Examples of the Processes of the Differential and Integral Calculus |
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Page iv
D. F. Gregory. read in connection with any of them , I have generally 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 ...
D. F. Gregory. read in connection with any of them , I have generally 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 ...
Page 39
... will enable us to do this with considerable facility . Assume pr sin 0 , so that x = p cos & , y = p sin o , p = r sin 0 , 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 , so that x = p cos & , y = p sin o , p = r sin 0 , x = r cos 0 . Taking first the two variables y and x , we CHANGE OF THE INDEPENDENT VARIABLE . 39.
Page 63
... assuming the given equation in y to be d y = F { ≈ + xp ( y ) } . Then if u = f ( y ) , and if we put ƒ F ( x ) = f1 ( * ) , and __ƒ F ( x ) = ƒ { ' ( x ) , and pF ( x ) = p1 ( ~ ) , dz d u = f ( y ) = ƒ¡ ( * ) + $ ; ( * ) ƒ ...
... assuming the given equation in y to be d y = F { ≈ + xp ( y ) } . Then if u = f ( y ) , and if we put ƒ F ( x ) = f1 ( * ) , and __ƒ F ( x ) = ƒ { ' ( x ) , and pF ( x ) = p1 ( ~ ) , dz d u = f ( y ) = ƒ¡ ( * ) + $ ; ( * ) ƒ ...
Page 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 ...
Page 71
... assuming a series as in the preceding examples , we find for determining the coefficient of the general term , an + 1 = 1 n + ... Assume this to be equal to Á ̧ + Â ̧x + Â1⁄2 x2 + & c . + A „ ¿ c + & c . + & c . and take the logarithmic ...
... assuming a series as in the preceding examples , we find for determining the coefficient of the general term , an + 1 = 1 n + ... Assume this to be equal to Á ̧ + Â ̧x + Â1⁄2 x2 + & c . + A „ ¿ c + & c . + & c . and take the logarithmic ...
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