old Testament, by reference to the original Hebrew. By WILLIAM WILSON, DD, Canon of Winchester, late Fellow of Queen's College, Oxford. Second Edition, carefully revised. 4to. cloth. 25*. YONGE (CHARLOTTE M.)— SCRIPTURE READINGS FOR SCHOOLS AND FAMILIES. By CHARLOTTE M. YONGE, Author of "The Heir of Redclyffe.
Page 17 - ... dealing with ordinary theorems and problems, thus directing the student to the selection of methods which are best adapted to the exigencies of each problem. In the more difficult portions of the subject, they...
Page 8 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages ; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Page 19 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.