Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 76
Сторінка 15
... multiply h ' , we find that the term in n ( n − 1 ) ... ( n − r + 1 ) - 1.2 - r ... u " - " u " ; ( n − 1 ) ... multiplying by 1.2 ... r , we obtain for the 7th differential coefficient of u " d ' ( u " ) dx = n ( n − 1 ) ... ( n − r ...
... multiply h ' , we find that the term in n ( n − 1 ) ... ( n − r + 1 ) - 1.2 - r ... u " - " u " ; ( n − 1 ) ... multiplying by 1.2 ... r , we obtain for the 7th differential coefficient of u " d ' ( u " ) dx = n ( n − 1 ) ... ( n − r ...
Сторінка 16
... multiplied by 1.2 ... r . Now expanding each term by the binomial theorem , we have for the coefficient of ' u ' h ... multiplying by 1.2 ... r , we find d ' ( u " ) r u : ( ' ' ) ' u ' ~ { dx + = 2n ( 2n − 1 ) ... ( 2n − r + 1 ) 4 n ...
... multiplied by 1.2 ... r . Now expanding each term by the binomial theorem , we have for the coefficient of ' u ' h ... multiplying by 1.2 ... r , we find d ' ( u " ) r u : ( ' ' ) ' u ' ~ { dx + = 2n ( 2n − 1 ) ... ( 2n − r + 1 ) 4 n ...
Сторінка 19
... Multiplying these together , taking only the coefficient of h ' and multiplying it by 1.2 ... r , we find d'u dx " = + - -2 { c ' ( 2x ) ' + r ( r − 1 ) c * - ' ( 2 x ) * −2 - r ( r − 1 ) ... ( r – 3 ) 1.2 - c ' − 2 ( 2x ) ' ~ ' + ...
... Multiplying these together , taking only the coefficient of h ' and multiplying it by 1.2 ... r , we find d'u dx " = + - -2 { c ' ( 2x ) ' + r ( r − 1 ) c * - ' ( 2 x ) * −2 - r ( r − 1 ) ... ( r – 3 ) 1.2 - c ' − 2 ( 2x ) ' ~ ' + ...
Сторінка 21
... multiplying by ( e * + 1 ) * + 1 we must have ( e * + 1 ) ' + ' d'u dx = a ‚ € TM ” + ɑ‚_16 ( ̃ − 1 ) 2 + & c . + α1e * ( 1 ) . Now as u = € ' - 2x - E -32 + € - & c . d'u = dx ( − ) ' { 1 ′ e ̄ I - 2 ' € -2x + 3 ′ € -3x -- ...
... multiplying by ( e * + 1 ) * + 1 we must have ( e * + 1 ) ' + ' d'u dx = a ‚ € TM ” + ɑ‚_16 ( ̃ − 1 ) 2 + & c . + α1e * ( 1 ) . Now as u = € ' - 2x - E -32 + € - & c . d'u = dx ( − ) ' { 1 ′ e ̄ I - 2 ' € -2x + 3 ′ € -3x -- ...
Сторінка 32
... multiplying by a + y , we have ( a + y ) 2 d2 u dy + ( a + y ) du d2 u dy = dx2 differentiating a third time and again multiplying by a + y , we see that ( a + y ) 3 ď3 u dy3 d2 u du + 3 ( a + y ) 2 + ( a + y ) dy3 dy and therefore d3 u ...
... multiplying by a + y , we have ( a + y ) 2 d2 u dy + ( a + y ) du d2 u dy = dx2 differentiating a third time and again multiplying by a + y , we see that ( a + y ) 3 ď3 u dy3 d2 u du + 3 ( a + y ) 2 + ( a + y ) dy3 dy and therefore d3 u ...
Зміст
1 | |
9 | |
28 | |
43 | |
52 | |
77 | |
79 | |
94 | |
224 | |
237 | |
249 | |
271 | |
282 | |
291 | |
340 | |
351 | |
129 | |
132 | |
144 | |
162 | |
175 | |
188 | |
200 | |
386 | |
400 | |
412 | |
440 | |
464 | |
506 | |
Інші видання - Показати все
Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³