Preface

Mathematics occupies a particular place among the exact sciences, providing the basis for specialization in any engineering discipline.
In order to solve engineering problems, it is necessary to possess a high level of mathematical culture. Mathematics develops the ability to reason logically and to understand the intrinsic unity of different approaches to the same problem. It deals with the general structure of argumentation, no matter the physical meaning of the used concepts. Then mathematical ideas and methods can be used for creation and development of theoretical models of various phenomena - in physics, engineering, economy, biology, etc. Any computer systems cannot replace the basic mathematical knowledge as tools for engineers to master technological needs currently and in the future.

This course is intended for students who would like to broaden and systematize their knowledge in elementary mathematics.

As it follows from the title, there are no pretensions to give an exhaustive treatment. Taking into account that students have already studied basic mathematics, the main attention is concentrated on common mathematical ideas and methods, which are necessary for learning university programs in mathematics as well as in special engineering sciences.

Many important concepts are introduced from the very outset by making use of the simplest mathematical topics, e.g., the real number system.
In particular, the arithmetic operations are used to introduce into practice the conception of mutually inverse operations.
A geometrical interpretation is widely used to demonstrate the simplicity and obviousness of many mathematical statements and rules.

The system of links refers to proofs, explanations, graphic illustrations, examples or some additional information.
The glossary allows to get the access to terms and definitions desired just at that moment as it is necessary, and so you have no to commit to memory all definitions and rules without distinction, retaining them just in case.

Each section of the course has been designed to provide an environment in which you can study mathematical concepts with minimal direction. Opening pages of sections results in a split screen. The matter of a topic as well as definitions, examples, and discussion are on the right side; the section menu is on the left.
On the top side of the screen are the navigational buttons of the contents, which return you to the menu of the desired section. The bottom buttons allow you to choose the previous topic or next topic.
In many topics, the system of links refers to proofs, explanations, graphic illustrations, examples or some additional information.

In order to master a chapter, work through the examples contained in each topic, and at least scan the basic ideas of mathematical proofs. The procedure of proving propositions forms the corresponding level of thinking, and so rigorous mathematical proofs have to consider as an end in itself.

Now the course is in developmental stage. Subsequently, a few new chapters will be appended to the course, and some existing topics will be enlarged.

The authors welcome your suggestions for improvements.