A Treatise on Differential Equations. Supplementary Volume |
From inside the book
Results 1-5 of 37
Page vii
... example , the table at the end of the volume was calcu- lated by Mr Sephton , because the table in the manuscript was rendered erroneous by the use of a wrong sign in a formula . ST JOHN'S COLLEGE , November , 1865 . I. TODHUNTER . LIST ...
... example , the table at the end of the volume was calcu- lated by Mr Sephton , because the table in the manuscript was rendered erroneous by the use of a wrong sign in a formula . ST JOHN'S COLLEGE , November , 1865 . I. TODHUNTER . LIST ...
Page 2
... example if m2 = m1 , the solution then reducing to 1 = const . The theory of the deduction of the true limiting form of the solution in such cases requires a distinct statement . Let the supposed general solution be represented by u = C ...
... example if m2 = m1 , the solution then reducing to 1 = const . The theory of the deduction of the true limiting form of the solution in such cases requires a distinct statement . Let the supposed general solution be represented by u = C ...
Page 10
... example p = xy ; here if n is negative , dp x = dy is infinite when x = 0 , and dy xn + 1 this is a singular solution . For the general solution is y = cen + 1 , and so x = 0 is not a case of 10 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
... example p = xy ; here if n is negative , dp x = dy is infinite when x = 0 , and dy xn + 1 this is a singular solution . For the general solution is y = cen + 1 , and so x = 0 is not a case of 10 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
Page 11
... example we have dp = ∞o gives x " = ∞ ; no inference ; dy d / 1 dx +1 ) ,, - 1 = ∞ gives xy " 1 = ∞ . - Hence x = 0 , provided n is between 0 and 1 , or y = 0 . Consider these separately : First . Let n be between 0 and −1 , and x ...
... example we have dp = ∞o gives x " = ∞ ; no inference ; dy d / 1 dx +1 ) ,, - 1 = ∞ gives xy " 1 = ∞ . - Hence x = 0 , provided n is between 0 and 1 , or y = 0 . Consider these separately : First . Let n be between 0 and −1 , and x ...
Page 12
... additional matter relating to Chapter VIII . begins with another example which was to be placed at the close of Art . 3 of that Chapter . ] Ex . The differential equation - ( √ x2 + 12 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
... additional matter relating to Chapter VIII . begins with another example which was to be placed at the close of Art . 3 of that Chapter . ] Ex . The differential equation - ( √ x2 + 12 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
Other editions - View all
Common terms and phrases
Algebra arbitrary constants Calculus of Variations Cambridge Chap Chapter Christ's College cloth College complete primitive condition Conic Sections contains Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₂ dx dx dx dy dx₁ dx² dy dp dy dx dy dy dy dz dz dy dz dz eliminate English equa expression Extra fcap factor fcap function Geometry given equation Grammar Hence homogeneous function Last Multiplier Latin linear partial differential m₁ Mathematical method ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole proposition reduced relation represent result Schools Second Edition singular solution theorem theory tion transformation Trigonometry u₁ values vanish x₁ Y₁ аф
Popular passages
Page 26 - AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. cloth. 5*. 6d. Hemming. — AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use; of Colleges and Schools.
Page 15 - ON SOUND AND ATMOSPHERIC VIBRATIONS. With the Mathematical Elements of Music. Designed for the Use of Students in the University. Second Edition, Revised and Enlarged. Crown 8vo.
Page 4 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Page 6 - PEILE (JOHN, MA)— AN INTRODUCTION TO GREEK AND LATIN ETYMOLOGY. By JOHN PEILE, MA, Fellow and Tutor of Christ's College, Cambridge, formerly Teacher of Sanskrit in the University of Cambridge. Third and Revised Edition. Crown 8vo.
Page 46 - Pure gold throughout." — GUARDIAN. " Unquestionably the clearest and most complete elementary treatise on this subject that we possess in any language.
Page 29 - 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.
Page 25 - THE FIRST THREE SECTIONS OF NEWTON'S PRINCIPIA, With Notes and Illustrations. Also a collection of Problems, principally intended as Examples of Newton's Methods. By PERCIVAL FROST, MA Third Edition.
Page 22 - DodgSOn.— AN 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.
Page 48 - PRACTICAL CHEMISTRY. THE OWENS COLLEGE JUNIOR COURSE OF PRACTICAL CHEMISTRY. By FRANCIS JONES, Chemical Master in the Grammar School, Manchester. With Preface by Professor ROSCOE, and Illustrations. New Edition.
Page 28 - KITCHENER— A GEOMETRICAL NOTE-BOOK, containing Easy Problems in Geometrical Drawing preparatory to the Study of Geometry. For the use of Schools.