Synopsis
Excerpt from Cours d'Analyse de l'École Polytechnique, Vol. 1
Il a été question tout à l'heure de polynômes; or les élé ments conduisent encore à d'autres expressions qu'on nomme transcendantes, par exemple l'exponentielle et le logarithme, et en second lieu le sinus, le cosinus, la tangente d'un arc. Les premières sont étudiées en Algèbre même, et les autres sont le sujet de la Trigonométrie, qui n'est visiblement qu'un chapitre Spécial d'algèbre, donnant, parmi bien d'autres con séquences, la résolution numérique des triangles. Maintenant on peut poser cette question N'existe-t-il de fonctions que celles dont nous venons de parler et leurs combinaisons? Si la réponse était affirmative, l'analyse laisserait apercevoir ses bornes, son champ serait fini et limité; mais il est bien loin d'en être ainsi, le Calcul différentiel et le Calcul intégral étendent indéfiniment leur domaine en fournissant l'origine et posant la base de l'étude d'un nombre infini de fonctions nouvelles. Ainsi l'on comprend que Lagrange ait donné à l'un de ses Ouvrages, qui est précisément consacré à une exposi tion des principes du Calcul différentiel et du Calcul intégral, le titre de Leçons sur le Calcul des fonctions. En suivant la pensée de ce grand géomètre, nous allons présenter sur les fonctions connues par les éléments quelques considérations qui serviront d'introduction à ce Cours, et dont il sera souvent fait usage par la suite.
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Paperback. Condition: New. Print on Demand. This book offers a comprehensive introduction to calculus, presenting the core concepts of differential and integral calculus with clear explanations and insightful examples. The author places a strong emphasis on geometric interpretations and applications, providing a solid foundation for understanding the subject's practical implications. The book begins by introducing the fundamental ideas of functions, limits, and derivatives, before delving into the applications of differential calculus to geometry and optimization problems. The author then covers the integral calculus, including techniques for calculating areas, volumes, and lengths of curves. Throughout the book, the author strikes a balance between theoretical rigor and accessibility, making it suitable for both beginners and students with some prior knowledge of calculus. The inclusion of advanced topics, such as the study of functions of several variables and the development of Fourier series, provides a glimpse into the broader landscape of mathematical analysis. Overall, this book is a valuable resource for students seeking a deeper understanding of calculus and its applications. It offers a comprehensive treatment of the subject, balancing theoretical depth with practical examples and insights, making it a valuable addition to any mathematics library. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9780259851172_0
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