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Home > Mathematics and Science Textbooks > Mathematics > The Elements of the Differential and Integral Calculus; Based on Kurzgefasstes Lehrbuch Der Differential- Und Integralrechnung Von W. Nernst Und A. Schonflies
The Elements of the Differential and Integral Calculus; Based on Kurzgefasstes Lehrbuch Der Differential- Und Integralrechnung Von W. Nernst Und A. Schonflies

The Elements of the Differential and Integral Calculus; Based on Kurzgefasstes Lehrbuch Der Differential- Und Integralrechnung Von W. Nernst Und A. Schonflies


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About the Book

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. 1900 Excerpt: ...C. There is no danger, however, that we shall run into error by usually hereafter writing our equations as we have thus far done, simply f(x)dx = F(x); for the exact reading of this equation is: one integral function of f(x) is F(x), while that of equation (2) is: all functions of the form F(x + C are integral functions oif(x). The constant C is called the constant of integration. Art. 5. The fundamental formulae of the Integral Calculus. Inasmuch as the Integral Calculus is the inverse of the Differential Calculus, a formula of the Integral Calculus may be derived from any formula of the Differential Calculus. Thus, if the equation be considered, it is clear that the equation ff(x)dx = F(x) may be at once deduced from it. In this way a first set of integral formulae may be obtained immediately from the formulae established in Chap. IV. Thus, for the power x"+i we have dx may be expressed in another form as sin xdx=--cos a;. In this wise we obtain the following preliminary TABLE OF INTEGRALS n+1 + = arc tan x =--arc cot a;. + + x Art. 6. The geometric signification of the constant of integration. There is but little in elementary mathematics analogous to the boundless number of integrals belonging to one and the same derivative, f(x). Indeed, in extracting the square root of a quantity we obtain two solutions, and a cube root' has three values, but nowhere does there occur as here, in finding the integral function for the derivative /(a;), an unlimited number of results. The formal explanation of this point has been presented previously. We now proceed to discuss the geometric meaning of the constant of integration. The integral on the left side is formally contained in the first integral of the Table. But in that ease the first integral formula refuse...


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Product Details
  • ISBN-13: 9781130496376
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 74
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1130496376
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 150 gr


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The Elements of the Differential and Integral Calculus; Based on Kurzgefasstes Lehrbuch Der Differential- Und Integralrechnung Von W. Nernst Und A. Schonflies
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