Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 64
Сторінка ix
... Elimination of Constants and Functions 43 V. Application of the Differential Calculus to the Development of Functions 32 52 VI . Evaluation of Functions which for certain values of the Variable become indeterminate 79 VII . Maxima and ...
... Elimination of Constants and Functions 43 V. Application of the Differential Calculus to the Development of Functions 32 52 VI . Evaluation of Functions which for certain values of the Variable become indeterminate 79 VII . Maxima and ...
Сторінка 35
... Eliminating we find dy du dy du dy - • du dr de = dx dx dy · - de dr dy da · dr de dr de du Eliminating we find dx du dx du du dr de de • dx dr dy dx dy dy dx - dr de dr de If r and be given explicitly in terms of x and y , we have at ...
... Eliminating we find dy du dy du dy - • du dr de = dx dx dy · - de dr dy da · dr de dr de du Eliminating we find dx du dx du du dr de de • dx dr dy dx dy dy dx - dr de dr de If r and be given explicitly in terms of x and y , we have at ...
Сторінка 36
... Eliminating de between these we find dx dx dy dx dy dr . dy = d Ꮎ de dr dr d Ꮎ . From this it follows that when dy = 0 , dr = 0. Hence we have dx == dx de . d Ꮎ Substituting these values in the double integral it becomes SSV dx dy da ...
... Eliminating de between these we find dx dx dy dx dy dr . dy = d Ꮎ de dr dr d Ꮎ . From this it follows that when dy = 0 , dr = 0. Hence we have dx == dx de . d Ꮎ Substituting these values in the double integral it becomes SSV dx dy da ...
Сторінка 37
... eliminating two of the three quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when dx = 0 , dp = 0. Hence supposing y to vary while a and ≈ are ...
... eliminating two of the three quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when dx = 0 , dp = 0. Hence supposing y to vary while a and ≈ are ...
Сторінка 42
... 2 + ( da ) * } * = ƒƒd0 dp sin 0 { a2b2 ( cos 0 ) 2 + ( c sin 0 ) 2 ( a2 sin2 p + b2 cos3p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
... 2 + ( da ) * } * = ƒƒd0 dp sin 0 { a2b2 ( cos 0 ) 2 + ( c sin 0 ) 2 ( a2 sin2 p + b2 cos3p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
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