Differential and Integral Calculus - Paperback

by Augustus de Morgan (Author)

DIFFERENTIAL AND INTEGRAL CALCULUS BY AUGUSTUS DE MORGAN CONTENTS: On the Ratio or Proportion of Two Magnitudes On the Ratio of Magnitudes that Vanish Together On the Ratios of Continuously Increasing or Decreasing Quantities The Notion of Infinitely Small Quantities On Functions Infinite Series Convergent and Divergent Series. Taylors Theorem, Derived Functions. Differential Coefficients The Notation of the Differential Calculus Algebraical Geometry On the Connexion of the Signs of Algebraical and the. Directions of Geometrical .Magnitudes The Drawing of a Tangent to a Curve. Rational Explanation of the Language of Leibnitz Orders of Infinity A Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines, The Same Problem Solved by the Principles of Leibnitz An Illustration from Dynamics Velocity, Acceleration, etc, Simple Harmonic Motion The Method of Fluxions Accelerated Motion Limiting Ratios of Magnitudes that Increase Without Limit. Recapitulation of Results Retched in the Theory of Functions, Approximations by the Differential Calculus Solution, of Equations by the Differential Calculus Partial and Total Differentials Application of the Theorem for Total Differentials to the Determination of Total Resultant Errors Rules for Differentiation.. Illustration of the Rules for Differentiation Differential Coefficients of Differential Coefficients Calculus of Finite Differences. Successive Differentiation Total and Partial Differential Coefficients. Implicit Differentiation Applications of the Theorem for Implicit Differentiation Inverse Functions. Implicit Functions. Fluxions, and the Idea of Time The Differential Coefficient Considered with Respect to Its Magnitude. The Integral Calculus Connexion of the Integral with the Differential Calculus Nature of Integration. Determination of Curvilinear Areas. The Parabola Method of Indivisibles. Concluding Remarks on the Study of the Calculus Bibliography of Standard Textbooks and Works of Reference on the Calculus.