A Treatise on the Differential Calculus |
From inside the book
Results 1-5 of 100
Page 1
... equation involving the symbols of the two quantities and any other symbols of invariable magni- tudes . Thus x and y are functions the one of the other in the equation or a = + b y2 b2 = 1 y ( a2 - x2 ) } a ... ( 1 ) , ( 2 ) , where a ...
... equation involving the symbols of the two quantities and any other symbols of invariable magni- tudes . Thus x and y are functions the one of the other in the equation or a = + b y2 b2 = 1 y ( a2 - x2 ) } a ... ( 1 ) , ( 2 ) , where a ...
Page 2
... equation ( 4 ) is easily seen to be a particular form of the equation ( 3 ) ; for we may write it thus , y − f ( x ) = 0 , y -f ( x ) being merely a particular instance of the general form F ( x , y ) . 4. Functions may be termed ...
... equation ( 4 ) is easily seen to be a particular form of the equation ( 3 ) ; for we may write it thus , y − f ( x ) = 0 , y -f ( x ) being merely a particular instance of the general form F ( x , y ) . 4. Functions may be termed ...
Page 3
... equation to a curve ; then , if the function f ( x ) is continuous for a certain range of values of x , every two points of the locus will be joined by a con- tinuous curve : on the other hand , if there is a dissolution of continuity ...
... equation to a curve ; then , if the function f ( x ) is continuous for a certain range of values of x , every two points of the locus will be joined by a con- tinuous curve : on the other hand , if there is a dissolution of continuity ...
Page 4
... equation involving only the ordinary operations of addition and subtraction , multiplication and division , evolution and involution of assigned degrees , y is said to be an algebraical function of x . If the equation of connection does ...
... equation involving only the ordinary operations of addition and subtraction , multiplication and division , evolution and involution of assigned degrees , y is said to be an algebraical function of x . If the equation of connection does ...
Page 14
... equation by dx , , Y 2 Du = du + du .... ( 3 ) . The quantity du denotes the differential of u taken with regard to Y1 as if y , were constant , du the differential of u taken with regard to y , as if y , were constant , and Du the ...
... equation by dx , , Y 2 Du = du + du .... ( 3 ) . The quantity du denotes the differential of u taken with regard to Y1 as if y , were constant , du the differential of u taken with regard to y , as if y , were constant , and Du the ...
Contents
6 | |
21 | |
22 | |
23 | |
25 | |
31 | |
32 | |
33 | |
160 | |
162 | |
164 | |
165 | |
166 | |
168 | |
170 | |
173 | |
34 | |
35 | |
37 | |
38 | |
44 | |
46 | |
50 | |
52 | |
55 | |
57 | |
58 | |
60 | |
61 | |
69 | |
72 | |
84 | |
99 | |
107 | |
109 | |
110 | |
122 | |
128 | |
133 | |
134 | |
136 | |
137 | |
140 | |
141 | |
146 | |
149 | |
150 | |
151 | |
152 | |
155 | |
159 | |
175 | |
178 | |
179 | |
181 | |
182 | |
185 | |
186 | |
187 | |
189 | |
191 | |
192 | |
194 | |
197 | |
203 | |
204 | |
206 | |
207 | |
209 | |
210 | |
217 | |
223 | |
231 | |
235 | |
237 | |
238 | |
239 | |
240 | |
241 | |
243 | |
245 | |
257 | |
259 | |
260 | |
261 | |
262 | |
Other editions - View all
Common terms and phrases
algebraical arbitrary functions asymptote axis Cambridge change sign College constant cosec curve d'u d'u d'u dz d²r d²u d²x d²z d2z d2z D³u d³x d³y d³z denoting df df df dx differential equations dr dr du dy du² dv₁ dx dx dx dy dx dx dz dx² dx³ dxdy dy df dy dx dy dy,dy dy² dy³ dz dx dz dy dz dz dz² eliminate expression f(y₁ find the Differential formula ƒ Y₁ Hence implicit function indefinitely independent variables indeterminate limit maxima and minima maximum or minimum minimum value negative partial differential coefficients points of inflection positive quantity proposed equation putting regard shews Suppose tangent Taylor's Theorem theorem total differential Trinity College whence y+dy Y₂ zero аф бу бх
Popular passages
Page 12 - Annotations on the Acts of the Apostles. Original and selected. Designed principally for the use of Candidates for the Ordinary BA Degree, Students for Holy Orders, &c., with College and Senate-House Examination Papers. By the Rev. TR MASKEW, MA Second Edition, enlarged. 12mo. 5».
Page 11 - Britannicae, or the several Editions of the Book of Common Prayer of the Church of England, from its compilation to the last revision, together with the Liturgy set forth for the use of the Church of Scotland, arranged to shew their respective variations. By WILLIAM KEELING, BD, late Fellow of St. John's College, Cambridge. Second Edition. 8vo. 12».
Page 17 - Wilson's Illustration of the Method of explaining the New Testament, by the early opinions of Jews and Christians concerning Christ.
Page 14 - Confirmation Day. Being a Book of Instruction for Young Persons how they ought to spend that solemn day, on which they renew the Vows of their Baptism, and are confirmed by the Bishop with prayer and the laying on of hands.
Page 11 - The Greek Testament : with a critically revised Text ; a Digest of Various Readings ; Marginal References to Verbal and Idiomatic Usage ; Prolegomena ;"and a Critical and Exegetical Commentary. For the Use of Theological Students and Ministers.
Page 17 - The Apology of Tertullian. With English Notes and a Preface, intended as an Introduction to the Study of Patristical and Ecclesiastical Latinity. By HA WOODHAM, LL.D. Second Edition. 8vo. 8*.
Page 19 - VARRONIANUS. A Critical and Historical Introduction to the Philological Study of the Latin Language. By the Rev.
Page 4 - Problems and Examples, adapted to the "Elementary Course of Mathematics." With an Appendix, containing the Questions proposed during the first three days of the Senate House Examination.
Page 11 - A HISTORY of the ARTICLES of RELIGION. Including, among other Documents, the X Articles (1536), the XIII Articles (1538), the XLII Articles (1552), the XI Articles (1559), the XXXIX Articles (1562 and 1571), the Lambeth Articles (1595), the Irish Articles (1615), with Illustrations from the Symbolical Books of the Roman and Reformed Communions, and from other contemporary sources. By C.
Page 7 - Treatise on the Motion of a Single Particle and of two Particles acting on one another. By A. SANDEMAN.