Mathematical Analysis: A Compilation of Individual Tasks . Differential Calculus of Functions of Many Variables" is a unique teaching aid, Created by a team of authors, which will be an indispensable assistant for students , Post-graduate students and teachers , seeking to better understand and master the complex aspects of differential calculus of functions of many variables. This book is not just a collection of tasks, but a real guide to the development of analytical thinking, logic and practical skills necessary for successful mastery of mathematical analysis at an advanced level. The focus of this manual is the differential calculus of functions of many variables, one of the key topics of mathematical analysis, which lies at the heart of modern research and applications in engineering, physics, economics and computer science. The author’s team carefully selected tasks covering a wide range of topics: from elementary questions of differentiation and gradients to complex problems on differential equations and optimization of multidimensional functions. Each task is a challenge for the mind, contributing to the consolidation of theoretical knowledge through practical application. Mathematical Analysis: A Collection of Individual Tasks . Differential calculus of functions of many variables" is intended for those who are already familiar with the basics of mathematical analysis and want to systematize their knowledge, prepare for exams or scientific research. It is perfect for senior students, graduate students, teachers, as well as anyone who is interested in mathematics and is looking for effective ways to deepen their knowledge. The peculiarity of this manual is an individual approach to solving problems, which allows each reader to choose his own path to understanding complex concepts. What makes this book particularly appealing is its structured approach to learning. The tasks deal in detail with the main topics of differential calculus: differentiation of functions of several variables, gradients, partial derivatives, differentials, extremums and methods of their location, as well as issues related to differential equations and their applications. Each task is accompanied by a detailed solution, which helps to understand not only “how”, but also “why” in this way. This approach contributes to the development of analytical thinking and independence in solving complex problems. Particular attention is paid to practical aspects - from typical tasks encountered in classrooms to non-standard situations that require a creative approach. As a result, the reader will not only consolidate theoretical knowledge, but also learn how to apply them in real scientific and engineering tasks. This makes the book a valuable tool for exam preparation, test papers, and research. The style of the authors is distinguished by clarity and logical presentation, which makes even the most complex topics accessible to understanding. Inspired by classical textbooks on mathematical analysis, the team of authors created a modern manual that combines the rigor of the scientific approach and the vivacity of the teaching style. In the book you can find references to well-known works in the field of differential analysis, as well as examples from practice, which makes learning not only useful, but also fascinating. If you are looking for a book that will help you not only understand the theory, but also learn how to solve complex problems, then “Mathematical Analysis: a Collection of Individual Tasks . Differential Calculus of Functions of Many Variables” will become your reliable companion It is ideal for those who want to prepare for serious academic tests, expand their knowledge or just love mathematics from a new side. This book is your key to unlocking the secrets of multidimensional analysis and developing skills that will be useful in any scientific or engineering activity.