Partial differential equations: an essay towards an entirely new method of integrating them1871 |
From inside the book
Results 1-5 of 20
Page 31
... elementary forms to which that general equation can be reduced are accepted as integrable . For- mulæ both algebraic and transcendental have been invented , -logarithmic , exponential and trigonometric , direct and inverse , and have ...
... elementary forms to which that general equation can be reduced are accepted as integrable . For- mulæ both algebraic and transcendental have been invented , -logarithmic , exponential and trigonometric , direct and inverse , and have ...
Page 33
... elementary form , D1Av = cv . Case II . When a and b are equal . In this case the form I. becomes B A ( d2 + ad ̧ „ ) 2 u + A ( dı + 2 d2 ) u + Cu = W. B A Hence D = d + ad ̧ , x = at + § as before ; and A1 = dt + dx B B whence A = A ...
... elementary form , D1Av = cv . Case II . When a and b are equal . In this case the form I. becomes B A ( d2 + ad ̧ „ ) 2 u + A ( dı + 2 d2 ) u + Cu = W. B A Hence D = d + ad ̧ , x = at + § as before ; and A1 = dt + dx B B whence A = A ...
Page 34
... elementary form , did & v = cv , which is the same as in the first case . Thus it appears that there are two elementary forms , and no more , viz . DAucu , and D'u = cAu . The question is - are we to accept these as integrable forms ...
... elementary form , did & v = cv , which is the same as in the first case . Thus it appears that there are two elementary forms , and no more , viz . DAucu , and D'u = cAu . The question is - are we to accept these as integrable forms ...
Page 12
... ELEMENTARY TREATISE ON PLANE TRIGONOMETRY . With Examples . By R. D. BEASLEY , M. A. , Head Master of Grantham Grammar School . Second Edition , revised and enlarged . Crown 8vo . cloth . 3s . 6d . This treatise is specially intended ...
... ELEMENTARY TREATISE ON PLANE TRIGONOMETRY . With Examples . By R. D. BEASLEY , M. A. , Head Master of Grantham Grammar School . Second Edition , revised and enlarged . Crown 8vo . cloth . 3s . 6d . This treatise is specially intended ...
Page 10
... ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS . Designed for the Use of Students in the Univer- With Diagrams . Crown 8vo . cloth . sities . 5s . 6d . It is hoped that the methods of solution here explained , and the instances ...
... ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS . Designed for the Use of Students in the Univer- With Diagrams . Crown 8vo . cloth . sities . 5s . 6d . It is hoped that the methods of solution here explained , and the instances ...
Other editions - View all
Common terms and phrases
A₁ ad¸u Algebra arbitrary constants arbitrary functions ARITHMETIC beginners brackets BROOKE FOSS WESTCOTT C₁ Cambridge Chapter CLASS-BOOK cloth coefficients commutative complete integral Crown 8vo d¸³u D₁ D₁u D₁x d₂ d³u Differential Calculus Dudu ELEMENTARY TREATISE English equa equivalent Essay Examination Papers Extra fcap F₁ Fcap final integral finite terms form of ƒ formula of Art GEOMETRY gives Grammar Greek h+ka Hence ht+kx independent variables integral in finite John's College kx)² liberty to assume Mathematical method MIXED MATHEMATICS obtained partial differential equation pendent variables preceding example principle proposed equation quasi-constants reference render root-integral Ruled Surfaces Schools Second Edition second order set of independent shew student substitute symbolical integral symbols of operation tion Trigonometry write
Popular passages
Page 26 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.
Page 5 - MORGAN — A COLLECTION OF PROBLEMS AND EXAMPLES IN MATHEMATICS. With Answers. By HA Morgan, MA, Sadlerian and Mathematical Lecturer of Jesus College, Cambridge.
Page 148 - ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS. Designed for the Use of Students in the Universities. With Diagrams. Second Edition. Crown 8vo. $s. 6d. ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS.
Page 141 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Page 20 - LOCKYER'S ELEMENTARY LESSONS IN ASTRONOMY. With Coloured Diagram of the Spectra of the Sun, Stars, and Nebulae, and numerous Illustrations. By J. NORMAN LOCKYER, FRS Seventh Thousand.
Page 141 - 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 28 - A GENERAL SURVEY OF THE HISTORY OF THE CANON OF THE NEW TESTAMENT DURING THE fIRST FOUR CENTURIES. Fourth Edition. With Preface on "Supernatural Religion.
Page 29 - 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 16 - New Edition. Crown 8vo. $s. KEY TO PLANE TRIGONOMETRY. Crown 8vo. los. 6d. A TREATISE ON SPHERICAL TRIGONOMETRY. New Edition, enlarged. Crown 8vo. 4-?. 6d. PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.
Page 146 - 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.