<p><b><i>Differential and Integral Calculus</i> by Augustus De Morgan is a comprehensive and authoritative exploration of both differential and integral calculus, offering readers a thorough understanding of these foundational branches of mathematics.</b></p>
<p><i>Differential and Integral Calculus</i> by Augustus De Morgan is a timeless work that provides a detailed and rigorous treatment of calculus, encompassing both differentiation and integration. This book serves as an invaluable resource for students, educators, and anyone seeking a comprehensive guide to the principles of calculus.</p>
<p>The book begins by introducing readers to the historical development of calculus and its significance in mathematics and science. Augustus De Morgan's clear and logical explanations set the stage for a deeper exploration of this essential subject.</p>
<p>Central to the book is the presentation of differential calculus, which includes topics such as limits, derivatives, and applications in various fields. De Morgan's rigorous approach ensures that readers grasp the foundational concepts and techniques of differentiation.</p>
<p>Furthermore, the book covers integral calculus, providing insights into the fundamental principles of integration, definite and indefinite integrals, and their practical applications. Readers will find step-by-step explanations and exercises that facilitate learning and problem-solving.</p>
<p>This book is an invaluable resource for students, educators, and anyone interested in gaining a deep understanding of calculus. Augustus De Morgan's meticulous scholarship and clear explanations make this work an essential guide to the foundations of differential and integral calculus.</p>
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.
