Includes bibliographical references and indexes.

v.1. Mathematical analysis 1 -- 1. Some general mathematical concepts and notation -- 2. The. real numbers -- 3. Limits -- 4. Continuous functions -- 5. Differential calculus -- 6. Integration -- 7. Functions of several variables -- 8. Differential calculus in several variables -- Some problems from the midterm examinations -- Examination topics -- References -- Subject index -- Name index.

v. 2. Mathematical analysis 2 -- 9. Continuous mappings (general theory) -- 10. Differential calculus from a general viewpoint -- 11. Multiple integrals -- 12. Surfaces and differential forms in Rn -- 13. Line and surface integrals -- 14. Elements of vector analysis and field theory -- 15. Integration of differential forms of manifolds -- 16. Uniform convergence and basic operations of analysis -- 17. Integrals depending on a parameter -- 18. Fourier series and Fourier transform -- 19. Asymptotic expansions -- Topics and questions for midterm examinations -- Examination topics -- References -- Index of basic notation -- Subject index -- Name index.

This two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books. The first volume constitutes a complete course on one-variable calculus along with the multivariable differential calculus elucidated in an up-to-day, clear manner, with a pleasant geometric flavor. The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions. - Publisher.

All Ages.