{"product_id":"2940016799407","title":"Elementary Illustrations of the Differential and Integral Calculus (Illustrated)","description":"DIFFERENTIAL AND INTEGRAL CALCULUS.\u003cbr\u003eELEMENTARY ILLUSTRATIONS.\u003cbr\u003e\u003cbr\u003eThe Differential and Integral Calculus, or, as it was formerly called, the Doctrine of Fluxions, has always been supposed to present remarkable obstacles to the beginner. It is matter of common observation that anyone who commences this study, even with the best elementary works, finds himself in the dark as to the real meaning of the processes which he learns, until, at a certain stage of his progress, depending upon his capacity, some accidental combination of his own ideas throws light upon the subject. \u003cbr\u003e\u003cbr\u003eThe reason of this may be that it is usual to introduce him at the same time to new principles, processes, and symbols, thus preventing his attention from being exclusively directed to one new thing at a time. It is our belief that this should be avoided; and we propose, therefore, to try the experiment, whether by undertaking the solution of some problems by common algebraic methods, without calling for the reception of more than one new symbol at once, or lessening the immediate evidence of each investigation by reference to general rules, the study of more methodical treatises may not be somewhat facilitated. \u003cbr\u003e\u003cbr\u003eWe would not, nevertheless, that the student should imagine we can remove all obstacles; we must introduce notions, the consideration of which has not hitherto occupied his mind; and shall therefore consider our object as gained, if we can succeed in so placing the subject before him, that two independent difficulties shall never occupy his mind at once.\u003cbr\u003e\u003cbr\u003eCONTENTS:\u003cbr\u003e\u003cbr\u003eOn the Ratio or Proportion of Two Magnitudes\u003cbr\u003eOn the Ratio of Magnitudes that Vanish Together\u003cbr\u003eOn the Ratios of Continuously Increasing or Decreasing Quantities\u003cbr\u003eThe Notion of Infinitely Small Quantities\u003cbr\u003eOn Functions\u003cbr\u003eInfinite Series\u003cbr\u003eConvergent and Divergent Series\u003cbr\u003eTaylor's Theorem Derived Functions\u003cbr\u003eDifferential Coefficients\u003cbr\u003eThe Notation of the Differential Calculus\u003cbr\u003eAlgebraic Geometry\u003cbr\u003eOn the Connexion of the Signs of Algebraic and the Directions of Geometrical Magnitudes\u003cbr\u003eThe Drawing of a Tangent to a Curve\u003cbr\u003eRational Explanation of the Language of Leibnitz\u003cbr\u003eOrders of Infinity\u003cbr\u003eA Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines\u003cbr\u003eThe Same Problem Solved by the Principles of Leibnitz\u003cbr\u003eAn Illustration from Dynamics: Velocity, Acceleration, etc.\u003cbr\u003eSimple Harmonic Motion\u003cbr\u003eThe Method of Fluxions\u003cbr\u003eAccelerated Motion Limiting Ratios of Magnitudes that Increase Without Limit\u003cbr\u003eRecapitulation of Results Reached in the Theory of Functions\u003cbr\u003eApproximations by the Differential Calculus\u003cbr\u003eSolution of Equations by the Differential Calculus\u003cbr\u003ePartial and Total Differentials\u003cbr\u003eApplication of the Theorem for Total Differentials to the Determination of Total Resultant Errors\u003cbr\u003eRules for Differentiation\u003cbr\u003eIllustration of the Rules for Differentiation\u003cbr\u003eDifferential Coefficients of Differential Coefficients\u003cbr\u003eCalculus of Finite Differences Successive Differentiation\u003cbr\u003eTotal and Partial Differential Coefficients Implicit Differentiation\u003cbr\u003eApplications of the Theorem for Implicit Differentiation\u003cbr\u003eInverse Functions\u003cbr\u003eImplicit Functions\u003cbr\u003eFluxions and the Idea of Time\u003cbr\u003eThe Differential Coefficient Considered with Respect to its Magnitude\u003cbr\u003eThe Integral Calculus\u003cbr\u003eConnexion of the Integral with the Differential Calculus\u003cbr\u003eNature of Integration\u003cbr\u003eDetermination of Curvilinear Areas the Parabola\u003cbr\u003eMethod of Indivisibles\u003cbr\u003eConcluding Remarks on the Study of the Calculus\u003cbr\u003eBibliography of Standard Text-books and Works of Reference on the Calculus","brand":"De Morgan","offers":[{"title":"Default Title","offer_id":47074521219312,"sku":"2940016799407","price":2.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940016799407_p0.jpg?v=1763641534","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940016799407","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}