Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 89
Сторінка iv
... assumed as known only those methods which are to be found in all Elementary Treatises . To this , how- ever , there is one exception : it will be seen that I have made constant use of the method known by the name of the Separation of ...
... assumed as known only those methods which are to be found in all Elementary Treatises . To this , how- ever , there is one exception : it will be seen that I have made constant use of the method known by the name of the Separation of ...
Сторінка 39
... will enable us to do this with considerable facility . Assume pr sin 0 , = y = p sin o , p = r sin 0 , so that ≈ = p cos p , x = r cos 0 . Taking first the two variables y and x , we CHANGE OF THE INDEPENDENT VARIABLE . 39.
... will enable us to do this with considerable facility . Assume pr sin 0 , = y = p sin o , p = r sin 0 , so that ≈ = p cos p , x = r cos 0 . Taking first the two variables y and x , we CHANGE OF THE INDEPENDENT VARIABLE . 39.
Сторінка 63
... assuming the given equation in y to be d y = F { x + x + ( y ) } . Then if u = f ( y ) , and if we put ƒ F ( x ) = ƒ1 ( * ) , and ~ _ƒF ( x ) = ƒ ' ( x ) , and μF ( ~ ) = $ . ( ~ ) , dx 20 d x2 u = f ( y ) = ƒ1 ( x ) + $ 1 ( ≈ ) ƒï ...
... assuming the given equation in y to be d y = F { x + x + ( y ) } . Then if u = f ( y ) , and if we put ƒ F ( x ) = ƒ1 ( * ) , and ~ _ƒF ( x ) = ƒ ' ( x ) , and μF ( ~ ) = $ . ( ~ ) , dx 20 d x2 u = f ( y ) = ƒ1 ( x ) + $ 1 ( ≈ ) ƒï ...
Сторінка 70
... assume a series with indeterminate coefficients , and then to compare the differential of the function with that of the assumed series ; so that by equating the coefficients of like powers of the variables conditions are found for ...
... assume a series with indeterminate coefficients , and then to compare the differential of the function with that of the assumed series ; so that by equating the coefficients of like powers of the variables conditions are found for ...
Сторінка 71
... assuming a series as in the preceding examples , we find for determining the coefficient of the general term , an + 1 ... Assume this to be equal to A + A1x + А2x2 + & c . + A „ ¿ ” + & c . and take the logarithmic differentials of both ...
... assuming a series as in the preceding examples , we find for determining the coefficient of the general term , an + 1 ... Assume this to be equal to A + A1x + А2x2 + & c . + A „ ¿ ” + & c . and take the logarithmic differentials of both ...
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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