The Persian translation of the book “Analysis by its History”, translated by Dr. Bijan Ahmadi Kakavandi, assistant professor of the Faculty of Mathematical Sciences of Shahid Beheshti University and Elham Nobari, faculty member of Mazandaran University of Science and Technology has been published recently by SBU Press in 508 pages. The book was originally authored by Ernst Hairer and Gerhard Wanner.
This work, which is the result of years of teaching by the authors, is a textbook on the subject of calculus and mathematical analysis, but its difference from other published works is in the historical narrative of the presentation of the material in such a way that the exercises in the book are also often taken from original historical issues.
Usually, the order of teaching concepts and rules in calculus and analysis is opposite to the historical order of discovery and expansion of these topics. For example, everyone interested in mathematics knows that the concept of integral was first invented by Archimedes in ancient Greece and the concept of set entered the world of mathematics at the end of the 19th century, but it should be known that the historical study of mathematics leads to a deeper understanding of the materials and strengthens the power of creativity and innovation in students. The authors of the book narrate the exciting story of the birth of this part of mathematics in a coherent, attractive and purposeful manner, as it really happened, by referring to the works and manuscripts of the great discoverers and architects of mathematical analysis. This book, consisting of four chapters, begins with Khwarizmi, Descartes, and Newton and reaches the differential and integral calculus of the 17th and 18th centuries, and portrays the emergence and evolution of mathematical precision in the 19th century and the efforts of people such as Cauchy, Weierstrass, and Peano in the field of univariate and multivariate analysis.
The content of the book covers the course of mathematical analysis in the undergraduate mathematics program, the course of general mathematics in technical fields, as well as parts of the course of numerical analysis. In fact, all people who deal with differential and integral calculus in some way or are a little interested in it, will find reading this book enjoyable and useful.