Examples of the Processes of the Differential and Integral Calculus |
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Page iv
... constant use of the method known by the name of the Separation of the Symbols of Operation , although the Theory of the process is not usually given in works which are likely to be in the hands of students . I have done so because I ...
... constant use of the method known by the name of the Separation of the Symbols of Operation , although the Theory of the process is not usually given in works which are likely to be in the hands of students . I have done so because I ...
Page 36
... constant . To introduce this condition we proceed as follows . Let for example there be a double integral ffVda dy , and let x = $ ( r , 0 ) , so that y = ¥ ( r , 0 ) , dx dx dx = dr + d Ꮎ , dr d Ꮎ dy dy dy = dr + do . dr do Since is ...
... constant . To introduce this condition we proceed as follows . Let for example there be a double integral ffVda dy , and let x = $ ( r , 0 ) , so that y = ¥ ( r , 0 ) , dx dx dx = dr + d Ꮎ , dr d Ꮎ dy dy dy = dr + do . dr do Since is ...
Page 37
... constant we have dy = Q1dq + R1dr , 0 = Q2dq + R2dr ; and eliminating dr between these we have dy = Ndq , N being a function of p , q , r . It follows that when dy = 0 , dq = 0 , and therefore if we suppose ≈ to vary while x and y are ...
... constant we have dy = Q1dq + R1dr , 0 = Q2dq + R2dr ; and eliminating dr between these we have dy = Ndq , N being a function of p , q , r . It follows that when dy = 0 , dq = 0 , and therefore if we suppose ≈ to vary while x and y are ...
Page 42
... dy ( d ) " } = ffd0d & sin 0 { a2b2 ( cos 0 ) 2 + ( c sin ( ) 2 ( a2 sin2 + b2 cos ̊p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
... dy ( d ) " } = ffd0d & sin 0 { a2b2 ( cos 0 ) 2 + ( c sin ( ) 2 ( a2 sin2 + b2 cos ̊p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
Page 43
... ) dy 2 dy -y + m = 0 . dx ( 4 ) Eliminate a and b from the equation y - ax2 - bx = 0 ; the result is d2y 2 dy dx9 x dx + 2y = 0 . ( 5 ) Eliminate the constants m and a from IV Elimination of Constants and Functions PAGE 1.
... ) dy 2 dy -y + m = 0 . dx ( 4 ) Eliminate a and b from the equation y - ax2 - bx = 0 ; the result is d2y 2 dy dx9 x dx + 2y = 0 . ( 5 ) Eliminate the constants m and a from IV Elimination of Constants and Functions PAGE 1.
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