""A Course In Mathematical Analysis V1: Derivatives And Differentials, Definite Integrals, Expansion In Series, Applications To Geometry"" is a comprehensive textbook written by Edouard Goursat. The book is aimed at students who are interested in developing their understanding of mathematical analysis. The book is divided into three main sections. The first section covers derivatives and differentials, including the definition of a derivative, the chain rule, and the product rule. The second section covers definite integrals, including the definition of a definite integral, the fundamental theorem of calculus, and techniques for evaluating integrals. The third section covers expansion in series, including Taylor series, power series, and Fourier series, and their applications to geometry. Throughout the book, Goursat provides detailed explanations of mathematical concepts and techniques, as well as numerous examples and exercises to help readers develop their problem-solving skills. The book is written in a clear and accessible style, making it suitable for both undergraduate and graduate students in mathematics and related fields. Overall, ""A Course In Mathematical Analysis V1: Derivatives And Differentials, Definite Integrals, Expansion In Series, Applications To Geometry"" is an essential resource for anyone seeking a deeper understanding of mathematical analysis.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.