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Elements of Analytical Geometry and of the Differential and Integral Calculus

Elements of Analytical Geometry and of the Differential and Integral Calculus


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1851 Excerpt: ...Ex. 6. What is the differential of 3a'cx'-d? Proposition VII.--Theorem. (178.) If u represents any function of x, and we change x into x]h, the new value of the function will consist of three parts: 1st. The primitive function u. 2d. The differential coefficient of the function multiplied by the first power of the increment h. 3d. A function of x and h multiplied by the second power of the increment h. We have seen in the preceding Propositions that when u is a function of x, and we change x into ar+A, the new value of the function consists of a series of terms which may be arranged in the order of the ascending powers of h, and the development is of the following form u'=A+Bh+Ch'+Dh'+, etc. Now when we suppose h equal to zero, the second member of this equation reduces to A, and u' on this supposition becomes u; hence A=M, and the development may be written W'=w+ba+ca, +da'+, etc., or u'=u+Bh+h'(C+Dh+, etc.). If now we represent C+DA+, etc., by C, where C is a function both of x and h, we have tt'=M+BA+CA'. (1), Transposing and dividing by h, we find and when we make h equal to zero, we have du j-=B; ax that is, B is the differential coefficient of the function. We see from equation (1) that u', the new value of the function, consists of the primitive function u, plus the differential coefficient of the function multiplied by h, plus a function of x and h multiplied by h This new value of the function will be frequently referred to hereafter under the form u'=u+Ah+Bh (2) Proposition VIII.--Theorem. (179.) The differential of the sum or difference of any number of functions dependent on the same variable, is equal to the mm or difference of their differentials taken separately. Let us suppose the function u to be composed of several variable terms, a...


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Product Details
  • ISBN-13: 9781151881908
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 58
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1151881902
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 122 gr


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