A treatise on the integral calculus and its applications1857 |
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... Variables in a Multiple Integral 180 XII . Definite Integrals 212 XIII . Expansion of Functions in Trigonometrical Series 250 XIV . Application of the Integral Calculus to Questions of Mean Value and Probability 262 INTEGRAL CALCULUS ...
... Variables in a Multiple Integral 180 XII . Definite Integrals 212 XIII . Expansion of Functions in Trigonometrical Series 250 XIV . Application of the Integral Calculus to Questions of Mean Value and Probability 262 INTEGRAL CALCULUS ...
Page 2
... variable x , we may also use the symbol ( x ) Ax as the type of the terms to be summed , and Σp ( x ) Ax for the sum . ... We may shew at once that p ( x ) Ax can never exceed a certain finite quantity . For let A denote the numerically ...
... variable x , we may also use the symbol ( x ) Ax as the type of the terms to be summed , and Σp ( x ) Ax for the sum . ... We may shew at once that p ( x ) Ax can never exceed a certain finite quantity . For let A denote the numerically ...
Page 6
... variable some function of a new variable . Suppose ( x ) the function to be integrated , and a and b the limits of the integral . It is evident that we may suppose x to be a function of a new variable z , provided that the function ...
... variable some function of a new variable . Suppose ( x ) the function to be integrated , and a and b the limits of the integral . It is evident that we may suppose x to be a function of a new variable z , provided that the function ...
Page 25
... variable x the equality still subsists . 19. To determine the partial fraction corresponding to a single factor of the first degree . φ ( α ) F ( x ) represents a fraction to be decomposed , and Suppose let F ( x ) contain the factor x ...
... variable x the equality still subsists . 19. To determine the partial fraction corresponding to a single factor of the first degree . φ ( α ) F ( x ) represents a fraction to be decomposed , and Suppose let F ( x ) contain the factor x ...
Page 64
... variable . 57. Suppose we have to find the value of u which satis- fies the equation d2u dy dx = ( x , y ) , where p ( x , y ) is a function of the independent variables x and y . The equation may be written or du if v = dx . d du dy ...
... variable . 57. Suppose we have to find the value of u which satis- fies the equation d2u dy dx = ( x , y ) , where p ( x , y ) is a function of the independent variables x and y . The equation may be written or du if v = dx . d du dy ...
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Common terms and phrases
Application c² sin² Cambridge circle cloth co-ordinates constant cos² cos³ Crown 8vo curve cycloid definite integral denote differential coefficient double integral dx dx dx dy dz dy dx dz dx element ellipse equal Eulerian integral example expression Fcap Fellow of St Find the area find the volume formula function Hence indefinitely Integral Calculus integrate with respect intrinsic equation John's College latus rectum length limits M.A. Fellow MACMILLAN & CO.'S numerous obtain ordinate parabola partial fractions perpendicular plane positive preceding article radius vector result revolution revolve round round the axis shew sin² solid suppose surface tangent tion tractory transformed integral Trinity College unity vanishes variables vertex x₁ Y₁ πα аф
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Page 13 - Prize Essay for 1877. 8vo. 8.r. 6V. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.
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