Partial Differential Equations: An Essay Towards an Entirely New Method of Integrating Them |
From inside the book
Results 1-5 of 17
Page
... render his Method thoroughly intelligible , and not the ex- hibition of integrals , he has for brevity's sake not always proceeded to the last steps of an integration when he con- ceived that the method had been made intelligible . The ...
... render his Method thoroughly intelligible , and not the ex- hibition of integrals , he has for brevity's sake not always proceeded to the last steps of an integration when he con- ceived that the method had been made intelligible . The ...
Page 2
... render the above equation ( 1 ) sufficient by itself for our purpose ; so that by a proper choice of values for § , n , 5 , ... any partial differential equation of n variables may be reduced to an equivalent equation of one variable ...
... render the above equation ( 1 ) sufficient by itself for our purpose ; so that by a proper choice of values for § , n , 5 , ... any partial differential equation of n variables may be reduced to an equivalent equation of one variable ...
Page 5
... rendered identical with the left - hand member of the proposed equation ; so that we shall have Dubu ; .. Da , and Dubu , and these two equations , taken simultaneously , are together exactly equivalent to the proposed equation ...
... rendered identical with the left - hand member of the proposed equation ; so that we shall have Dubu ; .. Da , and Dubu , and these two equations , taken simultaneously , are together exactly equivalent to the proposed equation ...
Page 57
... the values of m will render one of the above quantities a multiple of a - b . Ex . 5. To integrate ( ht + kx ) ( di̟u + 2add ̧u + a3d ̧3u ) + b ( d ̧u + ad ̧u ) + cu = 0 . In this example D1 = dt + ad ̧ ‚ § SYMBOLS OF OPERATION . 57.
... the values of m will render one of the above quantities a multiple of a - b . Ex . 5. To integrate ( ht + kx ) ( di̟u + 2add ̧u + a3d ̧3u ) + b ( d ̧u + ad ̧u ) + cu = 0 . In this example D1 = dt + ad ̧ ‚ § SYMBOLS OF OPERATION . 57.
Page 63
... render the general proof unnecessary . Ex . 11. To reduce to to ( d ) u + p , ( d ) u = 0 . Operate on this question with f ( dr ) ; : . ( tfdr + ƒ'dı ) Þ , ( dı ) u + ƒdı . Þ 。( dı ) u = filı . 0 . 0 As the form of f is arbitrary we ...
... render the general proof unnecessary . Ex . 11. To reduce to to ( d ) u + p , ( d ) u = 0 . Operate on this question with f ( dr ) ; : . ( tfdr + ƒ'dı ) Þ , ( dı ) u + ƒdı . Þ 。( dı ) u = filı . 0 . 0 As the form of f is arbitrary we ...
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.