The textbook covers a one-semester course and provides a bridge from high school mathematics to higher analysis suitable for users of two sorts, by students in the freshman year who need more advanced mathematics in other studies or by those who need it in applications. The exposition is structured to present the material in reasonable detail and focuses on comprehension rather than computation. The topics are usually introduced in a simplest possible form or framework and then are returned to one or more times in successively more complex form. Support of intuition through transmitted experience forms an important part of the learning. Numerous exercises and problems involve giving examples and analyzing concepts and proof ideas. They are spread throughout the text to enable the reader to master the material as he goes along. The presentation is kept as concrete as possible with emphasis toward applications.

The book integrates the treatment of the basic differential and integral calculus of functions of one variable with vector calculus or general linear algebra and analytic geometry surveying topics (e.g. properties of curves) which are important for applied as well as for pure mathematics. The role of approximation and numerical solution, and the corresponding error analysis is prominent.

The precalculus part reviews carefully selected basic properties of real and complex numbers, basic set theory and mathematical logic.

The linear algebra parts consists of chapters devoted to matrices, determinants, linear spaces, linear transformations and complete discussion of the theory of systems of linear algebraic equations.