Vector Analysis: Problems and Examples with Detailed Solutions

This collection of tasks can be considered as a short course in vector analysis, which reports without evidence the main facts with the illustration of them with specific examples. Therefore, the proposed problematic can be used, on the one hand, to repeat the basics of vector analysis, and on the other, as a textbook for persons who, without going into evidence of certain proposals and theorems, want to master the technique of vector analysis operations. When compiling a task book, the authors used the material contained in existing vector calculus courses and tasks collections. A significant part of the tasks is compiled by the authors themselves.
At the beginning of each paragraph, a summary of the main theoretical provisions, definitions and formulas is given, as well as a detailed solution to examples (in total about 100) The book also contains more than 300 tasks and examples for independent solutions, all of them are equipped with answers or instructions to the decision. There are several applied tasks that are selected in such a way that their analysis does not require additional information from special disciplines from the reader. The material of the sixth chapter dedicated to curved coordinates and the main operations of vector analysis in curved coordinates is included in the book in order to give the reader at least the minimum number of tasks for acquiring the necessary skills.
The collection of tasks is designed for students of day and evening departments of technical universities, engineers, as well as for students-jokes familiar with vector algebra and mathematical analysis in the volume of the first two courses