Examples of the Processes of the Differential and Integral Calculus |
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Page 37
... 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 da = 0 , dp = 0. Hence supposing y to vary while a and are constant we have dy = Q1dq + R1dr ...
... 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 da = 0 , dp = 0. Hence supposing y to vary while a and are constant we have dy = Q1dq + R1dr ...
Page 67
... quantities as before , ca n ( n = 3 ) c2 a2 a2 + B " = ( ) * 72 -n- + b b - + 1.2 b2 b2 & c . } , b continued so long as there are positive powers of ( 12 ) Let u = m + e sin u . Expand u and sin u in terms of e . The expression for u ...
... quantities as before , ca n ( n = 3 ) c2 a2 a2 + B " = ( ) * 72 -n- + b b - + 1.2 b2 b2 & c . } , b continued so long as there are positive powers of ( 12 ) Let u = m + e sin u . Expand u and sin u in terms of e . The expression for u ...
Page 99
... quantities , the result will be equal to v = x ( x + 2 ) . dv 27 If x = 0 ; v = 0 , = x + 2 = 2 , u = — a minimum ; da 4 dv 2 = - 2 ; v = = 0 , 2 I -2 , u∞ , a maximum . dx ( 9 ) u = ( x − 1 ) 2 - ( x + 1 ) 3 * x = 5 gives u = x = 1 ...
... quantities , the result will be equal to v = x ( x + 2 ) . dv 27 If x = 0 ; v = 0 , = x + 2 = 2 , u = — a minimum ; da 4 dv 2 = - 2 ; v = = 0 , 2 I -2 , u∞ , a maximum . dx ( 9 ) u = ( x − 1 ) 2 - ( x + 1 ) 3 * x = 5 gives u = x = 1 ...
Page 111
... quantities A from the conditions that they make the terms involving da ,, dx2 , ... dæ , vanish , that is to say , if we determine them by the conditions M1 = 0 , M2 = 0 , ... M , = 0 , + Mécanique Analytique , Vol . 1. p . 74 . the ...
... quantities A from the conditions that they make the terms involving da ,, dx2 , ... dæ , vanish , that is to say , if we determine them by the conditions M1 = 0 , M2 = 0 , ... M , = 0 , + Mécanique Analytique , Vol . 1. p . 74 . the ...
Page 112
... quantities and the quantities à satisfy the n + r equations , M1 = 0 , M1 = 0 ... M1 = 0 , L1 = 0 ... L , = 0 . As it is indifferent which of the variables we eliminate in order to determine A , ... A , the most general way of stating ...
... quantities and the quantities à satisfy the n + r equations , M1 = 0 , M1 = 0 ... M1 = 0 , L1 = 0 ... L , = 0 . As it is indifferent which of the variables we eliminate in order to determine A , ... A , the most general way of stating ...
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