Concepts, Problems and Solutions in Mathematical Analysis : 3000+ Solved Problems.
This collection of problems and exercises in mathematical analysis covers the maximum requirements of general courses in higher mathematics for higher technical schools. It contains over 3000 solved problems sequentially arranged in Chapters I to X covering branches of higher mathematics (with the exception of analytical geometry) given in college courses. Particular attention is given to the most important sections of the course that require established skills (the finding of limits, differentiation techniques, the graphing of functions, integration techniques, the applications of definite integrals, series, the solution of differential equations).
Since some institutes have extended courses of mathematics, the authors have included problems on field theory, the Fourier method, and the Fourier approximate calculations. Experience shows that problems given in this book not only fully satisfies the number of the requirements of the student, as far as practical mastering of the various sections of the course goes, but also enables the instructor to supply a varied choice of problems in each section.
Each chapter begins with a brief theoretical introduction that covers the basic definitions and formulas of that section of the course. This book contains a large number of problems for exercise, fully solved, which will serve as a complete guide to private students reading the subject with few or no opportunities of instruction. The problems are frequently illustrated by drawings.
This collection of problems is the result of many years of teaching higher mathematics in the technical schools of the Soviet Union. It includes, in addition to original problems and examples, a large number of commonly used problems.
Solutions are provided next to the problems throughout the book. This will save the time and lighten the work of Teachers as well. This book helps in acquiring a better understanding of the basic principles of mathematical analysis and in revising a large amount of the subject matter quickly. Care has been taken, as in the former Keys, to present the solutions in a simple natural manner, in order to meet the difficulties which are most likely to arise and to render the work intelligible and instructive.
The examples have been selected with a view to illustrate every part of the subject, and, as the number of them is more than three thousand, we trust they will supply ample exercise for the student. Complicated and difficult problems have been excluded, because they consume time and energy which may be spent more profitably on other branches of mathematics. Each set of examples has been carefully arranged, commencing with some which are very simple and proceeding gradually to others which are less obvious. The detailed solutions to all the problems are provided.
